info
large_stringlengths 120
50k
| question
large_stringlengths 504
10.4k
| avg@8_qwen3_4b_instruct_2507
float64 0
0.88
|
|---|---|---|
{"tests": "{\"inputs\": [\"4\\n20\\n13\\n8\\n4\", \"4\\n38\\n13\\n8\\n4\", \"4\\n38\\n14\\n8\\n4\", \"4\\n38\\n14\\n1\\n4\", \"4\\n62\\n14\\n1\\n4\", \"4\\n62\\n14\\n1\\n3\", \"4\\n85\\n14\\n1\\n3\", \"4\\n40\\n14\\n1\\n3\", \"4\\n40\\n1\\n1\\n3\", \"4\\n40\\n1\\n2\\n3\", \"4\\n34\\n13\\n8\\n4\", \"4\\n38\\n13\\n8\\n2\", \"4\\n38\\n14\\n8\\n3\", \"4\\n45\\n14\\n1\\n4\", \"4\\n75\\n14\\n1\\n4\", \"4\\n62\\n14\\n2\\n3\", \"4\\n47\\n14\\n1\\n3\", \"4\\n40\\n1\\n1\\n5\", \"4\\n34\\n13\\n7\\n4\", \"4\\n38\\n13\\n16\\n2\", \"4\\n38\\n12\\n8\\n3\", \"4\\n70\\n14\\n1\\n4\", \"4\\n131\\n14\\n1\\n4\", \"4\\n20\\n14\\n2\\n3\", \"4\\n47\\n14\\n1\\n2\", \"4\\n40\\n2\\n1\\n5\", \"4\\n19\\n13\\n16\\n2\", \"4\\n38\\n14\\n7\\n3\", \"4\\n70\\n14\\n1\\n5\", \"4\\n131\\n14\\n1\\n8\", \"4\\n47\\n11\\n1\\n2\", \"4\\n34\\n13\\n3\\n7\", \"4\\n51\\n14\\n7\\n3\", \"4\\n2\\n16\\n2\\n3\", \"4\\n47\\n18\\n1\\n2\", \"4\\n40\\n4\\n1\\n4\", \"4\\n24\\n13\\n3\\n7\", \"4\\n51\\n14\\n2\\n3\", \"4\\n70\\n2\\n1\\n1\", \"4\\n25\\n14\\n1\\n8\", \"4\\n47\\n18\\n2\\n2\", \"4\\n40\\n4\\n1\\n2\", \"4\\n24\\n13\\n6\\n7\", \"4\\n51\\n21\\n2\\n3\", \"4\\n67\\n2\\n1\\n1\", \"4\\n30\\n14\\n1\\n8\", \"4\\n20\\n18\\n1\\n2\", \"4\\n17\\n4\\n1\\n2\", \"4\\n24\\n1\\n6\\n7\", \"4\\n51\\n21\\n2\\n4\", \"4\\n67\\n3\\n1\\n1\", \"4\\n38\\n14\\n1\\n8\", \"4\\n20\\n18\\n2\\n2\", \"4\\n17\\n4\\n1\\n1\", \"4\\n30\\n1\\n6\\n7\", \"4\\n37\\n21\\n2\\n4\", \"4\\n67\\n4\\n1\\n1\", \"4\\n20\\n18\\n2\\n1\", \"4\\n6\\n4\\n1\\n1\", \"4\\n30\\n1\\n10\\n7\", \"4\\n29\\n4\\n1\\n1\", \"4\\n9\\n18\\n2\\n1\", \"4\\n30\\n1\\n10\\n12\", \"4\\n30\\n1\\n6\\n12\", \"4\\n30\\n1\\n6\\n18\", \"4\\n12\\n28\\n1\\n1\", \"4\\n12\\n30\\n1\\n1\", \"4\\n12\\n15\\n1\\n1\", \"4\\n68\\n13\\n8\\n4\", \"4\\n38\\n14\\n8\\n2\", \"4\\n26\\n14\\n1\\n4\", \"4\\n40\\n3\\n1\\n3\", \"4\\n40\\n1\\n2\\n6\", \"4\\n34\\n17\\n8\\n4\", \"4\\n69\\n13\\n8\\n2\", \"4\\n45\\n14\\n1\\n7\", \"4\\n75\\n14\\n2\\n4\", \"4\\n62\\n14\\n2\\n5\", \"4\\n40\\n1\\n2\\n5\", \"4\\n34\\n13\\n12\\n4\", \"4\\n38\\n13\\n31\\n2\", \"4\\n38\\n12\\n5\\n3\", \"4\\n122\\n14\\n1\\n4\", \"4\\n40\\n3\\n1\\n5\", \"4\\n34\\n9\\n3\\n4\", \"4\\n19\\n2\\n16\\n2\", \"4\\n38\\n23\\n7\\n3\", \"4\\n70\\n14\\n2\\n5\", \"4\\n131\\n20\\n1\\n4\", \"4\\n2\\n8\\n2\\n3\", \"4\\n47\\n11\\n2\\n2\", \"4\\n34\\n13\\n3\\n5\", \"4\\n51\\n14\\n7\\n1\", \"4\\n23\\n2\\n1\\n5\", \"4\\n47\\n19\\n1\\n8\", \"4\\n2\\n16\\n4\\n3\", \"4\\n47\\n29\\n1\\n2\", \"4\\n51\\n14\\n2\\n6\", \"4\\n47\\n29\\n2\\n2\", \"4\\n73\\n21\\n2\\n3\", \"4\\n114\\n2\\n1\\n1\"], \"outputs\": [\"1\\n12\\n2\\n0\\n\", \"17\\n12\\n2\\n0\\n\", \"17\\n5\\n2\\n0\\n\", \"17\\n5\\n0\\n0\\n\", \"29\\n5\\n0\\n0\\n\", \"29\\n5\\n0\\n2\\n\", \"12\\n5\\n0\\n2\\n\", \"3\\n5\\n0\\n2\\n\", \"3\\n0\\n0\\n2\\n\", \"3\\n0\\n1\\n2\\n\", \"15\\n12\\n2\\n0\\n\", \"17\\n12\\n2\\n1\\n\", \"17\\n5\\n2\\n2\\n\", \"4\\n5\\n0\\n0\\n\", \"10\\n5\\n0\\n0\\n\", \"29\\n5\\n1\\n2\\n\", \"46\\n5\\n0\\n2\\n\", \"3\\n0\\n0\\n4\\n\", \"15\\n12\\n6\\n0\\n\", \"17\\n12\\n0\\n1\\n\", \"17\\n1\\n2\\n2\\n\", \"3\\n5\\n0\\n0\\n\", \"130\\n5\\n0\\n0\\n\", \"1\\n5\\n1\\n2\\n\", \"46\\n5\\n0\\n1\\n\", \"3\\n1\\n0\\n4\\n\", \"18\\n12\\n0\\n1\\n\", \"17\\n5\\n6\\n2\\n\", \"3\\n5\\n0\\n4\\n\", \"130\\n5\\n0\\n2\\n\", \"46\\n10\\n0\\n1\\n\", \"15\\n12\\n2\\n6\\n\", \"14\\n5\\n6\\n2\\n\", \"1\\n0\\n1\\n2\\n\", \"46\\n3\\n0\\n1\\n\", \"3\\n0\\n0\\n0\\n\", \"2\\n12\\n2\\n6\\n\", \"14\\n5\\n1\\n2\\n\", \"3\\n1\\n0\\n0\\n\", \"0\\n5\\n0\\n2\\n\", \"46\\n3\\n1\\n1\\n\", \"3\\n0\\n0\\n1\\n\", \"2\\n12\\n1\\n6\\n\", \"14\\n4\\n1\\n2\\n\", \"66\\n1\\n0\\n0\\n\", \"1\\n5\\n0\\n2\\n\", \"1\\n3\\n0\\n1\\n\", \"16\\n0\\n0\\n1\\n\", \"2\\n0\\n1\\n6\\n\", \"14\\n4\\n1\\n0\\n\", \"66\\n2\\n0\\n0\\n\", \"17\\n5\\n0\\n2\\n\", \"1\\n3\\n1\\n1\\n\", \"16\\n0\\n0\\n0\\n\", \"1\\n0\\n1\\n6\\n\", \"36\\n4\\n1\\n0\\n\", \"66\\n0\\n0\\n0\\n\", \"1\\n3\\n1\\n0\\n\", \"1\\n0\\n0\\n0\\n\", \"1\\n0\\n3\\n6\\n\", \"28\\n0\\n0\\n0\\n\", \"0\\n3\\n1\\n0\\n\", \"1\\n0\\n3\\n1\\n\", \"1\\n0\\n1\\n1\\n\", \"1\\n0\\n1\\n3\\n\", \"1\\n3\\n0\\n0\\n\", \"1\\n1\\n0\\n0\\n\", \"1\\n2\\n0\\n0\\n\", \"13\\n12\\n2\\n0\\n\", \"17\\n5\\n2\\n1\\n\", \"11\\n5\\n0\\n0\\n\", \"3\\n2\\n0\\n2\\n\", \"3\\n0\\n1\\n1\\n\", \"15\\n16\\n2\\n0\\n\", \"20\\n12\\n2\\n1\\n\", \"4\\n5\\n0\\n6\\n\", \"10\\n5\\n1\\n0\\n\", \"29\\n5\\n1\\n4\\n\", \"3\\n0\\n1\\n4\\n\", \"15\\n12\\n1\\n0\\n\", \"17\\n12\\n30\\n1\\n\", \"17\\n1\\n4\\n2\\n\", \"59\\n5\\n0\\n0\\n\", \"3\\n2\\n0\\n4\\n\", \"15\\n0\\n2\\n0\\n\", \"18\\n1\\n0\\n1\\n\", \"17\\n22\\n6\\n2\\n\", \"3\\n5\\n1\\n4\\n\", \"130\\n1\\n0\\n0\\n\", \"1\\n2\\n1\\n2\\n\", \"46\\n10\\n1\\n1\\n\", \"15\\n12\\n2\\n4\\n\", \"14\\n5\\n6\\n0\\n\", \"22\\n1\\n0\\n4\\n\", \"46\\n18\\n0\\n2\\n\", \"1\\n0\\n0\\n2\\n\", \"46\\n28\\n0\\n1\\n\", \"14\\n5\\n1\\n1\\n\", \"46\\n28\\n1\\n1\\n\", \"72\\n4\\n1\\n2\\n\", \"13\\n1\\n0\\n0\\n\"]}", "source": "primeintellect"}
|
Our Chef is catering for a big corporate office party and is busy preparing different mouth watering dishes. The host has insisted that he serves his delicious cupcakes for dessert.
On the day of the party, the Chef was over-seeing all the food arrangements as well, ensuring that every item was in its designated position. The host was satisfied with everything except the cupcakes. He noticed they were arranged neatly in the shape of a rectangle. He asks the Chef to make it as square-like as possible.
The Chef is in no mood to waste his cupcakes by transforming it into a perfect square arrangement. Instead, to fool the host, he asks you to arrange the N cupcakes as a rectangle so that the difference between the length and the width is minimized.
Input
The first line of the input file contains an integer T, the number of test cases. Each of the following T lines contains a single integer N denoting the number of cupcakes.
Output
Output T lines, each indicating the minimum possible difference between the length and the width in a rectangular arrangement of the cupcakes.
Constraints
1 ≤ T ≤ 100
1 ≤ N ≤ 10^8
Example
Input:
4
20
13
8
4
Output:
1
12
2
0
Explanation
Case 1: 20 cupcakes can be arranged in 6 possible ways - 1 x 20, 2 x 10, 4 x 5, 5 x 4, 10 x 2 and 20 x 1. The corresponding differences between the length and the width are 19, 8, 1, 1, 8 and 19 respectively. Hence, 1 is the answer.
Case 4: 4 cupcakes can be arranged as a 2 x 2 square. Difference between the length and the width is 0. You can't do anything better than 0.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"6 1\\n2 1\\n2 3\\n2 5\\n5 4\\n5 6\\n\", \"4 3\\n1 2\\n1 3\\n1 4\\n\", \"5 5\\n1 2\\n2 3\\n3 4\\n3 5\\n\", \"2 1000000000\\n2 1\\n\", \"2 1\\n2 1\\n\", \"4 1\\n4 1\\n2 4\\n3 1\\n\", \"3 1000000000\\n3 2\\n2 1\\n\", \"4 1\\n1 3\\n1 4\\n2 1\\n\", \"4 1\\n2 3\\n1 4\\n2 1\\n\", \"6 1\\n2 1\\n4 3\\n2 5\\n5 4\\n5 6\\n\", \"6 1\\n2 1\\n2 3\\n2 5\\n2 4\\n5 6\\n\", \"4 5\\n1 2\\n1 3\\n1 4\\n\", \"6 2\\n2 1\\n4 3\\n4 5\\n1 4\\n5 6\\n\", \"6 0\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"6 2\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"4 5\\n1 2\\n1 3\\n2 4\\n\", \"2 3\\n2 1\\n\", \"4 6\\n4 2\\n2 1\\n3 1\\n\", \"5 8\\n1 2\\n2 3\\n3 4\\n3 5\\n\", \"6 1\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"6 1\\n2 1\\n4 3\\n4 5\\n1 4\\n5 6\\n\", \"4 1\\n4 3\\n1 4\\n2 1\\n\", \"6 1\\n2 1\\n4 3\\n4 5\\n2 4\\n5 6\\n\", \"4 0\\n4 1\\n2 4\\n3 1\\n\", \"4 0\\n1 3\\n1 4\\n2 1\\n\", \"6 1\\n3 1\\n2 3\\n2 5\\n5 4\\n5 6\\n\", \"5 5\\n1 2\\n2 3\\n3 4\\n2 5\\n\", \"4 0\\n4 2\\n2 4\\n3 1\\n\", \"2 2\\n2 1\\n\", \"4 2\\n4 1\\n2 4\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n4 6\\n1 4\\n5 6\\n\", \"6 1\\n4 1\\n4 3\\n4 5\\n2 4\\n5 6\\n\", \"4 0\\n1 2\\n1 4\\n2 1\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n5 6\\n\", \"4 5\\n1 2\\n2 3\\n2 4\\n\", \"4 2\\n4 1\\n2 1\\n3 1\\n\", \"6 1\\n6 1\\n4 3\\n2 5\\n5 4\\n5 6\\n\", \"6 1\\n2 1\\n4 3\\n4 6\\n1 4\\n5 6\\n\", \"4 2\\n4 3\\n1 4\\n2 1\\n\", \"6 0\\n2 1\\n4 1\\n2 5\\n1 4\\n5 6\\n\", \"4 0\\n1 3\\n1 3\\n2 1\\n\", \"5 3\\n1 2\\n2 3\\n3 4\\n2 5\\n\", \"6 3\\n2 1\\n4 3\\n2 5\\n1 4\\n5 6\\n\", \"4 0\\n4 4\\n2 4\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n1 6\\n1 4\\n5 6\\n\", \"6 1\\n4 1\\n4 3\\n4 5\\n2 1\\n5 6\\n\", \"4 2\\n4 2\\n2 1\\n3 1\\n\", \"6 0\\n2 1\\n4 1\\n2 3\\n1 4\\n5 6\\n\", \"4 3\\n4 2\\n2 1\\n3 1\\n\", \"6 0\\n2 1\\n4 1\\n2 6\\n1 4\\n5 6\\n\", \"2 0\\n2 1\\n\", \"4 3\\n1 2\\n1 3\\n2 4\\n\", \"6 1\\n2 1\\n6 3\\n2 5\\n1 4\\n5 6\\n\", \"4 5\\n1 2\\n2 3\\n1 4\\n\", \"6 2\\n3 1\\n2 3\\n2 5\\n5 4\\n5 6\\n\", \"4 5\\n1 4\\n1 3\\n2 4\\n\", \"4 0\\n4 2\\n2 1\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n4 6\\n1 4\\n5 1\\n\", \"6 1\\n4 1\\n4 3\\n4 5\\n2 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n4 6\\n\", \"4 0\\n1 2\\n1 3\\n2 1\\n\", \"4 5\\n4 2\\n2 1\\n3 1\\n\", \"6 2\\n3 1\\n2 3\\n2 5\\n2 4\\n5 6\\n\", \"6 2\\n2 1\\n4 3\\n2 6\\n1 4\\n5 1\\n\", \"6 0\\n4 1\\n4 3\\n4 5\\n2 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n3 6\\n\", \"6 0\\n4 1\\n4 3\\n4 5\\n4 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 4\\n1 6\\n\", \"6 1\\n3 1\\n4 3\\n2 5\\n5 3\\n1 6\\n\", \"6 0\\n2 1\\n4 3\\n4 5\\n2 4\\n5 6\\n\", \"4 0\\n4 1\\n1 4\\n3 1\\n\", \"6 2\\n2 1\\n4 3\\n4 6\\n2 4\\n5 6\\n\"], \"outputs\": [\"0.5000000000\\n\", \"2.0000000000\\n\", \"3.3333333333\\n\", \"1000000000.0000000000\\n\", \"1.0000000000\\n\", \"1.0000000000\\n\", \"1000000000.0000000000\\n\", \"0.6666666667\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"0.5000000000\\n\", \"3.3333333333\\n\", \"1.3333333333\\n\", \"0.0000000000\\n\", \"2.0000000000\\n\", \"5.0000000000\\n\", \"3.0000000000\\n\", \"6.0000000000\\n\", \"5.3333333333\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"0.6666666667\\n\", \"3.3333333333\\n\", \"0.0000000000\\n\", \"2.0000000000\\n\", \"2.0000000000\\n\", \"1.3333333333\\n\", \"0.5000000000\\n\", \"0.0000000000\\n\", \"0.6666666667\\n\", \"3.3333333333\\n\", \"1.3333333333\\n\", \"0.6666666667\\n\", \"0.6666666667\\n\", \"2.0000000000\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"2.0000000000\\n\", \"3.0000000000\\n\", \"0.0000000000\\n\", \"1.3333333333\\n\", \"0.6666666667\\n\", \"2.0000000000\\n\", \"0.0000000000\\n\", \"3.0000000000\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"3.0000000000\\n\", \"1.0000000000\\n\", \"5.0000000000\\n\", \"1.3333333333\\n\", \"5.0000000000\\n\", \"0.0000000000\\n\", \"1.0000000000\\n\", \"0.5000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"5.0000000000\\n\", \"1.3333333333\\n\", \"1.3333333333\\n\", \"0.0000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"1.0000000000\\n\", \"0.6666666667\\n\", \"0.0000000000\\n\", \"0.0000000000\\n\", \"1.3333333333\\n\"]}", "source": "primeintellect"}
|
You are given a tree (an undirected connected graph without cycles) and an integer s.
Vanya wants to put weights on all edges of the tree so that all weights are non-negative real numbers and their sum is s. At the same time, he wants to make the diameter of the tree as small as possible.
Let's define the diameter of a weighed tree as the maximum sum of the weights of the edges lying on the path between two some vertices of the tree. In other words, the diameter of a weighed tree is the length of the longest simple path in the tree, where length of a path is equal to the sum of weights over all edges in the path.
Find the minimum possible diameter that Vanya can get.
Input
The first line contains two integer numbers n and s (2 ≤ n ≤ 10^5, 1 ≤ s ≤ 10^9) — the number of vertices in the tree and the sum of edge weights.
Each of the following n−1 lines contains two space-separated integer numbers a_i and b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i) — the indexes of vertices connected by an edge. The edges are undirected.
It is guaranteed that the given edges form a tree.
Output
Print the minimum diameter of the tree that Vanya can get by placing some non-negative real weights on its edges with the sum equal to s.
Your answer will be considered correct if its absolute or relative error does not exceed 10^{-6}.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if \frac {|a-b|} {max(1, b)} ≤ 10^{-6}.
Examples
Input
4 3
1 2
1 3
1 4
Output
2.000000000000000000
Input
6 1
2 1
2 3
2 5
5 4
5 6
Output
0.500000000000000000
Input
5 5
1 2
2 3
3 4
3 5
Output
3.333333333333333333
Note
In the first example it is necessary to put weights like this:
<image>
It is easy to see that the diameter of this tree is 2. It can be proved that it is the minimum possible diameter.
In the second example it is necessary to put weights like this:
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"6 6\\n6 6 6 6 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 13\\n3 6\\n4 11\\n5 6\\n6 6\\n\", \"8 5\\n8 6 2 1 4 5 7 5\\n6 3 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"6 6\\n6 6 6 6 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 6\\n5 6\\n6 66\\n\", \"1 1\\n10000000\\n284517\\n1 10000000\\n\", \"1 1\\n1\\n642400\\n1 1\\n\", \"1 1\\n6577865\\n227563\\n1 5978566\\n\", \"5 6\\n26 75 98 33 53\\n382051 563872 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 137753 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n1 26\\n1 4\\n4 76\\n10 106\\n5 100\\n4 116\\n7 62\\n\", \"1 1\\n1\\n558976\\n1 1\\n\", \"1 1\\n411017\\n129875\\n1 8160563\\n\", \"1 1\\n8494441\\n646015\\n1 2198012\\n\", \"1 1\\n10000000\\n367941\\n1 10000000\\n\", \"10 20\\n1 2 3 4 5 6 7 8 9 10\\n1 2 3 4 5 6 7 8 9 10\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n\", \"1 1\\n11000000\\n284517\\n1 10000000\\n\", \"1 1\\n1\\n870006\\n1 1\\n\", \"1 1\\n11055843\\n227563\\n1 5978566\\n\", \"5 6\\n26 75 98 33 53\\n129196 563872 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 137753 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 100\\n4 116\\n7 62\\n\", \"6 6\\n6 6 6 6 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"8 5\\n8 6 2 1 4 5 7 5\\n6 4 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"6 6\\n6 6 6 6 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"1 1\\n1\\n271261\\n1 1\\n\", \"5 6\\n26 75 98 33 53\\n135548 563872 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 100\\n4 116\\n7 62\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 6 6 6 6\\n6 54 666 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 6 6 6 6\\n6 54 666 9233 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n3 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 89 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 9\\n6 6\\n6 6\\n\", \"1 1\\n10000000\\n496113\\n1 10000000\\n\", \"1 1\\n1\\n941321\\n1 1\\n\", \"5 6\\n26 75 98 33 53\\n382051 227556 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"1 1\\n1\\n558976\\n1 0\\n\", \"8 5\\n8 2 2 1 4 5 7 5\\n6 3 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"5 6\\n26 75 98 33 53\\n129196 563872 378058 483440 136309\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 137753 453796 348671 185533 919310 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 100\\n4 116\\n7 62\\n\", \"8 5\\n8 6 2 1 4 5 7 5\\n6 2 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"6 6\\n6 1 6 6 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"5 6\\n26 75 98 33 53\\n135548 884596 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 13\\n5 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 6 6 6 6\\n6 54 877 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 8\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 13176 66666 666666\\n1 9\\n3 13\\n3 6\\n4 9\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 89 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 4\\n6 6\\n6 6\\n\", \"1 1\\n10000000\\n815053\\n1 10000000\\n\", \"5 6\\n26 75 98 33 53\\n382051 227556 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 12\\n2 24\\n2 2\\n\", \"5 6\\n26 75 98 33 53\\n129196 563872 378058 483440 136309\\n5 56\\n3 9\\n5 38\\n5 12\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 186577 757031 137753 453796 348671 185533 919310 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 100\\n4 116\\n7 62\\n\", \"8 5\\n8 6 2 1 4 4 7 5\\n6 2 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"5 6\\n26 75 98 33 53\\n135548 884596 378058 483440 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n1 2\\n\", \"6 6\\n6 6 6 6 6 6\\n6 6 877 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 4958 66666 666666\\n1 6\\n1 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 83107 666666\\n1 6\\n2 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 2\\n4 15\\n6 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n9 89 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 4\\n6 6\\n6 6\\n\", \"5 6\\n26 75 98 33 53\\n129196 563872 378058 483440 136309\\n5 85\\n3 9\\n5 38\\n5 12\\n2 24\\n2 2\\n\", \"8 5\\n8 6 2 1 4 4 7 5\\n6 2 3 2 6 2 3 2\\n2 8\\n1 4\\n4 5\\n3 4\\n6 10\\n\", \"6 6\\n6 1 6 6 6 6\\n6 25 666 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n4 6\\n6 66\\n\", \"6 6\\n6 6 6 5 6 6\\n6 106 666 6666 66666 666666\\n1 6\\n2 13\\n5 6\\n4 11\\n4 6\\n6 6\\n\", \"6 6\\n12 6 6 6 6 6\\n6 6 877 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 4958 66666 666666\\n1 6\\n1 19\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 6 6 6 6\\n6 54 666 1440 66666 666666\\n1 6\\n2 6\\n2 6\\n3 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 13176 66666 931632\\n1 9\\n3 13\\n3 6\\n4 2\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n5 13\\n3 2\\n4 15\\n6 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n1 89 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 4\\n6 6\\n6 6\\n\", \"6 6\\n6 1 6 6 6 6\\n6 25 1234 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n4 6\\n6 66\\n\", \"5 6\\n26 75 98 33 53\\n135548 884596 378058 505065 203755\\n5 56\\n3 9\\n5 26\\n5 6\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 87\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n1 26\\n1 4\\n4 76\\n10 106\\n5 110\\n1 116\\n7 62\\n\", \"6 6\\n6 6 6 5 6 6\\n10 106 666 6666 66666 666666\\n1 6\\n2 13\\n5 6\\n4 11\\n4 6\\n6 6\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 100\\n4 90\\n7 62\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n3 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 9\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 9\\n6 6\\n6 6\\n\", \"1 1\\n411017\\n118782\\n1 8160563\\n\", \"1 1\\n01000000\\n284517\\n1 10000000\\n\", \"1 1\\n16748917\\n227563\\n1 5978566\\n\", \"1 1\\n1\\n271261\\n1 0\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 110\\n4 116\\n7 62\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 100\\n1 90\\n7 62\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n1 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 6 6 6 6\\n6 54 666 9233 66666 666666\\n1 6\\n2 6\\n3 6\\n3 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 6\\n4 15\\n6 6\\n6 6\\n\", \"1 1\\n663214\\n118782\\n1 8160563\\n\", \"8 5\\n8 2 2 1 6 5 7 5\\n6 3 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"1 1\\n01000000\\n46015\\n1 10000000\\n\", \"6 6\\n6 1 6 6 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 6\\n3 6\\n4 12\\n4 6\\n6 66\\n\", \"1 1\\n1\\n111474\\n1 0\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n1 4\\n4 76\\n10 106\\n5 110\\n1 116\\n7 62\\n\", \"6 6\\n6 6 6 5 6 6\\n6 66 666 6666 66666 666666\\n1 6\\n2 13\\n5 6\\n4 11\\n4 6\\n6 6\\n\", \"6 6\\n6 6 6 6 6 6\\n6 54 666 9233 66666 666666\\n1 6\\n2 6\\n2 6\\n3 12\\n5 6\\n6 66\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 8\\n4 10\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 13176 66666 931632\\n1 9\\n3 13\\n3 6\\n4 9\\n3 6\\n6 6\\n\", \"5 6\\n26 75 98 33 53\\n382051 227556 378058 483440 203755\\n5 56\\n3 9\\n2 38\\n5 12\\n2 24\\n2 2\\n\", \"1 1\\n89002\\n118782\\n1 8160563\\n\", \"8 5\\n14 2 2 1 6 5 7 5\\n6 3 3 2 6 2 3 2\\n2 8\\n1 4\\n4 7\\n3 4\\n6 10\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 186577 757031 137753 453796 348671 185533 919310 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n2 4\\n4 76\\n10 106\\n5 100\\n4 116\\n7 62\\n\", \"5 6\\n26 75 98 33 53\\n135548 884596 378058 505065 203755\\n5 56\\n3 9\\n5 38\\n5 6\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 120930 757031 262319 453796 348671 185533 966778 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n1 26\\n1 4\\n4 76\\n10 106\\n5 110\\n1 116\\n7 62\\n\", \"6 6\\n6 6 7 5 6 7\\n6 66 666 6666 83107 666666\\n1 6\\n2 13\\n3 6\\n4 11\\n3 6\\n6 6\\n\", \"6 6\\n6 6 7 5 6 6\\n6 66 666 6666 66666 666666\\n1 9\\n3 13\\n3 8\\n4 10\\n3 6\\n6 5\\n\", \"5 6\\n26 75 98 51 53\\n382051 227556 378058 483440 203755\\n5 56\\n3 9\\n2 38\\n5 12\\n2 24\\n2 2\\n\", \"1 1\\n89002\\n91059\\n1 8160563\\n\", \"5 6\\n26 75 98 54 53\\n129196 563872 378058 483440 136309\\n5 85\\n3 9\\n5 38\\n5 12\\n2 24\\n2 2\\n\", \"10 15\\n132 138 38 75 14 115 129 68 119 118\\n728344 513371 186577 757031 137753 453796 348671 185533 919310 521678\\n4 58\\n1 8\\n8 22\\n3 98\\n2 111\\n6 158\\n2 82\\n1 170\\n2 26\\n2 4\\n4 76\\n10 106\\n5 100\\n4 33\\n7 62\\n\"], \"outputs\": [\"36\\n11058\\n99996\\n4333326\\n0\\n0\\n\", \"22\\n24\\n14\\n10\\n39\\n\", \"36\\n396\\n3996\\n39996\\n399996\\n0\\n\", \"2845170000000\\n\", \"642400\\n\", \"1360500414658\\n\", \"11933189\\n3402522\\n14366204\\n2268348\\n13532928\\n1127744\\n\", \"43907798\\n5826752\\n4081726\\n15058400\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"558976\\n\", \"0\\n\", \"1419948722180\\n\", \"3679410000000\\n\", \"1\\n2\\n2\\n3\\n3\\n3\\n4\\n4\\n4\\n4\\n5\\n5\\n5\\n5\\n5\\n6\\n6\\n6\\n6\\n6\\n\", \"2845170000000\\n\", \"870006\\n\", \"1360500414658\\n\", \"11186603\\n3402522\\n8642378\\n2268348\\n13532928\\n1127744\\n\", \"43907798\\n5826752\\n4081726\\n15058400\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"36\\n11058\\n99996\\n4333326\\n0\\n0\\n\", \"28\\n24\\n14\\n10\\n39\\n\", \"36\\n396\\n3996\\n439992\\n3999996\\n0\\n\", \"271261\\n\", \"11205659\\n3402522\\n8788474\\n2268348\\n13532928\\n1127744\\n\", \"43907798\\n5826752\\n4081726\\n16802324\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"36\\n11058\\n159996\\n0\\n0\\n0\\n\", \"36\\n324\\n3996\\n439992\\n3999996\\n0\\n\", \"36\\n324\\n3996\\n455394\\n3999996\\n0\\n\", \"36\\n5058\\n99996\\n4333326\\n0\\n0\\n\", \"234\\n24858\\n279996\\n0\\n0\\n0\\n\", \"303\\n24927\\n279996\\n0\\n0\\n0\\n\", \"4961130000000\\n\", \"941321\\n\", \"11481683\\n3402522\\n8647128\\n1365336\\n5461344\\n455112\\n\", \"0\\n\", \"18\\n24\\n16\\n12\\n51\\n\", \"7611965\\n3402522\\n8642378\\n2268348\\n13532928\\n1127744\\n\", \"43907798\\n5826752\\n4081726\\n15058400\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n91880012\\n0\\n0\\n0\\n\", \"16\\n24\\n14\\n10\\n39\\n\", \"36\\n3396\\n33996\\n3739992\\n0\\n0\\n\", \"11205659\\n3402522\\n8788474\\n2268348\\n21230304\\n1769192\\n\", \"36\\n11058\\n399996\\n0\\n0\\n0\\n\", \"36\\n324\\n5262\\n439992\\n3999996\\n0\\n\", \"234\\n24858\\n413328\\n0\\n0\\n0\\n\", \"234\\n44388\\n293016\\n0\\n0\\n0\\n\", \"303\\n24927\\n279996\\n1466664\\n0\\n0\\n\", \"8150530000000\\n\", \"11481683\\n3402522\\n8647128\\n2730672\\n5762348\\n756116\\n\", \"7611965\\n3402522\\n8642378\\n4536696\\n13532928\\n1127744\\n\", \"43907798\\n5826752\\n4081726\\n17552986\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n91880012\\n0\\n0\\n0\\n\", \"16\\n24\\n14\\n11\\n42\\n\", \"11205659\\n3402522\\n8788474\\n2268348\\n21230304\\n756116\\n\", \"36\\n36\\n5262\\n439992\\n3999996\\n0\\n\", \"36\\n9350\\n153164\\n0\\n0\\n0\\n\", \"36\\n5058\\n116437\\n4415531\\n0\\n0\\n\", \"234\\n24858\\n13332\\n0\\n0\\n0\\n\", \"321\\n24927\\n279996\\n1466664\\n0\\n0\\n\", \"12851821\\n3402522\\n14366204\\n4536696\\n13532928\\n1127744\\n\", \"16\\n24\\n10\\n10\\n35\\n\", \"36\\n3355\\n33996\\n3739992\\n0\\n0\\n\", \"36\\n11298\\n399996\\n0\\n0\\n0\\n\", \"36\\n36\\n5262\\n40032\\n399996\\n0\\n\", \"36\\n162514\\n1599996\\n0\\n0\\n0\\n\", \"36\\n324\\n3996\\n408636\\n3999996\\n0\\n\", \"234\\n44388\\n293016\\n133332\\n5589792\\n0\\n\", \"234\\n402858\\n1332\\n0\\n0\\n0\\n\", \"273\\n24927\\n279996\\n1466664\\n0\\n0\\n\", \"36\\n6195\\n34564\\n3739992\\n0\\n0\\n\", \"11205659\\n3402522\\n4251778\\n2268348\\n21230304\\n1769192\\n\", \"58228485\\n5826752\\n4081726\\n19535216\\n56984181\\n67179393\\n33037922\\n111024711\\n13563628\\n2086712\\n46324028\\n0\\n0\\n0\\n0\\n\", \"60\\n11298\\n399996\\n0\\n0\\n0\\n\", \"43907798\\n5826752\\n4081726\\n16802324\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"36\\n11058\\n159996\\n0\\n0\\n0\\n\", \"234\\n24858\\n279996\\n0\\n0\\n0\\n\", \"234\\n24858\\n279996\\n0\\n0\\n0\\n\", \"0\\n\", \"0\\n\", \"1360500414658\\n\", \"0\\n\", \"43907798\\n5826752\\n4081726\\n16802324\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"43907798\\n5826752\\n4081726\\n16802324\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"36\\n11058\\n159996\\n0\\n0\\n0\\n\", \"36\\n324\\n3996\\n455394\\n3999996\\n0\\n\", \"36\\n5058\\n99996\\n4333326\\n0\\n0\\n\", \"234\\n24858\\n279996\\n0\\n0\\n0\\n\", \"0\\n\", \"18\\n24\\n16\\n12\\n51\\n\", \"0\\n\", \"36\\n3396\\n33996\\n3739992\\n0\\n0\\n\", \"0\\n\", \"43907798\\n5826752\\n4081726\\n16802324\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"36\\n11058\\n399996\\n0\\n0\\n0\\n\", \"36\\n324\\n3996\\n455394\\n3999996\\n0\\n\", \"234\\n24858\\n413328\\n0\\n0\\n0\\n\", \"234\\n44388\\n293016\\n0\\n0\\n0\\n\", \"11481683\\n3402522\\n8647128\\n2730672\\n5762348\\n756116\\n\", \"0\\n\", \"18\\n24\\n16\\n12\\n51\\n\", \"43907798\\n5826752\\n4081726\\n17552986\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n91880012\\n0\\n0\\n0\\n\", \"11205659\\n3402522\\n8788474\\n2268348\\n21230304\\n1769192\\n\", \"43907798\\n5826752\\n4081726\\n16802324\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n96247068\\n0\\n0\\n0\\n\", \"36\\n5058\\n116437\\n4415531\\n0\\n0\\n\", \"234\\n24858\\n413328\\n0\\n0\\n0\\n\", \"11481683\\n3402522\\n8647128\\n2730672\\n5762348\\n756116\\n\", \"0\\n\", \"12851821\\n3402522\\n14366204\\n4536696\\n13532928\\n1127744\\n\", \"43907798\\n5826752\\n4081726\\n17552986\\n56984181\\n67179393\\n33037922\\n108948627\\n13563628\\n2086712\\n43648529\\n91880012\\n0\\n0\\n0\\n\"]}", "source": "primeintellect"}
|
Lunar New Year is approaching, and Bob is planning to go for a famous restaurant — "Alice's".
The restaurant "Alice's" serves n kinds of food. The cost for the i-th kind is always c_i. Initially, the restaurant has enough ingredients for serving exactly a_i dishes of the i-th kind. In the New Year's Eve, m customers will visit Alice's one after another and the j-th customer will order d_j dishes of the t_j-th kind of food. The (i + 1)-st customer will only come after the i-th customer is completely served.
Suppose there are r_i dishes of the i-th kind remaining (initially r_i = a_i). When a customer orders 1 dish of the i-th kind, the following principles will be processed.
1. If r_i > 0, the customer will be served exactly 1 dish of the i-th kind. The cost for the dish is c_i. Meanwhile, r_i will be reduced by 1.
2. Otherwise, the customer will be served 1 dish of the cheapest available kind of food if there are any. If there are multiple cheapest kinds of food, the one with the smallest index among the cheapest will be served. The cost will be the cost for the dish served and the remain for the corresponding dish will be reduced by 1.
3. If there are no more dishes at all, the customer will leave angrily. Therefore, no matter how many dishes are served previously, the cost for the customer is 0.
If the customer doesn't leave after the d_j dishes are served, the cost for the customer will be the sum of the cost for these d_j dishes.
Please determine the total cost for each of the m customers.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 10^5), representing the number of different kinds of food and the number of customers, respectively.
The second line contains n positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7), where a_i denotes the initial remain of the i-th kind of dishes.
The third line contains n positive integers c_1, c_2, …, c_n (1 ≤ c_i ≤ 10^6), where c_i denotes the cost of one dish of the i-th kind.
The following m lines describe the orders of the m customers respectively. The j-th line contains two positive integers t_j and d_j (1 ≤ t_j ≤ n, 1 ≤ d_j ≤ 10^7), representing the kind of food and the number of dishes the j-th customer orders, respectively.
Output
Print m lines. In the j-th line print the cost for the j-th customer.
Examples
Input
8 5
8 6 2 1 4 5 7 5
6 3 3 2 6 2 3 2
2 8
1 4
4 7
3 4
6 10
Output
22
24
14
10
39
Input
6 6
6 6 6 6 6 6
6 66 666 6666 66666 666666
1 6
2 6
3 6
4 6
5 6
6 66
Output
36
396
3996
39996
399996
0
Input
6 6
6 6 6 6 6 6
6 66 666 6666 66666 666666
1 6
2 13
3 6
4 11
5 6
6 6
Output
36
11058
99996
4333326
0
0
Note
In the first sample, 5 customers will be served as follows.
1. Customer 1 will be served 6 dishes of the 2-nd kind, 1 dish of the 4-th kind, and 1 dish of the 6-th kind. The cost is 6 ⋅ 3 + 1 ⋅ 2 + 1 ⋅ 2 = 22. The remain of the 8 kinds of food will be \{8, 0, 2, 0, 4, 4, 7, 5\}.
2. Customer 2 will be served 4 dishes of the 1-st kind. The cost is 4 ⋅ 6 = 24. The remain will be \{4, 0, 2, 0, 4, 4, 7, 5\}.
3. Customer 3 will be served 4 dishes of the 6-th kind, 3 dishes of the 8-th kind. The cost is 4 ⋅ 2 + 3 ⋅ 2 = 14. The remain will be \{4, 0, 2, 0, 4, 0, 7, 2\}.
4. Customer 4 will be served 2 dishes of the 3-rd kind, 2 dishes of the 8-th kind. The cost is 2 ⋅ 3 + 2 ⋅ 2 = 10. The remain will be \{4, 0, 0, 0, 4, 0, 7, 0\}.
5. Customer 5 will be served 7 dishes of the 7-th kind, 3 dishes of the 1-st kind. The cost is 7 ⋅ 3 + 3 ⋅ 6 = 39. The remain will be \{1, 0, 0, 0, 4, 0, 0, 0\}.
In the second sample, each customer is served what they order except the last one, who leaves angrily without paying. For example, the second customer is served 6 dishes of the second kind, so the cost is 66 ⋅ 6 = 396.
In the third sample, some customers may not be served what they order. For example, the second customer is served 6 dishes of the second kind, 6 of the third and 1 of the fourth, so the cost is 66 ⋅ 6 + 666 ⋅ 6 + 6666 ⋅ 1 = 11058.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"7 4 2 1\\n1 3 5 4 2 7 6\\n\", \"6 2 3 3\\n7 10 50 12 1 8\\n\", \"1 1 100 99\\n100\\n\", \"2 1 49 2\\n50 50\\n\", \"2 1 100 2\\n1 101\\n\", \"2 2 49 2\\n50 50\\n\", \"7 4 2 1\\n1 3 4 4 2 7 6\\n\", \"6 2 3 2\\n7 10 50 12 1 8\\n\", \"2 1 100 2\\n2 101\\n\", \"7 4 2 1\\n1 1 5 4 2 7 6\\n\", \"6 2 3 3\\n7 4 50 12 1 8\\n\", \"6 2 3 2\\n5 10 50 12 1 8\\n\", \"2 1 100 2\\n2 001\\n\", \"2 2 71 2\\n50 50\\n\", \"7 4 2 1\\n1 3 4 1 2 7 6\\n\", \"2 2 71 0\\n50 50\\n\", \"2 1 71 0\\n50 50\\n\", \"2 1 55 0\\n50 50\\n\", \"2 1 55 1\\n50 50\\n\", \"2 1 55 1\\n88 50\\n\", \"2 1 98 1\\n88 50\\n\", \"2 2 49 2\\n66 50\\n\", \"1 1 100 99\\n110\\n\", \"2 2 49 2\\n50 88\\n\", \"2 2 71 2\\n16 50\\n\", \"2 2 37 0\\n50 50\\n\", \"2 1 71 0\\n50 31\\n\", \"2 1 3 0\\n50 50\\n\", \"2 1 55 1\\n88 25\\n\", \"2 1 55 1\\n88 76\\n\", \"2 1 49 2\\n66 50\\n\", \"6 2 3 3\\n7 4 5 12 1 8\\n\", \"1 1 100 120\\n110\\n\", \"2 2 87 2\\n50 88\\n\", \"6 2 2 2\\n5 10 50 12 1 8\\n\", \"2 2 140 2\\n16 50\\n\", \"2 1 3 0\\n50 64\\n\", \"2 1 55 0\\n88 25\\n\", \"2 1 55 1\\n171 76\\n\", \"2 1 16 2\\n66 50\\n\", \"2 2 87 2\\n81 88\\n\", \"6 2 2 2\\n5 9 50 12 1 8\\n\", \"2 2 140 4\\n16 50\\n\", \"2 1 3 0\\n10 64\\n\", \"2 1 15 2\\n66 50\\n\", \"2 2 58 2\\n81 88\\n\", \"6 2 2 3\\n5 9 50 12 1 8\\n\", \"2 2 140 7\\n16 50\\n\", \"2 1 3 1\\n10 64\\n\", \"2 1 15 4\\n66 50\\n\", \"2 2 58 2\\n81 61\\n\", \"6 1 2 3\\n5 9 50 12 1 8\\n\", \"2 2 140 7\\n14 50\\n\", \"2 1 3 1\\n10 13\\n\", \"2 2 18 2\\n81 61\\n\", \"6 1 2 3\\n1 9 50 12 1 8\\n\", \"2 2 5 7\\n14 50\\n\", \"2 2 33 2\\n81 61\\n\", \"6 2 2 3\\n1 9 50 12 1 8\\n\", \"2 2 9 7\\n14 50\\n\", \"2 2 2 2\\n81 61\\n\", \"6 2 0 3\\n1 9 50 12 1 8\\n\", \"2 2 2 7\\n14 50\\n\", \"2 2 2 1\\n81 61\\n\", \"6 3 0 3\\n1 9 50 12 1 8\\n\", \"2 2 4 7\\n14 50\\n\", \"6 2 0 3\\n1 9 50 12 1 15\\n\", \"2 2 2 7\\n14 63\\n\", \"2 1 2 7\\n14 63\\n\", \"2 1 2 7\\n14 22\\n\", \"2 1 2 7\\n14 19\\n\", \"2 1 1 7\\n14 19\\n\", \"7 1 2 1\\n1 3 5 4 2 7 6\\n\", \"6 2 3 3\\n7 10 51 12 1 8\\n\", \"2 2 37 2\\n50 50\\n\", \"7 4 2 1\\n1 5 4 1 2 7 6\\n\", \"2 2 71 0\\n50 78\\n\", \"2 1 55 1\\n50 88\\n\", \"2 1 55 1\\n121 50\\n\", \"2 1 73 1\\n88 50\\n\", \"2 2 49 3\\n66 50\\n\", \"2 1 100 2\\n2 100\\n\", \"7 4 2 1\\n1 1 5 4 2 12 6\\n\", \"6 2 3 3\\n7 4 22 12 1 8\\n\", \"1 1 100 99\\n111\\n\", \"2 2 49 0\\n50 88\\n\", \"6 2 3 2\\n5 4 50 12 1 8\\n\", \"2 1 3 0\\n60 50\\n\", \"2 1 55 1\\n88 45\\n\", \"2 1 55 1\\n24 76\\n\", \"2 2 15 2\\n66 50\\n\", \"6 2 3 3\\n7 4 5 12 1 1\\n\", \"2 2 87 2\\n50 147\\n\", \"6 2 2 2\\n5 5 50 12 1 8\\n\", \"2 1 16 2\\n63 50\\n\", \"2 2 87 2\\n81 102\\n\", \"6 2 2 2\\n5 9 19 12 1 8\\n\", \"2 1 58 2\\n81 88\\n\", \"6 2 2 3\\n8 9 50 12 1 8\\n\", \"2 2 195 7\\n16 50\\n\", \"2 1 10 2\\n66 50\\n\", \"2 2 16 2\\n81 61\\n\", \"6 1 2 3\\n5 9 50 15 1 8\\n\", \"2 4 140 7\\n14 50\\n\", \"2 1 3 1\\n6 13\\n\"], \"outputs\": [\"6\\n\", \"5\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"7\\n\", \"4\\n\", \"1\\n\", \"6\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"7\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"5\\n\", \"1\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"0\\n\", \"6\\n\", \"2\\n\", \"2\\n\", \"6\\n\", \"2\\n\", \"2\\n\", \"6\\n\", \"2\\n\", \"6\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"6\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"5\\n\", \"6\\n\", \"1\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"0\\n\", \"5\\n\", \"0\\n\", \"6\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"1\\n\", \"2\\n\"]}", "source": "primeintellect"}
|
There are n monsters standing in a row numbered from 1 to n. The i-th monster has h_i health points (hp). You have your attack power equal to a hp and your opponent has his attack power equal to b hp.
You and your opponent are fighting these monsters. Firstly, you and your opponent go to the first monster and fight it till his death, then you and your opponent go the second monster and fight it till his death, and so on. A monster is considered dead if its hp is less than or equal to 0.
The fight with a monster happens in turns.
1. You hit the monster by a hp. If it is dead after your hit, you gain one point and you both proceed to the next monster.
2. Your opponent hits the monster by b hp. If it is dead after his hit, nobody gains a point and you both proceed to the next monster.
You have some secret technique to force your opponent to skip his turn. You can use this technique at most k times in total (for example, if there are two monsters and k=4, then you can use the technique 2 times on the first monster and 1 time on the second monster, but not 2 times on the first monster and 3 times on the second monster).
Your task is to determine the maximum number of points you can gain if you use the secret technique optimally.
Input
The first line of the input contains four integers n, a, b and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ a, b, k ≤ 10^9) — the number of monsters, your attack power, the opponent's attack power and the number of times you can use the secret technique.
The second line of the input contains n integers h_1, h_2, ..., h_n (1 ≤ h_i ≤ 10^9), where h_i is the health points of the i-th monster.
Output
Print one integer — the maximum number of points you can gain if you use the secret technique optimally.
Examples
Input
6 2 3 3
7 10 50 12 1 8
Output
5
Input
1 1 100 99
100
Output
1
Input
7 4 2 1
1 3 5 4 2 7 6
Output
6
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"6\\n1 2\\n3 4\\n6 4\\n2 3\\n1 3\\n3 5\\n\", \"4\\n1 3\\n4 3\\n4 2\\n1 2\\n\", \"4\\n4 3\\n1 3\\n2 1\\n2 3\\n\", \"5\\n4 1\\n1 3\\n5 3\\n2 4\\n5 2\\n\", \"8\\n1 2\\n2 3\\n3 1\\n3 4\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"10\\n10 7\\n1 5\\n2 1\\n4 1\\n1 10\\n3 1\\n9 7\\n1 8\\n7 6\\n7 1\\n\", \"10\\n8 2\\n10 5\\n9 5\\n3 9\\n4 7\\n3 1\\n7 2\\n10 6\\n7 8\\n1 4\\n\", \"5\\n2 5\\n4 5\\n4 3\\n4 2\\n1 4\\n\", \"3\\n1 2\\n1 3\\n2 3\\n\", \"4\\n3 1\\n3 4\\n2 1\\n4 2\\n\", \"6\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n4 6\\n\", \"5\\n1 3\\n1 5\\n4 2\\n2 3\\n5 2\\n\", \"4\\n4 3\\n1 4\\n2 1\\n2 3\\n\", \"5\\n4 1\\n2 3\\n5 3\\n2 4\\n5 2\\n\", \"8\\n1 2\\n2 5\\n3 1\\n3 4\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"6\\n1 2\\n2 4\\n3 4\\n4 5\\n5 6\\n4 6\\n\", \"5\\n1 2\\n1 5\\n4 2\\n2 3\\n5 2\\n\", \"6\\n1 2\\n3 4\\n6 4\\n2 3\\n1 5\\n3 5\\n\", \"6\\n1 2\\n3 4\\n6 4\\n2 3\\n1 3\\n2 5\\n\", \"4\\n4 3\\n1 4\\n3 1\\n2 3\\n\", \"8\\n1 2\\n1 5\\n3 1\\n3 4\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"6\\n1 2\\n2 4\\n3 4\\n3 5\\n5 6\\n4 6\\n\", \"6\\n1 2\\n3 4\\n6 2\\n2 3\\n1 5\\n3 5\\n\", \"6\\n1 2\\n2 3\\n1 4\\n4 5\\n5 6\\n4 6\\n\", \"8\\n1 2\\n2 5\\n4 1\\n3 4\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"5\\n1 2\\n1 5\\n4 2\\n2 3\\n5 4\\n\", \"6\\n1 2\\n3 4\\n6 4\\n2 5\\n1 5\\n3 5\\n\", \"5\\n4 1\\n1 2\\n5 3\\n2 4\\n5 2\\n\", \"8\\n1 2\\n2 3\\n3 1\\n3 7\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"10\\n8 2\\n10 5\\n9 5\\n4 9\\n4 7\\n3 1\\n7 2\\n10 6\\n7 8\\n1 4\\n\", \"8\\n1 2\\n2 5\\n3 1\\n3 4\\n4 5\\n5 6\\n4 7\\n6 8\\n\", \"6\\n1 2\\n3 4\\n6 3\\n2 3\\n1 3\\n2 5\\n\", \"6\\n1 2\\n2 3\\n1 4\\n1 5\\n5 6\\n4 6\\n\", \"10\\n8 2\\n10 5\\n9 5\\n4 9\\n4 7\\n3 1\\n7 3\\n10 6\\n7 8\\n1 4\\n\", \"8\\n1 2\\n2 3\\n5 1\\n3 4\\n3 5\\n5 6\\n6 7\\n6 8\\n\", \"6\\n1 2\\n3 4\\n6 3\\n2 3\\n1 6\\n2 5\\n\", \"4\\n4 3\\n1 4\\n3 2\\n2 4\\n\", \"5\\n4 1\\n2 3\\n1 3\\n2 4\\n5 2\\n\", \"6\\n1 2\\n1 4\\n6 2\\n2 5\\n1 5\\n3 5\\n\", \"8\\n1 2\\n2 4\\n3 1\\n3 7\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"10\\n8 2\\n10 5\\n8 5\\n4 9\\n4 7\\n3 1\\n7 2\\n10 6\\n7 8\\n1 4\\n\", \"6\\n1 2\\n2 3\\n1 4\\n1 5\\n1 6\\n4 6\\n\", \"10\\n8 2\\n10 5\\n9 5\\n4 9\\n4 7\\n3 1\\n7 5\\n10 6\\n7 8\\n1 4\\n\", \"8\\n1 2\\n2 5\\n3 1\\n3 7\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"6\\n1 2\\n2 3\\n1 4\\n1 5\\n2 6\\n3 6\\n\", \"10\\n10 2\\n10 5\\n9 5\\n3 9\\n4 7\\n3 1\\n7 2\\n10 6\\n7 8\\n1 4\\n\", \"8\\n1 2\\n2 5\\n3 1\\n3 8\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"6\\n1 4\\n2 4\\n3 4\\n3 5\\n5 6\\n4 6\\n\", \"8\\n1 2\\n2 5\\n4 1\\n3 4\\n4 5\\n5 6\\n8 7\\n6 8\\n\", \"8\\n1 2\\n2 3\\n5 1\\n3 4\\n4 5\\n5 6\\n6 7\\n1 8\\n\", \"6\\n1 2\\n3 4\\n6 3\\n2 3\\n1 3\\n4 5\\n\", \"6\\n1 2\\n1 4\\n6 4\\n2 3\\n1 3\\n2 5\\n\", \"6\\n1 2\\n1 4\\n6 2\\n2 3\\n1 5\\n3 5\\n\", \"8\\n1 2\\n2 3\\n5 1\\n3 4\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"4\\n4 3\\n1 4\\n3 1\\n2 4\\n\", \"6\\n1 2\\n1 4\\n6 4\\n2 3\\n1 3\\n1 5\\n\", \"10\\n8 2\\n10 2\\n9 5\\n4 9\\n4 7\\n3 1\\n7 3\\n10 6\\n7 8\\n1 4\\n\", \"4\\n2 3\\n4 3\\n4 2\\n1 2\\n\", \"6\\n1 2\\n2 4\\n3 6\\n4 5\\n5 6\\n4 6\\n\", \"5\\n1 2\\n1 5\\n5 2\\n2 3\\n5 4\\n\", \"8\\n1 2\\n2 3\\n5 1\\n3 5\\n4 5\\n5 6\\n6 7\\n6 8\\n\", \"8\\n1 2\\n2 5\\n3 1\\n3 4\\n4 5\\n5 6\\n3 7\\n6 8\\n\", \"6\\n1 2\\n3 4\\n6 1\\n2 3\\n1 3\\n2 5\\n\", \"5\\n4 1\\n2 3\\n1 5\\n2 4\\n5 2\\n\", \"5\\n1 2\\n1 5\\n5 2\\n1 3\\n5 4\\n\", \"6\\n1 2\\n2 3\\n1 4\\n1 5\\n1 6\\n3 6\\n\", \"5\\n4 1\\n4 3\\n1 5\\n2 4\\n5 2\\n\", \"4\\n4 3\\n2 4\\n3 1\\n2 3\\n\", \"5\\n1 2\\n1 5\\n4 1\\n2 3\\n5 2\\n\"], \"outputs\": [\"0 0 0 1 1 2 \", \"0 0 0 0 \", \"0 0 0 1 \", \"0 0 0 0 0 \", \"0 0 0 1 2 3 4 4 \", \"0 1 1 1 1 1 0 1 1 0 \", \"2 0 3 1 5 7 0 0 4 6 \", \"1 0 1 0 0 \", \"0 0 0 \", \"0 0 0 0 \", \"3 2 1 0 0 0 \", \"0 0 0 1 0 \", \"0 0 0 0\\n\", \"2 0 0 1 0\\n\", \"0 0 0 0 0 1 2 2\\n\", \"2 1 1 0 0 0\\n\", \"0 0 1 1 0\\n\", \"0 0 0 1 0 2\\n\", \"0 0 0 1 1 2\\n\", \"0 1 0 0\\n\", \"0 1 0 0 0 1 2 2\\n\", \"2 1 0 0 0 0\\n\", \"0 0 0 1 0 1\\n\", \"1 2 3 0 0 0\\n\", \"0 0 1 0 0 1 2 2\\n\", \"0 0 1 0 0\\n\", \"0 0 1 2 0 3\\n\", \"0 0 2 0 1\\n\", \"0 0 0 4 3 2 1 3\\n\", \"2 0 3 1 3 5 0 0 2 4\\n\", \"0 0 0 0 0 1 1 2\\n\", \"0 0 0 1 1 1\\n\", \"0 1 2 0 0 0\\n\", \"0 2 0 0 2 4 0 1 1 3\\n\", \"0 0 0 1 0 1 2 2\\n\", \"0 0 0 1 1 0\\n\", \"1 0 0 0\\n\", \"0 0 0 0 1\\n\", \"0 0 1 1 0 1\\n\", \"0 0 0 0 0 0 0 1\\n\", \"2 0 3 1 1 3 0 0 2 2\\n\", \"0 1 2 0 1 0\\n\", \"1 2 2 0 0 2 0 1 0 1\\n\", \"0 0 0 1 0 0 0 1\\n\", \"1 0 0 2 2 0\\n\", \"0 0 0 0 0 1 0 1 0 0\\n\", \"0 0 0 1 0 0 1 0\\n\", \"1 1 0 0 0 0\\n\", \"0 0 1 0 0 1 3 2\\n\", \"0 0 0 0 0 1 2 1\\n\", \"0 0 0 1 2 1\\n\", \"0 0 0 1 1 2\\n\", \"0 0 0 1 0 1\\n\", \"0 0 0 0 0 1 2 2\\n\", \"0 1 0 0\\n\", \"0 0 0 1 1 2\\n\", \"0 2 0 0 2 4 0 1 1 3\\n\", \"1 0 0 0\\n\", \"2 1 1 0 0 0\\n\", \"0 0 1 1 0\\n\", \"0 0 0 1 0 1 2 2\\n\", \"0 0 0 0 0 1 1 2\\n\", \"0 0 0 1 1 1\\n\", \"0 0 1 0 0\\n\", \"0 0 1 1 0\\n\", \"0 0 0 1 1 0\\n\", \"0 0 1 0 0\\n\", \"1 0 0 0\\n\", \"0 0 1 1 0\\n\"]}", "source": "primeintellect"}
|
A subway scheme, classic for all Berland cities is represented by a set of n stations connected by n passages, each of which connects exactly two stations and does not pass through any others. Besides, in the classic scheme one can get from any station to any other one along the passages. The passages can be used to move in both directions. Between each pair of stations there is no more than one passage.
Berland mathematicians have recently proved a theorem that states that any classic scheme has a ringroad. There can be only one ringroad. In other words, in any classic scheme one can find the only scheme consisting of stations (where any two neighbouring ones are linked by a passage) and this cycle doesn't contain any station more than once.
This invention had a powerful social impact as now the stations could be compared according to their distance from the ringroad. For example, a citizen could say "I live in three passages from the ringroad" and another one could reply "you loser, I live in one passage from the ringroad". The Internet soon got filled with applications that promised to count the distance from the station to the ringroad (send a text message to a short number...).
The Berland government decided to put an end to these disturbances and start to control the situation. You are requested to write a program that can determine the remoteness from the ringroad for each station by the city subway scheme.
Input
The first line contains an integer n (3 ≤ n ≤ 3000), n is the number of stations (and trains at the same time) in the subway scheme. Then n lines contain descriptions of the trains, one per line. Each line contains a pair of integers xi, yi (1 ≤ xi, yi ≤ n) and represents the presence of a passage from station xi to station yi. The stations are numbered from 1 to n in an arbitrary order. It is guaranteed that xi ≠ yi and that no pair of stations contain more than one passage. The passages can be used to travel both ways. It is guaranteed that the given description represents a classic subway scheme.
Output
Print n numbers. Separate the numbers by spaces, the i-th one should be equal to the distance of the i-th station from the ringroad. For the ringroad stations print number 0.
Examples
Input
4
1 3
4 3
4 2
1 2
Output
0 0 0 0
Input
6
1 2
3 4
6 4
2 3
1 3
3 5
Output
0 0 0 1 1 2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n2\\n1\\n\", \"1\\n1000000000\\n\", \"1\\n0000000000\\n\", \"2\\n2\\n2\\n\", \"1\\n0010000000\\n\", \"2\\n2\\n4\\n\", \"1\\n0001000000\\n\", \"2\\n4\\n4\\n\", \"1\\n0001000001\\n\", \"2\\n4\\n1\\n\", \"1\\n0001000011\\n\", \"2\\n3\\n1\\n\", \"1\\n0001001011\\n\", \"2\\n3\\n2\\n\", \"1\\n0001011011\\n\", \"2\\n3\\n0\\n\", \"1\\n0001011111\\n\", \"2\\n4\\n0\\n\", \"1\\n0001111111\\n\", \"1\\n0001011101\\n\", \"1\\n0001011001\\n\", \"1\\n0011011001\\n\", \"1\\n0111011001\\n\", \"1\\n1111011001\\n\", \"1\\n1011011001\\n\", \"1\\n1011001001\\n\", \"1\\n1011001101\\n\", \"1\\n1011000101\\n\", \"1\\n1011000001\\n\", \"1\\n1001000001\\n\", \"1\\n1001000011\\n\", \"1\\n1001100011\\n\", \"1\\n1001110011\\n\", \"1\\n1001110010\\n\", \"1\\n1001010010\\n\", \"1\\n1001010000\\n\", \"1\\n1000010000\\n\", \"1\\n1100010000\\n\", \"1\\n1100011000\\n\", \"1\\n1100010001\\n\", \"1\\n1000010001\\n\", \"1\\n1001010001\\n\", \"1\\n1000000001\\n\", \"1\\n1001010101\\n\", \"1\\n1011010101\\n\", \"1\\n1011010001\\n\", \"1\\n1011011000\\n\", \"1\\n1011011010\\n\", \"1\\n1011001010\\n\", \"1\\n1011001011\\n\", \"1\\n1010001011\\n\", \"1\\n1010001001\\n\", \"1\\n1010011000\\n\", \"1\\n1010011100\\n\", \"1\\n1010001100\\n\", \"1\\n0010001100\\n\", \"1\\n0010101100\\n\", \"1\\n0010100100\\n\", \"1\\n0010100101\\n\", \"1\\n0010100001\\n\", \"1\\n1010100001\\n\", \"1\\n1110100001\\n\", \"1\\n1110100000\\n\", \"1\\n1110100010\\n\", \"1\\n1110100011\\n\", \"1\\n0110100011\\n\", \"1\\n0110110011\\n\", \"1\\n0110111011\\n\", \"1\\n0010111011\\n\", \"1\\n1010111011\\n\", \"1\\n1010111001\\n\", \"1\\n1110111001\\n\", \"1\\n1110011001\\n\", \"1\\n1110011011\\n\", \"1\\n1100011011\\n\", \"1\\n1000011011\\n\", \"1\\n1000010011\\n\", \"1\\n1010011011\\n\", \"1\\n1010011001\\n\", \"1\\n1011011101\\n\", \"1\\n1111011101\\n\", \"1\\n1111011111\\n\", \"1\\n1111011011\\n\", \"1\\n1111010011\\n\", \"1\\n1101010011\\n\", \"1\\n1001010011\\n\", \"1\\n1011010011\\n\", \"1\\n1011010010\\n\", \"1\\n1011010000\\n\", \"1\\n1011110000\\n\", \"1\\n1011110100\\n\", \"1\\n1011010100\\n\", \"1\\n0011010100\\n\", \"1\\n0010010100\\n\", \"1\\n0000010100\\n\", \"1\\n0000011100\\n\", \"1\\n0000011101\\n\", \"1\\n0001011110\\n\", \"1\\n0000011110\\n\", \"1\\n0000011010\\n\", \"1\\n0010011010\\n\", \"1\\n0010011000\\n\"], \"outputs\": [\"2\\n1\\n\", \"1000000000\\n\", \"0\\n\", \"2\\n2\\n\", \"10000000\\n\", \"2\\n4\\n\", \"1000000\\n\", \"4\\n4\\n\", \"1000001\\n\", \"4\\n1\\n\", \"1000011\\n\", \"3\\n1\\n\", \"1001011\\n\", \"3\\n2\\n\", \"1011011\\n\", \"3\\n0\\n\", \"1011111\\n\", \"4\\n0\\n\", \"1111111\\n\", \"1011101\\n\", \"1011001\\n\", \"11011001\\n\", \"111011001\\n\", \"1111011001\\n\", \"1011011001\\n\", \"1011001001\\n\", \"1011001101\\n\", \"1011000101\\n\", \"1011000001\\n\", \"1001000001\\n\", \"1001000011\\n\", \"1001100011\\n\", \"1001110011\\n\", \"1001110010\\n\", \"1001010010\\n\", \"1001010000\\n\", \"1000010000\\n\", \"1100010000\\n\", \"1100011000\\n\", \"1100010001\\n\", \"1000010001\\n\", \"1001010001\\n\", \"1000000001\\n\", \"1001010101\\n\", \"1011010101\\n\", \"1011010001\\n\", \"1011011000\\n\", \"1011011010\\n\", \"1011001010\\n\", \"1011001011\\n\", \"1010001011\\n\", \"1010001001\\n\", \"1010011000\\n\", \"1010011100\\n\", \"1010001100\\n\", \"10001100\\n\", \"10101100\\n\", \"10100100\\n\", \"10100101\\n\", \"10100001\\n\", \"1010100001\\n\", \"1110100001\\n\", \"1110100000\\n\", \"1110100010\\n\", \"1110100011\\n\", \"110100011\\n\", \"110110011\\n\", \"110111011\\n\", \"10111011\\n\", \"1010111011\\n\", \"1010111001\\n\", \"1110111001\\n\", \"1110011001\\n\", \"1110011011\\n\", \"1100011011\\n\", \"1000011011\\n\", \"1000010011\\n\", \"1010011011\\n\", \"1010011001\\n\", \"1011011101\\n\", \"1111011101\\n\", \"1111011111\\n\", \"1111011011\\n\", \"1111010011\\n\", \"1101010011\\n\", \"1001010011\\n\", \"1011010011\\n\", \"1011010010\\n\", \"1011010000\\n\", \"1011110000\\n\", \"1011110100\\n\", \"1011010100\\n\", \"11010100\\n\", \"10010100\\n\", \"10100\\n\", \"11100\\n\", \"11101\\n\", \"1011110\\n\", \"11110\\n\", \"11010\\n\", \"10011010\\n\", \"10011000\\n\"]}", "source": "primeintellect"}
|
You have integer n. Calculate how many ways are there to fully cover belt-like area of 4n-2 triangles with diamond shapes.
Diamond shape consists of two triangles. You can move, rotate or flip the shape, but you cannot scale it.
2 coverings are different if some 2 triangles are covered by the same diamond shape in one of them and by different diamond shapes in the other one.
Please look at pictures below for better understanding.
<image> On the left you can see the diamond shape you will use, and on the right you can see the area you want to fill.
<image> These are the figures of the area you want to fill for n = 1, 2, 3, 4.
You have to answer t independent test cases.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^{4}) — the number of test cases.
Each of the next t lines contains a single integer n (1 ≤ n ≤ 10^{9}).
Output
For each test case, print the number of ways to fully cover belt-like area of 4n-2 triangles using diamond shape. It can be shown that under given constraints this number of ways doesn't exceed 10^{18}.
Example
Input
2
2
1
Output
2
1
Note
In the first test case, there are the following 2 ways to fill the area:
<image>
In the second test case, there is a unique way to fill the area:
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n4\\n0010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0011\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0110\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1111\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0101\\n1111\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0101\\n1111\\n1101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n1000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0110\\n4\\n0100\\n1110\\n0111\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0110\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0111\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0001\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0111\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0100\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0111\\n0010\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0111\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0000\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0110\\n0001\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0001\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1011\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0101\\n0011\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1011\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0000\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n1100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0001\\n0011\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n1101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n0010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0011\\n4\\n0100\\n0110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0100\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0111\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0101\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0001\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0001\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0000\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0111\\n0111\\n4\\n1100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0101\\n1110\\n1101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n0010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0110\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0001\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0011\\n4\\n0100\\n0110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0111\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1001\\n0001\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0000\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0111\\n0111\\n4\\n1100\\n1110\\n0001\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0101\\n1110\\n1101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0110\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0001\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1111\\n0101\\n0011\\n4\\n0100\\n0110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0111\\n0111\\n4\\n0100\\n1010\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n1000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1001\\n0001\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0000\\n0010\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0111\\n0111\\n4\\n1100\\n1110\\n0001\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0110\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0111\\n0111\\n4\\n0100\\n1010\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n1000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1001\\n0001\\n0111\\n4\\n0100\\n0110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0110\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0111\\n0111\\n4\\n0100\\n1010\\n0101\\n0100\\n\", \"5\\n4\\n0110\\n0011\\n0001\\n1000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1001\\n0001\\n0111\\n4\\n0100\\n0110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0110\\n4\\n0000\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0111\\n0111\\n4\\n0100\\n1010\\n0001\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0110\\n4\\n0000\\n1110\\n0001\\n0100\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0100\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0111\\n0111\\n4\\n0100\\n1010\\n0001\\n0100\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0100\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0111\\n0111\\n4\\n0101\\n1010\\n0001\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n0010\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0001\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0111\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1100\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n1101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0001\\n1111\\n0101\\n0011\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0110\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0100\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n1111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0111\\n0010\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1101\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0110\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0110\\n0000\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0111\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0001\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1011\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n1111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1011\\n0101\\n0111\\n4\\n1100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0000\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1001\\n0101\\n0111\\n4\\n1100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0110\\n1111\\n0001\\n0011\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0100\\n1111\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n0010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0111\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0011\\n4\\n0100\\n0100\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n0100\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0100\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0111\\n0011\\n4\\n0100\\n1110\\n0101\\n0100\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1101\\n0101\\n0111\\n4\\n0101\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0001\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0100\\n1110\\n1101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0011\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0001\\n0111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0001\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0001\\n4\\n0100\\n0110\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0101\\n0111\\n4\\n0101\\n1111\\n0101\\n0110\\n\", \"5\\n4\\n1010\\n0011\\n0000\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0111\\n0111\\n4\\n0100\\n1011\\n0101\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n0001\\n1000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0111\\n1001\\n0001\\n1111\\n4\\n0100\\n1110\\n0101\\n0110\\n\", \"5\\n4\\n0001\\n0010\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1001\\n0111\\n0111\\n4\\n1100\\n1110\\n0001\\n0110\\n\", \"5\\n4\\n0010\\n0011\\n1001\\n0000\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1111\\n0101\\n0111\\n4\\n0101\\n1111\\n0101\\n0111\\n\", \"5\\n4\\n0010\\n0011\\n0000\\n1010\\n2\\n10\\n01\\n2\\n00\\n00\\n4\\n0101\\n1110\\n0101\\n0110\\n4\\n0100\\n1110\\n1101\\n0100\\n\"], \"outputs\": [\"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nYES\\n\", \"NO\\nNO\\nYES\\nNO\\nYES\\n\", \"NO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nYES\\n\", \"NO\\nNO\\nYES\\nYES\\nNO\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nYES\\nNO\\nNO\\n\"]}", "source": "primeintellect"}
|
Polygon is not only the best platform for developing problems but also a square matrix with side n, initially filled with the character 0.
On the polygon, military training was held. The soldiers placed a cannon above each cell in the first row and a cannon to the left of each cell in the first column. Thus, exactly 2n cannons were placed.
<image> Initial polygon for n=4.
Cannons shoot character 1. At any moment of time, no more than one cannon is shooting. When a 1 flies out of a cannon, it flies forward (in the direction of the shot) until it collides with a polygon border or another 1. After that, it takes the cell in which it was before the collision and remains there. Take a look at the examples for better understanding.
More formally:
* if a cannon stands in the row i, to the left of the first column, and shoots with a 1, then the 1 starts its flight from the cell (i, 1) and ends in some cell (i, j);
* if a cannon stands in the column j, above the first row, and shoots with a 1, then the 1 starts its flight from the cell (1, j) and ends in some cell (i, j).
For example, consider the following sequence of shots:
<image>
1. Shoot the cannon in the row 2. 2. Shoot the cannon in the row 2. 3. Shoot the cannon in column 3.
You have a report from the military training on your desk. This report is a square matrix with side length n consisting of 0 and 1. You wonder if the training actually happened. In other words, is there a sequence of shots such that, after the training, you get the given matrix?
Each cannon can make an arbitrary number of shots. Before the training, each cell of the polygon contains 0.
Input
The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.
Each test case starts with a line containing an integer n (1 ≤ n ≤ 50) — the size of the polygon.
This is followed by n lines of length n, consisting of 0 and 1 — the polygon matrix after the training.
The total area of the matrices in all test cases in one test does not exceed 10^5.
Output
For each test case print:
* YES if there is a sequence of shots leading to a given matrix;
* NO if such a sequence does not exist.
The letters in the words YES and NO can be printed in any case.
Example
Input
5
4
0010
0011
0000
0000
2
10
01
2
00
00
4
0101
1111
0101
0111
4
0100
1110
0101
0111
Output
YES
NO
YES
YES
NO
Note
The first test case was explained in the statement.
The answer to the second test case is NO, since a 1 in a cell (1, 1) flying out of any cannon would continue its flight further.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 3\\n14\\n2 4\\n2 1\\n1 0\\n\", \"3 1\\n139\\n2 1\\n\", \"2 3\\n14\\n2 4\\n2 1\\n1 1\\n\", \"2 3\\n11\\n2 4\\n2 1\\n1 0\\n\", \"2 3\\n11\\n1 4\\n2 1\\n1 0\\n\", \"2 3\\n14\\n2 4\\n2 1\\n2 0\\n\", \"2 3\\n11\\n1 4\\n2 2\\n1 0\\n\", \"2 3\\n11\\n1 5\\n2 2\\n1 0\\n\", \"3 1\\n139\\n3 1\\n\", \"2 3\\n11\\n1 5\\n2 4\\n1 0\\n\", \"2 3\\n11\\n1 4\\n2 4\\n1 0\\n\", \"2 3\\n11\\n1 4\\n2 1\\n2 0\\n\", \"2 2\\n14\\n2 4\\n2 1\\n2 0\\n\", \"2 3\\n11\\n2 4\\n2 2\\n1 0\\n\", \"3 1\\n139\\n3 2\\n\", \"2 2\\n21\\n2 4\\n2 1\\n2 0\\n\", \"2 3\\n11\\n2 8\\n2 2\\n1 0\\n\", \"2 2\\n21\\n2 6\\n2 1\\n2 0\\n\", \"2 3\\n11\\n2 8\\n2 2\\n2 0\\n\", \"2 2\\n34\\n2 6\\n2 1\\n2 0\\n\", \"2 3\\n11\\n2 8\\n2 2\\n2 1\\n\", \"2 3\\n11\\n2 8\\n1 2\\n2 1\\n\", \"2 2\\n11\\n2 8\\n1 2\\n2 1\\n\", \"3 1\\n219\\n2 1\\n\", \"2 2\\n11\\n1 5\\n2 2\\n1 0\\n\", \"3 1\\n139\\n1 1\\n\", \"2 3\\n11\\n2 4\\n1 4\\n1 0\\n\", \"2 1\\n21\\n2 6\\n2 1\\n2 0\\n\", \"2 2\\n34\\n2 6\\n2 2\\n2 0\\n\", \"2 3\\n11\\n2 8\\n2 2\\n2 2\\n\", \"2 2\\n34\\n2 0\\n2 1\\n4 0\\n\", \"2 2\\n11\\n2 8\\n1 3\\n2 1\\n\", \"3 1\\n219\\n2 2\\n\", \"2 2\\n11\\n1 5\\n2 4\\n1 0\\n\", \"2 3\\n17\\n2 4\\n2 1\\n1 0\\n\", \"2 3\\n11\\n1 4\\n1 4\\n1 0\\n\", \"2 2\\n34\\n2 6\\n2 1\\n4 0\\n\", \"2 3\\n15\\n2 4\\n2 1\\n1 0\\n\", \"2 3\\n18\\n2 4\\n2 1\\n1 0\\n\", \"2 2\\n14\\n2 4\\n2 1\\n2 -1\\n\", \"2 3\\n19\\n2 8\\n1 2\\n2 1\\n\", \"3 1\\n156\\n2 1\\n\"], \"outputs\": [\"15\\n12\\n2\\n\", \"120\\n\", \"15\\n12\\n12\\n\", \"15\\n12\\n2\\n\", \"10\\n10\\n2\\n\", \"15\\n12\\n11\\n\", \"10\\n15\\n3\\n\", \"12\\n18\\n3\\n\", \"28\\n\", \"12\\n30\\n5\\n\", \"10\\n25\\n5\\n\", \"10\\n10\\n5\\n\", \"15\\n12\\n\", \"15\\n13\\n3\\n\", \"42\\n\", \"15\\n6\\n\", \"19\\n13\\n3\\n\", \"21\\n6\\n\", \"19\\n13\\n11\\n\", \"28\\n8\\n\", \"19\\n13\\n12\\n\", \"19\\n27\\n6\\n\", \"19\\n27\\n\", \"60\\n\", \"12\\n18\\n\", \"140\\n\", \"15\\n25\\n5\\n\", \"21\\n\", \"28\\n12\\n\", \"19\\n13\\n13\\n\", \"4\\n8\\n\", \"19\\n36\\n\", \"90\\n\", \"12\\n30\\n\", \"15\\n12\\n2\\n\", \"10\\n10\\n2\\n\", \"28\\n8\\n\", \"15\\n12\\n2\\n\", \"15\\n12\\n2\\n\", \"15\\n12\\n\", \"19\\n27\\n6\\n\", \"90\\n\"]}", "source": "primeintellect"}
|
Let a and b be some non-negative integers. Let's define strange addition of a and b as following:
1. write down the numbers one under another and align them by their least significant digit;
2. add them up digit by digit and concatenate the respective sums together.
Assume that both numbers have an infinite number of leading zeros.
For example, let's take a look at a strange addition of numbers 3248 and 908:
<image>
You are given a string c, consisting of n digits from 0 to 9. You are also given m updates of form:
* x~d — replace the digit at the x-th position of c with a digit d.
Note that string c might have leading zeros at any point of time.
After each update print the number of pairs (a, b) such that both a and b are non-negative integers and the result of a strange addition of a and b is equal to c.
Note that the numbers of pairs can be quite large, so print them modulo 998244353.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 5 ⋅ 10^5) — the length of the number c and the number of updates.
The second line contains a string c, consisting of exactly n digits from 0 to 9.
Each of the next m lines contains two integers x and d (1 ≤ x ≤ n, 0 ≤ d ≤ 9) — the descriptions of updates.
Output
Print m integers — the i-th value should be equal to the number of pairs (a, b) such that both a and b are non-negative integers and the result of a strange addition of a and b is equal to c after i updates are applied.
Note that the numbers of pairs can be quite large, so print them modulo 998244353.
Example
Input
2 3
14
2 4
2 1
1 0
Output
15
12
2
Note
After the first update c is equal to 14. The pairs that sum up to 14 are: (0, 14), (1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7), (8, 6), (9, 5), (10, 4), (11, 3), (12, 2), (13, 1), (14, 0).
After the second update c is equal to 11.
After the third update c is equal to 01.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n1 2 2 1\\n4 8 9 2\\n\", \"1\\n0 0 0 0\\n\", \"1\\n0 0 1 0\\n\", \"2\\n1 2 2 1\\n4 8 9 4\\n\", \"2\\n1 2 2 1\\n4 8 12 4\\n\", \"1\\n0 0 2 0\\n\", \"1\\n0 0 1 -1\\n\", \"2\\n1 2 3 1\\n4 8 12 4\\n\", \"1\\n4 0 0 0\\n\", \"1\\n1 -1 3 0\\n\", \"1\\n7 0 0 -2\\n\", \"1\\n7 -1 1 -2\\n\", \"1\\n0 -4 7 -2\\n\", \"1\\n10 -1 1 -2\\n\", \"1\\n19 -1 1 -2\\n\", \"1\\n0 -1 1 -8\\n\", \"1\\n25 -1 1 -2\\n\", \"1\\n-1 -1 1 -8\\n\", \"1\\n16 -1 1 -2\\n\", \"1\\n24 -1 2 -2\\n\", \"1\\n-2 -1 1 -7\\n\", \"1\\n24 -2 1 -2\\n\", \"1\\n0 -1 9 -1\\n\", \"1\\n11 -1 0 -2\\n\", \"1\\n1 0 15 -1\\n\", \"1\\n1 0 28 -1\\n\", \"1\\n1 0 28 0\\n\", \"1\\n1 0 11 0\\n\", \"1\\n1 0 11 1\\n\", \"1\\n1 0 0 0\\n\", \"1\\n2 0 0 0\\n\", \"1\\n0 -1 2 0\\n\", \"2\\n1 0 2 1\\n4 8 9 4\\n\", \"1\\n1 -1 0 0\\n\", \"1\\n1 -1 2 0\\n\", \"1\\n0 -2 2 0\\n\", \"1\\n0 0 1 -2\\n\", \"1\\n1 -1 0 -1\\n\", \"1\\n4 0 0 -1\\n\", \"1\\n0 -2 2 -1\\n\", \"1\\n0 0 1 -3\\n\", \"1\\n2 -1 0 0\\n\", \"1\\n1 -1 1 0\\n\", \"1\\n4 0 0 -2\\n\", \"1\\n0 -4 2 -1\\n\", \"1\\n0 0 1 -4\\n\", \"1\\n2 -1 -1 0\\n\", \"1\\n0 -1 1 0\\n\", \"1\\n0 -4 2 -2\\n\", \"1\\n1 0 1 -4\\n\", \"1\\n2 -1 -1 1\\n\", \"1\\n0 -1 0 0\\n\", \"1\\n7 0 1 -2\\n\", \"1\\n0 -4 4 -2\\n\", \"1\\n1 0 1 -5\\n\", \"1\\n2 -2 -1 0\\n\", \"1\\n1 0 1 -1\\n\", \"1\\n1 0 1 -8\\n\", \"1\\n2 -1 0 -1\\n\", \"1\\n1 0 2 -1\\n\", \"1\\n0 -3 7 -2\\n\", \"1\\n1 -1 1 -8\\n\", \"1\\n4 -1 0 -1\\n\", \"1\\n1 0 1 0\\n\", \"1\\n0 -3 2 -2\\n\", \"1\\n4 -1 -1 -1\\n\", \"1\\n1 0 2 0\\n\", \"1\\n0 -3 2 -1\\n\", \"1\\n1 -1 6 0\\n\", \"1\\n0 -3 2 0\\n\", \"1\\n-1 -1 1 -15\\n\", \"1\\n1 0 6 0\\n\", \"1\\n16 -1 2 -2\\n\", \"1\\n0 0 2 -1\\n\", \"1\\n-1 -1 1 -7\\n\", \"1\\n2 0 1 0\\n\", \"1\\n0 -1 2 -1\\n\", \"1\\n24 -1 1 -2\\n\", \"1\\n0 -1 3 -1\\n\", \"1\\n-2 -1 1 -6\\n\", \"1\\n0 -1 6 -1\\n\", \"1\\n-2 -1 2 -6\\n\", \"1\\n24 -2 0 -2\\n\", \"1\\n0 -1 8 -1\\n\", \"1\\n0 -1 2 -6\\n\", \"1\\n11 -2 0 -2\\n\", \"1\\n0 0 2 -6\\n\", \"1\\n11 -3 0 -2\\n\", \"1\\n0 0 9 -1\\n\", \"1\\n0 0 0 -1\\n\", \"1\\n1 0 9 -1\\n\", \"1\\n11 -1 0 -1\\n\", \"1\\n1 -1 0 -2\\n\", \"1\\n1 0 15 0\\n\", \"1\\n1 -2 0 -2\\n\", \"1\\n2 -2 0 -2\\n\", \"1\\n2 -2 0 -3\\n\", \"1\\n2 -2 0 -6\\n\", \"1\\n2 -2 -1 -6\\n\", \"1\\n1 0 22 1\\n\", \"1\\n2 -4 -1 -6\\n\", \"1\\n1 1 22 1\\n\"], \"outputs\": [\"3\\n12\\n\", \"0\\n\", \"1\\n\", \"3\\n13\\n\", \"3\\n16\\n\", \"2\\n\", \"0\\n\", \"4\\n16\\n\", \"4\\n\", \"3\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"9\\n\", \"18\\n\", \"-1\\n\", \"24\\n\", \"-2\\n\", \"15\\n\", \"23\\n\", \"-3\\n\", \"22\\n\", \"8\\n\", \"10\\n\", \"14\\n\", \"27\\n\", \"28\\n\", \"11\\n\", \"12\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n13\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"5\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"6\\n\", \"2\\n\", \"-2\\n\", \"6\\n\", \"15\\n\", \"1\\n\", \"-2\\n\", \"2\\n\", \"1\\n\", \"23\\n\", \"2\\n\", \"-3\\n\", \"5\\n\", \"-3\\n\", \"22\\n\", \"7\\n\", \"-1\\n\", \"9\\n\", \"0\\n\", \"8\\n\", \"8\\n\", \"0\\n\", \"8\\n\", \"10\\n\", \"0\\n\", \"15\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"23\\n\", \"-2\\n\", \"23\\n\"]}", "source": "primeintellect"}
|
There is a famous olympiad, which has more than a hundred participants. The Olympiad consists of two stages: the elimination stage, and the final stage. At least a hundred participants will advance to the final stage. The elimination stage in turn consists of two contests.
A result of the elimination stage is the total score in two contests, but, unfortunately, the jury lost the final standings and has only standings for the first and for the second contest separately.
In each contest, the participants are ranked by their point score in non-increasing order. When two participants have a tie (earned the same score), they are ranked by their passport number (in accordance with local regulations, all passport numbers are distinct).
In the first contest, the participant on the 100-th place scored a points. Also, the jury checked all participants from the 1-st to the 100-th place (inclusive) in the first contest and found out that all of them have at least b points in the second contest.
Similarly, for the second contest, the participant on the 100-th place has c points. And the jury checked that all the participants from the 1-st to the 100-th place (inclusive) have at least d points in the first contest.
After two contests, all participants are ranked by their total score in two contests in non-increasing order. When participants have the same total score, tie-breaking with passport numbers is used. The cutoff score to qualify to the final stage is the total score of the participant on the 100-th place.
Given integers a, b, c, d, please help the jury determine the smallest possible value of the cutoff score.
Input
You need to process t test cases.
The first line contains an integer t (1 ≤ t ≤ 3025) — the number of test cases. Then descriptions of t test cases follow.
The first line of each test case contains four integers a, b, c, d (0 ≤ a,\,b,\,c,\,d ≤ 9; d ≤ a; b ≤ c).
One can show that for any test case satisfying the constraints above, there is at least one olympiad scenario possible.
Output
For each test case print a single integer — the smallest possible cutoff score in some olympiad scenario satisfying the given information.
Example
Input
2
1 2 2 1
4 8 9 2
Output
3
12
Note
For the first test case, consider the following olympiad scenario: there are 101 participants in the elimination stage, each having 1 point for the first contest and 2 points for the second contest. Hence the total score of the participant on the 100-th place is 3.
For the second test case, consider the following olympiad scenario:
* there are 50 participants with points 5 and 9 for the first and second contest respectively;
* 50 participants with points 4 and 8 for the first and second contest respectively;
* and 50 participants with points 2 and 9 for the first and second contest respectively.
Hence the total point score of the participant on the 100-th place is 12.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"4\\n1 1 0\\n2 7 3\\n6 1 4\\n5 4 0\\n\", \"1\\n2 1 1\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n1 1 1\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n\", \"1\\n150 150 150\\n\", \"1\\n2 1 0\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n1 1 2\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1001000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1001000000\\n\", \"4\\n1 1 0\\n3 7 3\\n6 1 4\\n5 4 0\\n\", \"4\\n1 1 0\\n3 7 3\\n6 1 6\\n5 4 0\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"4\\n1 1 0\\n3 7 3\\n6 1 6\\n5 4 1\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"4\\n1 1 0\\n3 12 3\\n9 1 6\\n5 4 1\\n\", \"5\\n1000001001 1 1000000000\\n1000000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000100000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000100000 1 1000000000\\n\", \"10\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001010000\\n1000000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000001001 1 1000000000\\n1000000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 0000000000\\n\", \"4\\n1 1 0\\n1 12 3\\n14 1 6\\n5 4 1\\n\", \"10\\n1 1001000000 1000000000\\n1 1000000000 1000000000\\n1 1001000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000001 1 1000000000\\n1000000000 1 1001010000\\n0001000000 1 1000000000\\n1010000000 1 1000000000\\n1000001000 1 1000000000\\n\", \"10\\n1 1000100000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000011000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"5\\n1000001001 2 1000000000\\n1100000100 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000001000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1100000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000100000 1 1000000000\\n1000000000 1 1000000000\\n1000100000 1 1000000000\\n\", \"10\\n1 1000100000 1000000000\\n1 1010000000 1000000000\\n1 1000000000 1000011000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1100000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000100000 1 1000000000\\n1000000000 1 1000000000\\n1000100000 1 1000000000\\n\", \"10\\n1000000101 1 1000000000\\n1000000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000010\\n\", \"10\\n1000000000 1 1000000000\\n1000000101 1 1000000000\\n1000000000 1 1000000000\\n1000000000 4 1000000000\\n1000001100 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"10\\n1000000000 1 1000000000\\n1000001000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1010000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000100000 1000000000\\n1 1010000000 1000000000\\n1 1000000000 1000011000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1010000000\\n1 1000100000 1000000000\\n2 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000101 1 1000000000\\n1010000000 1 1000000000\\n1000000000 4 1000000000\\n1000001100 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"10\\n1000000000 1 1000000000\\n1000000101 1 1000000000\\n1010000000 1 1000000000\\n1000000000 4 1000000000\\n1000001100 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1010000000 1 1000000100\\n\", \"5\\n1000001001 2 1000000000\\n1100000000 1 1001000000\\n1001000000 1 1000000000\\n1010000000 1 1000000001\\n1010000000 1 1000010000\\n\", \"10\\n1000000000 1 1000000000\\n1000001000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000001100 1 1000000000\\n1000000001 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1010000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000001001 2 1000000000\\n1100000000 2 1001000000\\n1001000000 1 1000000000\\n1010000000 1 1000000001\\n1010000000 1 1000010000\\n\", \"10\\n1000000000 1 1000000000\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000000\\n1100000000 1 0100000010\\n1000000000 4 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000100100\\n1000000000 2 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n0100000101 1 1000000000\\n1010000000 1 1000000000\\n1010000000 4 1000000000\\n1000001100 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1010000000 1 1000000100\\n\", \"5\\n1001000000 1 1000000000\\n1000000000 1 1001000001\\n1001000000 2 1000000011\\n1010001000 2 1000000100\\n1000000000 1 1001000000\\n\", \"10\\n1000000000 2 1000000100\\n1000000000 1 1000000100\\n1000000000 2 1000000000\\n1000000000 2 1110000100\\n1000001000 1 1000000010\\n1000001010 1 0000000000\\n1000000000 1 1000000000\\n1000010000 1 1000000101\\n1000000000 2 1000100100\\n1000000001 1 1000000000\\n\", \"5\\n1101000000 1 1100000000\\n1001000100 1 1001000001\\n1001000000 2 1000000011\\n1010001000 3 1000000100\\n1000000010 2 1001000011\\n\", \"5\\n1101000000 1 1110000000\\n1101000100 1 1001000001\\n1001000000 2 1000000011\\n1010001000 3 1010000100\\n1000000010 2 1001000011\\n\", \"1\\n150 214 150\\n\", \"1\\n2 2 0\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1001000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 3 150\\n\", \"1\\n2 2 1\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"1\\n150 3 89\\n\", \"1\\n2 2 2\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000010000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 3 33\\n\", \"4\\n1 1 0\\n3 12 3\\n6 1 6\\n5 4 1\\n\", \"1\\n4 2 2\\n\", \"5\\n1000000001 1 1000000000\\n1000000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000011000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n197 3 33\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"1\\n197 3 7\\n\", \"4\\n1 1 0\\n3 12 3\\n14 1 6\\n5 4 1\\n\", \"5\\n1000001001 2 1000000000\\n1000000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n197 4 7\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"1\\n197 4 0\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000000000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000000000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"1\\n4 1 1\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1001000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n\", \"1\\n150 83 150\\n\", \"1\\n2 1 2\\n\", \"1\\n1 1 0\\n\", \"1\\n79 214 150\\n\", \"4\\n1 1 0\\n6 7 3\\n6 1 4\\n5 4 0\\n\", \"1\\n2 3 0\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1001000000 1 1000000000\\n1000000000 1 1001000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000100\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 1 150\\n\", \"4\\n1 1 0\\n3 7 2\\n6 1 6\\n5 4 0\\n\", \"1\\n1 2 1\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 2 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1100000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 3 73\\n\", \"1\\n4 1 2\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000010100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000010010\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 2 33\\n\", \"4\\n1 1 0\\n3 12 3\\n6 1 6\\n5 4 2\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000001 1 1000000000\\n1000000000 1 1001010000\\n0001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000011000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n347 3 33\\n\", \"4\\n1 1 0\\n3 12 3\\n9 1 6\\n5 4 0\\n\", \"1\\n197 6 7\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000100\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000001001 2 1000000000\\n1000000100 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n197 4 2\\n\", \"1\\n197 6 0\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1100000000 1 0100000000\\n1000000000 1 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 4 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 4 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"1\\n6 1 1\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 2 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000100000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n150 160 150\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1100000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000100000 1 1000000000\\n\", \"1\\n79 75 150\\n\", \"1\\n3 3 0\\n\", \"5\\n1000000000 1 1000010000\\n1000000000 1 1001000000\\n1001000000 1 1000000000\\n1000000000 1 1001000000\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000100\\n1 1000000000 1000000100\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 2 150\\n\", \"10\\n1000000101 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1001000000 1 1000000010\\n1010000000 1 1000000000\\n1000000000 2 1000000000\\n\", \"1\\n150 3 19\\n\", \"1\\n5 1 2\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1100010100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000010010\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n268 2 33\\n\", \"4\\n1 1 0\\n3 10 3\\n6 1 6\\n5 4 2\\n\", \"1\\n233 3 33\\n\", \"5\\n1000001001 1 1000000000\\n1000000000 1 1001010000\\n1001000100 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 0000000000\\n\", \"1\\n197 6 12\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000100\\n1000001000 1 1000000010\\n1000000010 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1100000000 1 0100000000\\n1000000000 2 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000001 1 1000000000\\n1000000000 1 1000000000\\n1000000000 4 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"1\\n6 1 0\\n\", \"5\\n1000000000 2 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000100000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n150 160 290\\n\", \"1\\n79 136 150\\n\", \"10\\n1 1000000000 1000000100\\n1 1000000000 1000000100\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 2 223\\n\", \"10\\n1000000101 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1000000010\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1001000000 1 1000000011\\n1010000000 1 1000000000\\n1000000000 2 1000000000\\n\", \"1\\n150 2 19\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1100011100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000010010\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1001000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"4\\n1 1 1\\n3 10 3\\n6 1 6\\n5 4 2\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1000000000 1 0000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1001000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000001 1 1000000000\\n1000000000 1 1011010000\\n0001000000 1 1000000000\\n1010000000 1 1000000000\\n1000001000 1 1000000000\\n\", \"1\\n233 3 2\\n\", \"5\\n1010001001 1 1000000000\\n1000000000 1 1001010000\\n1001000100 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 0000000000\\n\", \"1\\n270 6 12\\n\", \"10\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000100\\n1000001000 1 1000000010\\n1000000010 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000001001 2 1000000000\\n1100000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1100000000 1 0100000000\\n1000000000 2 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 2 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000001 1 1000000000\\n1000000000 1 1000000000\\n1000000000 4 1000000000\\n1000001100 1 1000000010\\n1000000000 1 0100000000\\n1000000000 1 1000100000\\n1000000010 1 1000000110\\n1000010000 1 1000000110\\n1000000000 1 1000000100\\n\", \"10\\n1000000000 1 1000000000\\n1000001000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1010000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000000 2 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000100000\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n150 57 290\\n\", \"1\\n79 136 136\\n\", \"10\\n1 1000000000 1000000100\\n1 1000000000 1000000100\\n1 1000000000 1001000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n150 2 73\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000000\\n1000000000 1 1000000011\\n1010000000 1 1000000000\\n1000000000 2 1000000000\\n\", \"1\\n150 2 8\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000010\\n1000000000 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1100011100\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n\", \"10\\n1 1000000000 1000000000\\n1 1000000000 1000000010\\n1 1000000000 1000010010\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1001000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"4\\n1 1 1\\n3 10 3\\n6 1 6\\n5 4 4\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1000000000 2 0000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1001000000\\n1000000000 1 1000000000\\n\", \"5\\n1000000001 1 1000000000\\n1000000000 1 1011010000\\n0001000000 1 1000000000\\n1011000000 1 1000000000\\n1000001000 1 1000000000\\n\", \"10\\n1 1000100000 1000000000\\n1 1010000000 1000000000\\n1 1000000000 1000011000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1010000000\\n1 1000000000 1000000000\\n2 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"1\\n233 6 2\\n\", \"5\\n1010001001 1 1000000000\\n1000000000 1 1001110000\\n1001000100 1 1000000000\\n1010000000 1 1000000000\\n1000000000 1 0000000000\\n\", \"1\\n270 2 12\\n\", \"10\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000100\\n1000001000 1 1000000010\\n1000001010 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000001001 2 1000000000\\n1100000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000001\\n1000000000 1 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1100000000 1 0100000000\\n1000000000 3 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 2 1000000000\\n\", \"5\\n1000000000 2 1000000000\\n1000000000 1 1000000100\\n1000000000 2 1000100000\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n150 17 290\\n\", \"1\\n79 136 79\\n\", \"1\\n120 2 73\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000001\\n1000000000 1 1000000011\\n1010000000 1 1000000000\\n1000000000 2 1000000000\\n\", \"1\\n159 2 8\\n\", \"10\\n1 1000000000 1000000000\\n2 1000000000 1000000010\\n1 1000000000 1000010010\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n2 1001000000 1000000000\\n1 1000000000 1000000000\\n1 1000000000 1000000000\\n1 1000001001 1000000000\\n1 1000000000 1001000000\\n\", \"4\\n1 1 1\\n3 5 3\\n6 1 6\\n5 4 4\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1000000000 2 0000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1001000000\\n1000000000 1 1000100000\\n\", \"5\\n1000000001 1 1000000000\\n1000000000 1 1011010000\\n0001000000 1 1000000000\\n1011000000 1 1000000000\\n1000001000 1 1000000010\\n\", \"1\\n233 6 0\\n\", \"5\\n1010001001 1 1000000000\\n1000000000 1 1001110000\\n1001000100 1 1000000010\\n1010000000 1 1000000000\\n1000000000 1 0000000000\\n\", \"1\\n270 2 20\\n\", \"10\\n1000000000 1 1000000100\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1100000100\\n1000001000 1 1000000010\\n1000001010 1 0000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000100\\n1000010000 1 1000000100\\n1000000000 1 1000000000\\n\", \"5\\n1000001001 2 1000000000\\n1100000000 1 1001010000\\n1001000000 1 1000000000\\n1010000000 1 1000000001\\n1000000000 1 1000010000\\n\", \"10\\n1000000000 1 1000000000\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n1000000000 2 1000000000\\n1000001000 1 1000000010\\n1100000000 1 0100000000\\n1000000000 3 1000000000\\n1000000000 1 1000000110\\n1000010000 1 1000000100\\n1000000000 2 1000000000\\n\", \"10\\n1000000000 1 1000000000\\n1000001000 1 1000000000\\n1000010000 1 1000000000\\n1000000000 1 1000000000\\n1000000100 1 1000000000\\n1000000001 1 1000000000\\n1000000000 2 1000000000\\n1000000000 1 1010000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n\", \"5\\n1001000000 2 1000000000\\n1000000000 1 1000000100\\n1000000000 2 1000100000\\n1000000100 1 1000000000\\n1000000000 1 1000000000\\n\", \"1\\n150 17 307\\n\", \"1\\n79 136 83\\n\", \"1\\n120 2 124\\n\", \"5\\n1000000000 1 1000000000\\n1000000000 1 1001000001\\n1000000000 1 1000000011\\n1010000000 1 1000000000\\n1000000000 2 1001000000\\n\", \"1\\n273 2 8\\n\", \"4\\n1 1 1\\n3 5 5\\n6 1 6\\n5 4 4\\n\", \"10\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000000000 1 1000000000\\n1000001000 1 1000000010\\n1001000000 2 0000000000\\n1010000000 1 1000000000\\n1000000000 1 1000000100\\n1000000000 1 1001000000\\n1000000000 1 1000100000\\n\"], \"outputs\": [\"\\nYES\\nYES\\nNO\\nNO\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\n\", \"YES\\nYES\\nYES\\nNO\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nYES\\n\", \"NO\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nNO\\n\", \"NO\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\nYES\\nNO\\nNO\\nNO\\n\", \"YES\\nNO\\nNO\\nYES\\n\", \"NO\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nNO\\nYES\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\nNO\\nYES\\nNO\\nYES\\nNO\\n\", \"NO\\nYES\\nNO\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\nNO\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nNO\\n\", \"YES\\nNO\\nNO\\nNO\\nNO\\n\", \"YES\\nNO\\nNO\\nYES\\nNO\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nNO\\nYES\\nYES\\n\", \"NO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nNO\\n\", \"YES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nNO\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"NO\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"NO\\n\", \"NO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"NO\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nNO\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"NO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nNO\\nYES\\n\", \"YES\\nNO\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nYES\\nYES\\nNO\\nYES\\n\", \"NO\\n\", \"YES\\nYES\\nYES\\nYES\\n\", \"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nYES\\nYES\\nYES\\n\"]}", "source": "primeintellect"}
|
You have r red and b blue beans. You'd like to distribute them among several (maybe, one) packets in such a way that each packet:
* has at least one red bean (or the number of red beans r_i ≥ 1);
* has at least one blue bean (or the number of blue beans b_i ≥ 1);
* the number of red and blue beans should differ in no more than d (or |r_i - b_i| ≤ d)
Can you distribute all beans?
Input
The first line contains the single integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first and only line of each test case contains three integers r, b, and d (1 ≤ r, b ≤ 10^9; 0 ≤ d ≤ 10^9) — the number of red and blue beans and the maximum absolute difference in each packet.
Output
For each test case, if you can distribute all beans, print YES. Otherwise, print NO.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).
Example
Input
4
1 1 0
2 7 3
6 1 4
5 4 0
Output
YES
YES
NO
NO
Note
In the first test case, you can form one packet with 1 red and 1 blue bean. The absolute difference |1 - 1| = 0 ≤ d.
In the second test case, you can form two packets: 1 red and 4 blue beans in the first packet and 1 red and 3 blue beans in the second one.
In the third test case, since b = 1, you can form only one packet with 6 red and 1 blue beans. The absolute difference |6 - 1| = 5 > d.
In the fourth test case, since d = 0 so each packet should contain the same number of red and blue beans, but r ≠ b.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"3 3\\n.#.\\n...\\n.#.\\n\", \"4 3\\n##.\\n...\\n.#.\\n.#.\\n\", \"5 5\\n.....\\n.#...\\n.....\\n.....\\n#.###\\n\", \"3 4\\n..##\\n....\\n..#.\\n\", \"2 42\\n..........#.......#..........###........#.\\n.....#######.......#..#....#...##.........\\n\", \"6 8\\n...##...\\n.#.#.#.#\\n#.#.#.#.\\n.#.#.#.#\\n#.#.#.#.\\n#.......\\n\", \"4 3\\n#.#\\n.##\\n...\\n.#.\\n\", \"4 7\\n..#....\\n##.##.#\\n.##....\\n...##.#\\n\", \"4 4\\n.#..\\n..##\\n.#.#\\n..#.\\n\", \"4 3\\n#.#\\n...\\n...\\n.##\\n\", \"2 2\\n##\\n.#\\n\", \"5 5\\n#####\\n#####\\n#####\\n#####\\n#####\\n\", \"4 4\\n##..\\n..#.\\n...#\\n...#\\n\", \"4 3\\n.#.\\n...\\n##.\\n#.#\\n\", \"5 5\\n....#\\n#..#.\\n.#.#.\\n#...#\\n.#...\\n\", \"4 3\\n..#\\n#.#\\n...\\n#..\\n\", \"5 5\\n...#.\\n.....\\n.....\\n.....\\n..#.#\\n\", \"4 4\\n#...\\n.#.#\\n##..\\n...#\\n\", \"3 3\\n...\\n...\\n...\\n\", \"2 42\\n.....#.......................#......#.....\\n..#................##.#......#..#.#.......\\n\", \"4 4\\n..#.\\n#.#.\\n#..#\\n...#\\n\", \"4 4\\n...#\\n....\\n#..#\\n#...\\n\", \"10 10\\n#.........\\n...#..#...\\n..........\\n..........\\n.......#.#\\n..........\\n..........\\n......##..\\n#..#......\\n.........#\\n\", \"4 4\\n...#\\n.##.\\n.#.#\\n..#.\\n\", \"5 5\\n.####\\n#.###\\n#####\\n#.###\\n#####\\n\", \"5 6\\n.....#\\n......\\n......\\n.#...#\\n.#....\\n\", \"20 20\\n..................#.\\n.#.............#....\\n....................\\n....................\\n....#...........#...\\n....................\\n......#......#......\\n....................\\n........#...#.......\\n....................\\n.........#...#......\\n....................\\n....................\\n......#.........#...\\n....................\\n.........#.....#....\\n........#...#.......\\n....#.............#.\\n..................#.\\n.#..................\\n\", \"5 5\\n.####\\n#.#.#\\n#####\\n#####\\n#####\\n\", \"5 6\\n#..#..\\n..#..#\\n.#..#.\\n...#.#\\n..#...\\n\", \"5 5\\n.##..\\n.##..\\n.#.#.\\n..#..\\n..#..\\n\", \"5 5\\n...#.\\n.#..#\\n#.#.#\\n#....\\n#.#..\\n\", \"3 3\\n###\\n###\\n###\\n\", \"5 5\\n#....\\n.....\\n..##.\\n#.#..\\n...#.\\n\", \"5 5\\n..#.#\\n##.##\\n#...#\\n##.##\\n.....\\n\", \"5 5\\n.#.#.\\n#..#.\\n.#.##\\n.#.##\\n##.#.\\n\", \"5 5\\n....#\\n.#.#.\\n...##\\n.....\\n.#...\\n\", \"2 42\\n.########.#.########.#..#############.##..\\n#####.#############.#####.#.#.#####.####..\\n\", \"2 10\\n..........\\n..........\\n\", \"4 4\\n#...\\n.##.\\n#.#.\\n.#..\\n\", \"4 3\\n.#.\\n#.#\\n##.\\n..#\\n\", \"5 2\\n.#\\n##\\n..\\n#.\\n#.\\n\", \"3 3\\n..#\\n#.#\\n#..\\n\", \"5 5\\n.....\\n.###.\\n..##.\\n..##.\\n...#.\\n\", \"10 10\\n.........#\\n#.......#.\\n.#.....#..\\n..#...#...\\n...##.....\\n...#..#...\\n..#....#..\\n.#......#.\\n#........#\\n....#.....\\n\", \"6 6\\n...#..\\n.##...\\n......\\n.#.#..\\n......\\n..#...\\n\", \"5 5\\n.....\\n.#/..\\n.....\\n.....\\n#.###\\n\", \"6 8\\n...##...\\n.#.#.#.#\\n#.#.#.#.\\n#.#.#.#.\\n#.#.#.#.\\n#.......\\n\", \"4 7\\n..#....\\n##.##.#\\n.##....\\n#.##...\\n\", \"5 5\\n....#\\n#..#.\\n.#.#.\\n#./.#\\n.#...\\n\", \"5 5\\n#....\\n.....\\n..##.\\n#.#..\\n...#/\\n\", \"4 3\\n##.\\n...\\n...\\n.##\\n\", \"2 2\\n\\\"#\\n.#\\n\", \"5 5\\n#####\\n\\\"####\\n#####\\n#####\\n#####\\n\", \"4 4\\n$#..\\n..#.\\n...#\\n...#\\n\", \"4 4\\n#...\\n.#.#\\n.##.\\n...#\\n\", \"10 10\\n#.........\\n...#..#...\\n..........\\n..........\\n.......#.#\\n..........\\n..........\\n......##..\\n......#..#\\n.........#\\n\", \"4 4\\n...#\\n.##.\\n.#.#\\n.#..\\n\", \"5 5\\n.##\\\"#\\n#.###\\n#####\\n#.###\\n#####\\n\", \"5 5\\n.####\\n#.#.$\\n#####\\n#####\\n#####\\n\", \"5 5\\n....#\\n.#.#.\\n.#..#\\n.....\\n.#...\\n\", \"2 42\\n.########.#.########.#..#############.##..\\n#####.#\\\"###########.#####.#.#.#####.####..\\n\", \"4 3\\n.#.\\n.##\\n##.\\n..#\\n\", \"5 2\\n.#\\n##\\n.-\\n#.\\n#.\\n\", \"5 5\\n.....\\n.###.\\n..##.\\n..##.\\n.#...\\n\", \"4 3\\n##/\\n...\\n.#.\\n.#.\\n\", \"5 5\\n.....\\n.#/..\\n....-\\n.....\\n#.###\\n\", \"4 3\\n#.#\\n...\\n...\\n/##\\n\", \"5 5\\n#####\\n\\\"####\\n#####\\n#####\\n#$###\\n\", \"5 5\\n#....\\n.....\\n.##..\\n#.#..\\n...#/\\n\", \"5 5\\n....#\\n.#.#/\\n.#..#\\n.....\\n.#...\\n\", \"2 42\\n.########.#.########.#..#############.##..\\n#####.#\\\"###########.$####.#.#.#####.####..\\n\", \"5 2\\n.#\\n##\\n.-\\n#.\\n.#\\n\", \"4 3\\n#-#\\n...\\n...\\n/##\\n\", \"5 5\\n#####\\n#####\\n#####\\n#####\\n#$###\\n\", \"5 5\\n#....\\n.....\\n.##..\\n..##.\\n...#/\\n\", \"5 5\\n....#\\n.#.#/\\n.#..#\\n.....\\n.#./.\\n\", \"5 2\\n.#\\n##\\n.-\\n.#\\n.#\\n\", \"5 5\\n#####\\n#####\\n###$#\\n#####\\n#$###\\n\", \"5 2\\n.#\\n##\\n.-\\n.#\\n#.\\n\", \"5 5\\n#####\\n####$\\n###$#\\n#####\\n#$###\\n\", \"5 5\\n###\\\"#\\n####$\\n###$#\\n#####\\n#$###\\n\"], \"outputs\": [\"2\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"4\\n\", \"8\\n\", \"4\\n\", \"-1\\n\", \"6\\n\", \"-1\\n\", \"2\\n\", \"6\\n\", \"4\\n\", \"10\\n\", \"6\\n\", \"2\\n\", \"4\\n\", \"16\\n\", \"2\\n\", \"6\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"6\\n\", \"-1\\n\", \"2\\n\", \"6\\n\", \"2\\n\", \"-1\\n\", \"6\\n\", \"6\\n\", \"4\\n\", \"4\\n\", \"-1\\n\", \"18\\n\", \"6\\n\", \"-1\\n\", \"4\\n\", \"2\\n\", \"8\\n\", \"6\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"2\\n\"]}", "source": "primeintellect"}
|
"The Chamber of Secrets has been opened again" — this news has spread all around Hogwarts and some of the students have been petrified due to seeing the basilisk. Dumbledore got fired and now Harry is trying to enter the Chamber of Secrets. These aren't good news for Lord Voldemort. The problem is, he doesn't want anybody to be able to enter the chamber. The Dark Lord is going to be busy sucking life out of Ginny.
The Chamber of Secrets is an n × m rectangular grid in which some of the cells are columns. A light ray (and a basilisk's gaze) passes through the columns without changing its direction. But with some spell we can make a column magic to reflect the light ray (or the gaze) in all four directions when it receives the ray. This is shown in the figure below.
<image> The left light ray passes through a regular column, and the right ray — through the magic column.
The basilisk is located at the right side of the lower right cell of the grid and is looking to the left (in the direction of the lower left cell). According to the legend, anyone who meets a basilisk's gaze directly dies immediately. But if someone meets a basilisk's gaze through a column, this person will get petrified. We know that the door to the Chamber is located on the left side of the upper left corner of the grid and anyone who wants to enter will look in the direction of its movement (in the direction of the upper right cell) from that position.
<image> This figure illustrates the first sample test.
Given the dimensions of the chamber and the location of regular columns, Lord Voldemort has asked you to find the minimum number of columns that we need to make magic so that anyone who wants to enter the chamber would be petrified or just declare that it's impossible to secure the chamber.
Input
The first line of the input contains two integer numbers n and m (2 ≤ n, m ≤ 1000). Each of the next n lines contains m characters. Each character is either "." or "#" and represents one cell of the Chamber grid. It's "." if the corresponding cell is empty and "#" if it's a regular column.
Output
Print the minimum number of columns to make magic or -1 if it's impossible to do.
Examples
Input
3 3
.#.
...
.#.
Output
2
Input
4 3
##.
...
.#.
.#.
Output
2
Note
The figure above shows the first sample test. In the first sample we should make both columns magic. The dragon figure represents the basilisk and the binoculars represent the person who will enter the Chamber of secrets. The black star shows the place where the person will be petrified. Yellow lines represent basilisk gaze moving through columns.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\nRRRRR\\n\", \"4\\nBRBG\\n\", \"3\\nRRG\\n\", \"20\\nRRGBBRBRGRGBBGGRGRRR\\n\", \"50\\nRBGBGGRRGGRGGBGBGRRBGGBGBRRBBGBBGBBBGBBRBBRBRBRGRG\\n\", \"25\\nBBGBGRBGGBRRBGRRBGGBBRBRB\\n\", \"50\\nRBGGBGGRBGRBBBGBBGRBBBGGGRBBBGBBBGRGGBGGBRBGBGRRGG\\n\", \"50\\nGRBGGRBRGRBGGBBBBBGGGBBBBRBRGBRRBRGBBBRBBRRGBGGGRB\\n\", \"3\\nBGB\\n\", \"50\\nRBRRGBGRRRBGRRBGRRGRBBRBBRRBRGGBRBRRBGGRBGGBRBRGRB\\n\", \"5\\nRGGBG\\n\", \"45\\nGGGBBRBBRRGRBBGGBGRBRGGBRBRGBRRGBGRRBGRGRBRRG\\n\", \"2\\nBB\\n\", \"1\\nB\\n\", \"50\\nRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\\n\", \"40\\nGBRRGRBGBRRGBRGGGBRGBGBRGBBRRGRGGBBGBGBB\\n\", \"10\\nGRRBRBRBGR\\n\", \"40\\nGBBRRGBGGGRGGGRRRRBRBGGBBGGGBGBBBBBRGGGG\\n\", \"35\\nGBBGBRGBBGGRBBGBRRGGRRRRRRRBRBBRRGB\\n\", \"15\\nBRRBRGGBBRRRRGR\\n\", \"50\\nGBGRGRRBRRRRRGGBBGBRRRBBBRBBBRRGRBBRGBRBGGRGRBBGGG\\n\", \"40\\nBRGRGGRGGRBBRRRBRBBGGGRRGBGBBGRBBRGBRRGG\\n\", \"50\\nRRRRRRRRRRRRGGRRRRRRRRRBRRRRRRRRRRRRRRBBRRRRRRRRRR\\n\", \"30\\nGRGGGBGGRGBGGRGRBGBGBRRRRRRGRB\\n\", \"20\\nRRGGRBBGBBRBGRRBRRBG\\n\", \"2\\nBG\\n\", \"10\\nBRBGBGRRBR\\n\", \"10\\nGGBRBRGGRB\\n\", \"30\\nBBBBGGBRBGBBGBGBGBGGGRGRRGGBBB\\n\", \"50\\nGGGBBRGGGGGRRGGRBGGRGBBRBRRBGRGBBBGBRBGRGBBGRGGBRB\\n\", \"4\\nRBBR\\n\", \"20\\nGBGBGGRRRRGRBBGRGRGR\\n\", \"50\\nRRRRRRRRGRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\\n\", \"30\\nBGBRGBBBGRGBBRGBGRBBBRGGRRGRRB\\n\", \"20\\nRRRGRGGBBGRGRBRBBGRR\\n\", \"25\\nBBGBGRBGGBRGBGRRBRGBBRBRB\\n\", \"50\\nBRGGGBGRRBBRBBBGRBRRBGRBRBBBBGGGBBBBBGGBRGRBRGGBRG\\n\", \"3\\nBHB\\n\", \"50\\nGGGBBRGRGGBRBGRBBRGRRBBBRBBBRRRBGBBGGRRRRRBRRGRGBG\\n\", \"30\\nBRGRRRRRRBGBGBRGRGGBGRGGBGGGRG\\n\", \"20\\nRGRGRGBBRGRRRRGGBGBG\\n\", \"30\\nRGBRGBBBGRGBBRGBGRBBBRGGRBGRRB\\n\", \"4\\nGRBB\\n\", \"5\\nBRGGG\\n\", \"25\\nBBGRGRBGGBRRBGRRBGGBBBBRB\\n\", \"40\\nGGGGRBBBBBGBGGGBBGGBRBRRRRGGGRGGGBGRRBBG\\n\", \"35\\nGBBGBRGBBGGRRBGBRRGGRRRRRRRBRBBBRGB\\n\", \"50\\nGGGBBRGRGGBRBGRBBRGRRBRBRBBBRRBBGBBGGRRRRRBRRGRGBG\\n\", \"40\\nGGRRBGRBBRGBBGBGRRGGGBBRBRRRBBRGGRGGRGRB\\n\", \"50\\nRRRRRRRRRRBBRRRRRRRRRRRRRRBRRRRRRRRRGGRRRRRRRRRRRR\\n\", \"30\\nBBBGGRRGRGGGBGBGBGBBGBRBGGBBBB\\n\", \"50\\nGGGBBRGGGGGRRGGRBGGRGBBRBRRBGRGBBBGBGBGRGBBGRGRBRB\\n\", \"50\\nRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRGRRRRRRRR\\n\", \"5\\nGRGBG\\n\", \"10\\nGRQBRBRBGR\\n\", \"15\\nRGRRRRBBGGRBRRB\\n\", \"2\\nGB\\n\", \"3\\nGBB\\n\", \"10\\nFRQBRBRBGR\\n\", \"15\\nRGRRRRBRGGRBBRB\\n\", \"2\\nGC\\n\", \"30\\nBRRGBRGGRBBBRGBGRBBGRGBBBGRBGR\\n\", \"4\\nGRCB\\n\", \"3\\nBBG\\n\", \"10\\nFRQBRBRBFR\\n\", \"2\\nCG\\n\", \"4\\nGCRB\\n\", \"3\\nBGA\\n\", \"10\\nRFBRBRBQRF\\n\", \"2\\nHC\\n\", \"4\\nBRCG\\n\", \"10\\nRFCRBRBQRF\\n\", \"2\\nGD\\n\", \"4\\nBRBH\\n\", \"10\\nRFCRBSBQRF\\n\", \"2\\nHD\\n\", \"10\\nFRQBSBRCFR\\n\", \"2\\nDH\\n\", \"10\\nRFCRBSBQSF\\n\", \"2\\nDI\\n\", \"10\\nSFCRBSBQRF\\n\", \"2\\nID\\n\", \"10\\nSGCRBSBQRF\\n\", \"2\\nIC\\n\", \"10\\nRGCRBSBQSF\\n\", \"2\\nCI\\n\", \"10\\nRGCRCSBQSF\\n\", \"2\\nCJ\\n\", \"10\\nRGCRCSBQRF\\n\", \"2\\nJC\\n\", \"2\\nBJ\\n\", \"3\\nCBG\\n\", \"2\\nBA\\n\", \"1\\nC\\n\", \"10\\nGRRBBBRRGR\\n\", \"2\\nDG\\n\", \"10\\nGGRRBRGGBB\\n\", \"4\\nBRBR\\n\"], \"outputs\": [\"4\\n\", \"0\\n\", \"1\\n\", \"6\\n\", \"13\\n\", \"6\\n\", \"17\\n\", \"18\\n\", \"0\\n\", \"12\\n\", \"1\\n\", \"11\\n\", \"1\\n\", \"0\\n\", \"49\\n\", \"9\\n\", \"1\\n\", \"20\\n\", \"14\\n\", \"6\\n\", \"19\\n\", \"13\\n\", \"43\\n\", \"9\\n\", \"6\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"11\\n\", \"16\\n\", \"1\\n\", \"5\\n\", \"47\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"18\\n\", \"0\\n\", \"19\\n\", \"9\\n\", \"5\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"8\\n\", \"20\\n\", \"14\\n\", \"17\\n\", \"13\\n\", \"43\\n\", \"11\\n\", \"15\\n\", \"47\\n\", \"0\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"5\\n\", \"0\\n\", \"7\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"4\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
There are n stones on the table in a row, each of them can be red, green or blue. Count the minimum number of stones to take from the table so that any two neighboring stones had different colors. Stones in a row are considered neighboring if there are no other stones between them.
Input
The first line contains integer n (1 ≤ n ≤ 50) — the number of stones on the table.
The next line contains string s, which represents the colors of the stones. We'll consider the stones in the row numbered from 1 to n from left to right. Then the i-th character s equals "R", if the i-th stone is red, "G", if it's green and "B", if it's blue.
Output
Print a single integer — the answer to the problem.
Examples
Input
3
RRG
Output
1
Input
5
RRRRR
Output
4
Input
4
BRBG
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"4 2\\n0 0\\n0 2\\n2 2\\n2 0\\n4 4\\n\", \"6 3\\n0 0\\n1 0\\n1 1\\n2 1\\n2 2\\n0 2\\n2 2 3\\n\", \"6 3\\n0 0\\n1 0\\n1 1\\n2 1\\n2 2\\n0 2\\n3 2 3\\n\", \"4 4\\n0 0\\n0 1\\n1 1\\n1 0\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 2\\n2 2\\n2 0\\n200000 200000\\n\", \"4 4\\n1679 -198\\n9204 -198\\n9204 -5824\\n1679 -5824\\n18297 92466 187436 175992\\n\", \"6 3\\n0 0\\n2 0\\n2 2\\n1 2\\n1 1\\n0 1\\n4 2 2\\n\", \"4 4\\n-8423 7689\\n6902 7689\\n6902 2402\\n-8423 2402\\n20612 20612 91529 35617\\n\", \"6 2\\n0 0\\n1 0\\n1 1\\n2 1\\n2 2\\n0 2\\n2 2\\n\", \"4 4\\n-1 0\\n0 1\\n1 1\\n1 0\\n1 1 1 1\\n\", \"4 4\\n-8423 7689\\n6902 7689\\n6902 2402\\n-8423 2402\\n20612 20612 123030 35617\\n\", \"4 2\\n0 0\\n0 2\\n2 2\\n2 -1\\n200000 200000\\n\", \"4 4\\n1679 -198\\n9204 -198\\n10154 -5824\\n1679 -5824\\n18297 92466 187436 175992\\n\", \"4 4\\n-8423 70\\n6902 7689\\n6902 2402\\n-8423 2402\\n20612 20612 91529 35617\\n\", \"4 2\\n0 0\\n0 2\\n2 2\\n2 0\\n2 4\\n\", \"4 4\\n-1 0\\n0 1\\n1 0\\n1 0\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 2\\n2 2\\n4 -1\\n200000 200000\\n\", \"4 4\\n-7116 70\\n6902 7689\\n6902 2402\\n-8423 2402\\n20612 20612 91529 35617\\n\", \"4 5\\n-1 0\\n0 1\\n1 0\\n1 0\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 2\\n3 2\\n4 -1\\n200000 200000\\n\", \"4 5\\n-2 0\\n0 1\\n1 0\\n1 0\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 2\\n3 2\\n0 -1\\n200000 200000\\n\", \"4 5\\n-2 0\\n0 1\\n1 0\\n1 0\\n1 1 0 1\\n\", \"4 2\\n0 0\\n0 4\\n3 2\\n0 -1\\n200000 200000\\n\", \"4 5\\n-2 1\\n0 1\\n1 0\\n1 0\\n1 1 0 1\\n\", \"4 5\\n-2 1\\n0 1\\n1 0\\n0 0\\n1 1 0 1\\n\", \"4 5\\n-2 1\\n0 1\\n1 0\\n0 0\\n1 1 0 0\\n\", \"4 5\\n-2 1\\n0 1\\n1 0\\n0 1\\n1 1 0 0\\n\", \"4 2\\n0 0\\n0 2\\n2 2\\n2 0\\n26847 200000\\n\", \"4 4\\n1679 -198\\n9204 -198\\n9616 -5824\\n1679 -5824\\n18297 92466 187436 175992\\n\", \"4 2\\n0 0\\n0 2\\n2 2\\n2 0\\n4 5\\n\", \"6 3\\n0 0\\n1 0\\n1 1\\n2 1\\n2 2\\n0 2\\n0 2 3\\n\", \"4 4\\n-1 0\\n0 1\\n1 1\\n1 0\\n2 1 1 1\\n\", \"4 2\\n0 0\\n0 2\\n4 2\\n2 -1\\n200000 200000\\n\", \"4 4\\n1679 -198\\n9204 -198\\n10154 -5824\\n476 -5824\\n18297 92466 187436 175992\\n\", \"4 4\\n-8423 70\\n6902 7689\\n6902 2402\\n-8423 3124\\n20612 20612 91529 35617\\n\", \"4 4\\n-1 0\\n0 1\\n2 0\\n1 0\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 4\\n2 2\\n4 -1\\n200000 200000\\n\", \"4 4\\n-7116 70\\n6902 7689\\n6902 2402\\n-8423 2402\\n20612 20612 156230 35617\\n\", \"4 3\\n0 0\\n0 2\\n3 2\\n4 -1\\n200000 200000\\n\", \"4 5\\n-2 0\\n0 1\\n1 0\\n1 1\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 2\\n3 0\\n0 -1\\n200000 200000\\n\", \"4 5\\n-2 0\\n0 1\\n1 0\\n1 0\\n1 0 0 1\\n\", \"4 2\\n0 0\\n0 4\\n3 3\\n0 -1\\n200000 200000\\n\", \"4 5\\n-2 1\\n0 1\\n1 0\\n-1 0\\n1 1 0 1\\n\", \"4 5\\n-2 1\\n0 1\\n1 0\\n0 1\\n2 1 0 0\\n\", \"4 5\\n-2 1\\n0 1\\n1 -1\\n0 1\\n1 1 0 0\\n\", \"4 2\\n0 0\\n0 2\\n0 2\\n2 0\\n26847 200000\\n\", \"4 4\\n1679 -198\\n9204 -198\\n9616 -5824\\n1679 -5824\\n18297 92466 187436 99171\\n\", \"4 4\\n-16074 7689\\n6902 7689\\n6902 2402\\n-8423 2402\\n20612 20612 123030 35617\\n\", \"4 2\\n0 0\\n0 1\\n2 2\\n2 0\\n4 5\\n\", \"6 3\\n0 0\\n1 0\\n1 1\\n2 0\\n2 2\\n0 2\\n0 2 3\\n\", \"4 4\\n-1 0\\n0 1\\n1 0\\n1 0\\n2 1 1 1\\n\", \"4 3\\n0 0\\n0 2\\n4 2\\n2 -1\\n200000 200000\\n\", \"4 4\\n-8423 70\\n6902 7689\\n6902 2402\\n-8423 3124\\n20612 25075 91529 35617\\n\", \"4 4\\n-1 0\\n0 1\\n2 0\\n1 -1\\n1 1 1 1\\n\", \"4 2\\n0 0\\n0 0\\n2 2\\n4 -1\\n200000 200000\\n\", \"4 4\\n-7116 70\\n6902 7689\\n6902 2402\\n-8423 4776\\n20612 20612 156230 35617\\n\", \"4 3\\n0 0\\n0 3\\n3 2\\n4 -1\\n200000 200000\\n\", \"4 5\\n-2 0\\n0 1\\n1 0\\n1 1\\n2 1 1 1\\n\", \"5 2\\n0 0\\n0 2\\n3 0\\n0 -1\\n200000 200000\\n\", \"4 5\\n-2 0\\n0 1\\n1 0\\n1 0\\n1 0 0 2\\n\"], \"outputs\": [\"YES\\n1 -1 2 -1 \\n\", \"NO\\n\", \"YES\\n1 -1 2 -1 3 -1 \\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n-1 1 -1 2 -1 3 \\n\", \"YES\\n1 -1 2 -1 \\n\", \"NO\\n\", \"NO\", \"YES\\n1 -1 2 -1 \", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\", \"NO\"]}", "source": "primeintellect"}
|
Robot Bender decided to make Fray a birthday present. He drove n nails and numbered them from 1 to n in some order. Bender decided to make a picture using metal rods. The picture is a closed polyline, which vertices should be nails (in the given order). The segments of the polyline should be parallel to the coordinate axes. Polyline is allowed to have self-intersections. Bender can take a rod and fold it exactly once in any place to form an angle of 90 degrees. Then he can attach the place of the fold to some unoccupied nail and attach two ends of this rod to adjacent nails. A nail is considered unoccupied if there is no rod attached to it (neither by it's end nor the by the fold place). No rod could be used twice. It is not required to use all the rods.
Help Bender to solve this difficult task.
Input
The first line contains two positive integers n and m (4 ≤ n ≤ 500, 2 ≤ m ≤ 500, n is even) — the amount of nails and the amount of rods. i-th of the following n lines contains a pair of integers, denoting the coordinates of the i-th nail. Nails should be connected in the same order as they are given in the input. The last line contains m integers — the lenghts of the rods. All coordinates do not exceed 104 by absolute value. Lengths of the rods are between 1 and 200 000. No rod can be used twice. It is guaranteed that all segments of the given polyline are parallel to coordinate axes. No three consecutive nails lie on the same line.
Output
If it is impossible to solve Bender's problem, output NO. Otherwise, output YES in the first line, and in the second line output n numbers — i-th of them should be the number of rod, which fold place is attached to the i-th nail, or -1, if there is no such rod.
If there are multiple solutions, print any of them.
Examples
Input
4 2
0 0
0 2
2 2
2 0
4 4
Output
YES
1 -1 2 -1
Input
6 3
0 0
1 0
1 1
2 1
2 2
0 2
3 2 3
Output
YES
1 -1 2 -1 3 -1
Input
6 3
0 0
1 0
1 1
2 1
2 2
0 2
2 2 3
Output
NO
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"4\\n1 2\\n2 3\\n3 4\\n4 1\\n\", \"4\\n1 1\\n2 2\\n3 3\\n4 4\\n\", \"3\\n1 2\\n1 2\\n1 1\\n\", \"4\\n2 3\\n1 772\\n3 870\\n3 668\\n\", \"6\\n4 843\\n2 107\\n10 943\\n9 649\\n7 806\\n6 730\\n\", \"3\\n2 828\\n4 392\\n4 903\\n\", \"49\\n1 758\\n5 3\\n5 3\\n4 2\\n4 36\\n3 843\\n5 107\\n1 943\\n1 649\\n2 806\\n3 730\\n2 351\\n2 102\\n1 4\\n3 4\\n3 955\\n2 841\\n2 377\\n5 2\\n3 440\\n4 324\\n3 3\\n3 83\\n2 2\\n2 1\\n4 1\\n1 931\\n3 4\\n2 5\\n2 5\\n4 73\\n5 830\\n3 4\\n3 5\\n5 291\\n1 2\\n5 3\\n4 4\\n2 3\\n3 151\\n4 2\\n4 431\\n5 1\\n2 5\\n2 4\\n4 2\\n4 4\\n3 1\\n5 2\\n\", \"5\\n1 1\\n1 2\\n2 3\\n3 4\\n4 3\\n\", \"11\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n\", \"3\\n1 1\\n1 1\\n2 2\\n\", \"9\\n162 942\\n637 967\\n356 108\\n768 53\\n656 656\\n575 32\\n32 575\\n53 53\\n351 222\\n\", \"8\\n83 978\\n930 674\\n542 22\\n834 116\\n116 271\\n640 930\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n102 377\\n394 102\\n549 440\\n630 324\\n624 624\\n\", \"2\\n7 7\\n5 359\\n\", \"2\\n1 1\\n1 1\\n\", \"1\\n500 1000\\n\", \"10\\n423 360\\n947 538\\n507 484\\n31 947\\n414 351\\n169 901\\n901 21\\n592 22\\n763 200\\n656 485\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 414\\n656 789\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n735 808\\n54 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 390\\n128 549\\n468 511\\n729 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"5\\n1 4\\n6 6\\n4 3\\n3 4\\n4 758\\n\", \"1\\n1000 1000\\n\", \"2\\n465 706\\n706 706\\n\", \"3\\n1 2\\n1 2\\n2 1\\n\", \"4\\n2 3\\n1 934\\n3 870\\n3 668\\n\", \"6\\n4 862\\n2 107\\n10 943\\n9 649\\n7 806\\n6 730\\n\", \"3\\n2 828\\n4 1\\n4 903\\n\", \"11\\n1 1\\n2 2\\n3 3\\n4 4\\n5 7\\n6 6\\n7 7\\n8 8\\n9 9\\n10 10\\n11 11\\n\", \"9\\n162 942\\n637 967\\n356 108\\n768 53\\n656 656\\n575 23\\n32 575\\n53 53\\n351 222\\n\", \"2\\n1 0\\n1 1\\n\", \"10\\n564 360\\n947 538\\n507 484\\n31 947\\n414 351\\n169 901\\n901 21\\n592 22\\n763 200\\n656 485\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 414\\n656 789\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n54 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 390\\n128 549\\n468 511\\n729 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"4\\n2 0\\n1 934\\n3 870\\n3 668\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 414\\n656 504\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n54 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 568\\n128 549\\n468 511\\n729 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 414\\n656 504\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n54 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 568\\n128 549\\n468 511\\n633 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 318\\n656 504\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n6 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 568\\n128 549\\n468 511\\n633 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"9\\n162 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n7 706\\n82 22\\n351 13\\n\", \"11\\n1 1\\n2 2\\n3 3\\n4 4\\n5 5\\n6 6\\n7 7\\n8 8\\n9 9\\n10 20\\n11 11\\n\", \"49\\n1 758\\n5 3\\n5 3\\n4 2\\n4 36\\n3 843\\n5 107\\n1 943\\n1 649\\n2 806\\n3 730\\n2 351\\n2 102\\n1 4\\n3 4\\n3 955\\n2 841\\n2 377\\n5 2\\n3 440\\n4 324\\n3 3\\n3 83\\n2 2\\n2 1\\n4 1\\n1 931\\n3 4\\n2 5\\n2 5\\n4 73\\n5 830\\n3 4\\n3 5\\n5 31\\n1 2\\n5 3\\n4 4\\n2 3\\n3 151\\n4 2\\n4 431\\n5 1\\n2 5\\n2 4\\n4 2\\n4 4\\n3 1\\n5 2\\n\", \"5\\n1 1\\n1 2\\n2 3\\n3 6\\n4 3\\n\", \"8\\n83 978\\n930 674\\n542 22\\n834 116\\n116 271\\n640 101\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n102 377\\n394 80\\n549 440\\n630 324\\n624 624\\n\", \"2\\n7 7\\n5 415\\n\", \"1\\n265 1000\\n\", \"5\\n1 4\\n6 10\\n4 3\\n3 4\\n4 758\\n\", \"2\\n797 706\\n706 706\\n\", \"6\\n4 862\\n2 194\\n10 943\\n9 649\\n7 806\\n6 730\\n\", \"3\\n2 828\\n4 1\\n6 903\\n\", \"49\\n1 758\\n5 3\\n5 3\\n4 2\\n4 36\\n3 843\\n5 107\\n1 943\\n1 649\\n2 806\\n3 730\\n2 351\\n2 102\\n1 4\\n3 4\\n3 955\\n2 841\\n3 377\\n5 2\\n3 440\\n4 324\\n3 3\\n3 83\\n2 2\\n2 1\\n4 1\\n1 931\\n3 4\\n2 5\\n2 5\\n4 73\\n5 830\\n3 4\\n3 5\\n5 31\\n1 2\\n5 3\\n4 4\\n2 3\\n3 151\\n4 2\\n4 431\\n5 1\\n2 5\\n2 4\\n4 2\\n4 4\\n3 1\\n5 2\\n\", \"5\\n1 1\\n1 2\\n1 3\\n3 6\\n4 3\\n\", \"9\\n162 942\\n637 967\\n356 108\\n768 53\\n656 656\\n575 23\\n8 575\\n53 53\\n351 222\\n\", \"8\\n83 978\\n930 674\\n542 22\\n834 116\\n116 271\\n640 100\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n102 377\\n394 80\\n549 440\\n630 324\\n26 624\\n\", \"2\\n7 13\\n5 415\\n\", \"2\\n1 0\\n1 0\\n\", \"1\\n192 1000\\n\", \"10\\n564 360\\n947 538\\n507 484\\n31 947\\n414 351\\n169 901\\n901 11\\n592 22\\n763 200\\n656 485\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 414\\n656 789\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n54 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 568\\n128 549\\n468 511\\n729 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"5\\n1 4\\n6 10\\n3 3\\n3 4\\n4 758\\n\", \"2\\n797 706\\n706 852\\n\", \"4\\n2 0\\n1 934\\n3 870\\n3 375\\n\", \"6\\n4 862\\n2 194\\n10 943\\n9 649\\n7 806\\n6 948\\n\", \"49\\n1 758\\n5 3\\n5 3\\n4 2\\n4 36\\n4 843\\n5 107\\n1 943\\n1 649\\n2 806\\n3 730\\n2 351\\n2 102\\n1 4\\n3 4\\n3 955\\n2 841\\n3 377\\n5 2\\n3 440\\n4 324\\n3 3\\n3 83\\n2 2\\n2 1\\n4 1\\n1 931\\n3 4\\n2 5\\n2 5\\n4 73\\n5 830\\n3 4\\n3 5\\n5 31\\n1 2\\n5 3\\n4 4\\n2 3\\n3 151\\n4 2\\n4 431\\n5 1\\n2 5\\n2 4\\n4 2\\n4 4\\n3 1\\n5 2\\n\", \"9\\n162 942\\n637 967\\n356 108\\n768 53\\n561 656\\n575 23\\n8 575\\n53 53\\n351 222\\n\", \"8\\n83 978\\n930 674\\n542 37\\n834 116\\n116 271\\n640 100\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n138 377\\n394 80\\n549 440\\n630 324\\n26 624\\n\", \"2\\n7 12\\n5 415\\n\", \"2\\n1 1\\n1 0\\n\", \"10\\n564 360\\n947 538\\n507 484\\n31 947\\n414 351\\n131 901\\n901 11\\n592 22\\n763 200\\n656 485\\n\", \"5\\n1 4\\n6 16\\n3 3\\n3 4\\n4 758\\n\", \"4\\n2 1\\n1 934\\n3 870\\n3 375\\n\", \"9\\n162 942\\n637 967\\n356 116\\n768 53\\n561 656\\n575 23\\n8 575\\n53 53\\n351 222\\n\", \"8\\n83 978\\n930 674\\n542 37\\n277 116\\n116 271\\n640 100\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n138 377\\n394 70\\n549 440\\n630 324\\n26 624\\n\", \"2\\n7 17\\n5 415\\n\", \"2\\n2 1\\n1 0\\n\", \"10\\n564 360\\n947 538\\n507 484\\n31 947\\n414 351\\n156 901\\n901 11\\n592 22\\n763 200\\n656 485\\n\", \"9\\n162 942\\n637 967\\n356 116\\n768 53\\n561 656\\n575 23\\n8 575\\n53 53\\n351 157\\n\", \"8\\n83 978\\n930 674\\n179 37\\n277 116\\n116 271\\n640 100\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n84 377\\n394 70\\n549 440\\n630 324\\n26 624\\n\", \"2\\n8 17\\n5 415\\n\", \"2\\n2 1\\n1 1\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 414\\n656 504\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n6 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 568\\n128 549\\n468 511\\n633 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 894\\n617 330\\n\", \"9\\n162 708\\n637 967\\n356 116\\n768 53\\n561 656\\n575 23\\n8 575\\n53 53\\n351 157\\n\", \"8\\n83 978\\n930 674\\n27 37\\n277 116\\n116 271\\n640 100\\n659 930\\n705 987\\n\", \"7\\n351 955\\n7 841\\n84 377\\n269 70\\n549 440\\n630 324\\n26 624\\n\", \"2\\n8 17\\n5 568\\n\", \"2\\n2 2\\n1 1\\n\", \"9\\n162 708\\n637 967\\n356 116\\n768 53\\n561 656\\n575 23\\n8 575\\n53 22\\n351 157\\n\", \"7\\n351 955\\n7 841\\n84 377\\n269 70\\n549 440\\n630 239\\n26 624\\n\", \"2\\n8 17\\n5 802\\n\", \"2\\n3 2\\n1 1\\n\", \"50\\n507 31\\n31 250\\n414 763\\n169 304\\n901 9\\n592 610\\n763 318\\n656 504\\n411 422\\n360 468\\n625 504\\n538 201\\n549 619\\n484 797\\n596 282\\n42 310\\n603 656\\n351 623\\n292 293\\n837 180\\n375 658\\n21 192\\n597 729\\n22 512\\n349 635\\n200 56\\n669 647\\n485 887\\n282 939\\n577 808\\n6 417\\n1000 310\\n419 652\\n939 617\\n901 669\\n789 568\\n128 549\\n468 511\\n633 837\\n894 729\\n649 894\\n484 22\\n808 586\\n422 286\\n311 427\\n618 656\\n814 933\\n515 901\\n310 752\\n617 330\\n\", \"9\\n162 708\\n637 967\\n356 116\\n768 53\\n561 656\\n575 17\\n8 575\\n53 22\\n351 157\\n\", \"7\\n351 955\\n7 841\\n84 377\\n269 70\\n549 450\\n630 239\\n26 624\\n\", \"9\\n162 708\\n178 967\\n356 116\\n768 53\\n561 656\\n575 17\\n8 575\\n53 22\\n351 157\\n\", \"7\\n351 955\\n7 841\\n84 377\\n269 70\\n549 450\\n630 239\\n26 216\\n\", \"9\\n162 708\\n178 967\\n356 116\\n768 53\\n561 656\\n575 17\\n4 575\\n53 22\\n351 157\\n\", \"7\\n328 955\\n7 841\\n84 377\\n269 70\\n549 450\\n630 239\\n26 216\\n\", \"9\\n162 708\\n19 967\\n356 116\\n768 53\\n561 656\\n575 17\\n4 575\\n53 22\\n351 157\\n\", \"9\\n162 708\\n19 967\\n356 116\\n768 53\\n561 656\\n575 17\\n4 575\\n53 22\\n351 13\\n\", \"9\\n162 708\\n19 252\\n356 116\\n768 53\\n561 656\\n575 17\\n4 575\\n53 22\\n351 13\\n\", \"9\\n162 708\\n19 252\\n356 116\\n768 53\\n561 656\\n575 12\\n4 575\\n53 22\\n351 13\\n\", \"9\\n162 708\\n19 252\\n356 116\\n768 53\\n561 656\\n575 12\\n7 575\\n53 22\\n351 13\\n\", \"9\\n162 708\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n7 575\\n53 22\\n351 13\\n\", \"9\\n162 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n7 575\\n53 22\\n351 13\\n\", \"9\\n162 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n7 706\\n53 22\\n351 13\\n\", \"9\\n154 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n7 706\\n82 22\\n351 13\\n\", \"9\\n154 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n7 706\\n82 22\\n351 23\\n\", \"9\\n154 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n8 706\\n82 22\\n351 23\\n\", \"9\\n154 185\\n19 252\\n350 116\\n768 53\\n561 656\\n575 12\\n3 706\\n82 22\\n351 23\\n\", \"9\\n154 185\\n19 252\\n350 222\\n768 53\\n561 656\\n575 12\\n3 706\\n82 22\\n351 23\\n\", \"9\\n154 185\\n19 252\\n350 222\\n768 53\\n561 656\\n575 6\\n3 706\\n82 22\\n351 23\\n\", \"9\\n154 185\\n19 252\\n350 222\\n768 53\\n561 656\\n575 6\\n3 706\\n82 32\\n351 23\\n\", \"3\\n1 4\\n1 2\\n1 1\\n\", \"4\\n2 3\\n1 772\\n3 870\\n3 282\\n\", \"6\\n4 843\\n2 107\\n10 943\\n9 649\\n6 806\\n6 730\\n\", \"3\\n2 828\\n4 91\\n4 903\\n\", \"49\\n1 758\\n5 3\\n5 3\\n4 2\\n4 36\\n3 843\\n6 107\\n1 943\\n1 649\\n2 806\\n3 730\\n2 351\\n2 102\\n1 4\\n3 4\\n3 955\\n2 841\\n2 377\\n5 2\\n3 440\\n4 324\\n3 3\\n3 83\\n2 2\\n2 1\\n4 1\\n1 931\\n3 4\\n2 5\\n2 5\\n4 73\\n5 830\\n3 4\\n3 5\\n5 291\\n1 2\\n5 3\\n4 4\\n2 3\\n3 151\\n4 2\\n4 431\\n5 1\\n2 5\\n2 4\\n4 2\\n4 4\\n3 1\\n5 2\\n\", \"5\\n1 1\\n1 2\\n2 3\\n3 4\\n3 3\\n\", \"3\\n1 1\\n1 0\\n2 2\\n\", \"9\\n162 942\\n637 967\\n356 108\\n768 53\\n656 656\\n575 32\\n32 575\\n53 18\\n351 222\\n\"], \"outputs\": [\"0\\n\", \"4\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"3\\n\", \"0\\n\", \"1\\n\", \"11\\n\", \"1\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"8\\n\", \"30\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"6\\n\", \"3\\n\", \"10\\n\", \"7\\n\", \"1\\n\", \"8\\n\", \"30\\n\", \"4\\n\", \"31\\n\", \"32\\n\", \"33\\n\", \"9\\n\", \"11\\n\", \"0\\n\", \"2\\n\", \"6\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"6\\n\", \"3\\n\", \"0\\n\", \"2\\n\", \"7\\n\", \"6\\n\", \"7\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"8\\n\", \"30\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"6\\n\", \"0\\n\", \"7\\n\", \"6\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"8\\n\", \"3\\n\", \"3\\n\", \"7\\n\", \"6\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"8\\n\", \"7\\n\", \"6\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"32\\n\", \"7\\n\", \"6\\n\", \"7\\n\", \"2\\n\", \"2\\n\", \"7\\n\", \"7\\n\", \"2\\n\", \"2\\n\", \"33\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"8\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"6\\n\"]}", "source": "primeintellect"}
|
Sereja and his friends went to a picnic. The guys had n soda bottles just for it. Sereja forgot the bottle opener as usual, so the guys had to come up with another way to open bottles.
Sereja knows that the i-th bottle is from brand ai, besides, you can use it to open other bottles of brand bi. You can use one bottle to open multiple other bottles. Sereja can open bottle with opened bottle or closed bottle.
Knowing this, Sereja wants to find out the number of bottles they've got that they won't be able to open in any way. Help him and find this number.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of bottles. The next n lines contain the bottles' description. The i-th line contains two integers ai, bi (1 ≤ ai, bi ≤ 1000) — the description of the i-th bottle.
Output
In a single line print a single integer — the answer to the problem.
Examples
Input
4
1 1
2 2
3 3
4 4
Output
4
Input
4
1 2
2 3
3 4
4 1
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 5\\n1 2 1 1 2\\n1 2\\n1 3\\n2 4\\n2 5\\n1 2 3\\n1 1 2\\n2 1\\n2 2\\n2 4\\n\", \"10 10\\n418 45 865 869 745 901 177 773 854 462\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n5 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 288\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n418 31 865 869 745 901 177 773 854 462\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n5 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 288\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 1\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 2\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n146 197 856 768 825 894 86 472 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 731\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n418 44 865 869 745 901 177 773 854 462\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n3 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n678 44 714 869 745 901 177 773 854 244\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n3 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 437\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 2\\n2 4\\n1 6 505\\n1 4 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 37 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 4 467\\n1 3 643\\n2 1\\n1 3 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 1 244\\n\", \"10 10\\n137 197 856 768 825 894 86 179 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 3 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 37 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 3 631\\n2 4\\n1 7 364\\n\", \"10 10\\n418 31 865 869 745 901 177 773 854 462\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n5 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 2\\n2 4\\n1 6 505\\n1 8 467\\n1 6 643\\n2 1\\n1 8 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 37 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 6 631\\n2 4\\n1 7 364\\n\", \"10 10\\n418 31 865 869 745 901 177 773 854 462\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n3 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n137 197 856 768 825 894 86 472 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 2\\n2 4\\n1 6 505\\n1 8 467\\n1 8 643\\n2 1\\n1 8 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 472 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 731\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 245\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 692\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 179 218 326\\n7 8\\n4 7\\n5 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 2 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 1\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n5 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 1271 894 37 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 3 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 5 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 123 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 2\\n2 4\\n1 6 505\\n1 8 467\\n1 6 643\\n2 1\\n1 8 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 179 218 326\\n7 8\\n4 7\\n5 9\\n8 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n5 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 161\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 123 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 2\\n2 4\\n1 6 505\\n1 8 467\\n1 6 643\\n2 1\\n1 8 631\\n2 4\\n1 2 364\\n\", \"10 10\\n418 44 865 869 745 901 177 773 854 244\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n3 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n418 44 714 869 745 901 177 773 854 244\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n3 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n678 44 714 869 745 901 177 773 854 244\\n4 8\\n1 4\\n3 6\\n1 5\\n1 10\\n3 9\\n1 2\\n4 7\\n1 3\\n2 2\\n1 6 246\\n1 4 296\\n1 2 378\\n1 8 648\\n2 6\\n1 5 406\\n1 6 981\\n1 2 868\\n2 7\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 750\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 768 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 179 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 1033\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 32\\n1 8 467\\n1 3 643\\n2 1\\n1 3 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n2 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 223\\n2 1\\n1 8 631\\n2 1\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 507\\n1 8 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 37 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 744\\n1 8 467\\n1 3 643\\n2 1\\n1 6 631\\n2 4\\n1 7 364\\n\", \"10 10\\n137 197 856 768 825 894 86 472 218 369\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 731\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 1 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 174 218 326\\n7 8\\n4 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n6 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 692\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 190 86 179 218 326\\n7 8\\n4 7\\n5 9\\n7 10\\n1 2\\n1 4\\n3 6\\n3 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\", \"10 10\\n137 197 856 768 825 894 86 317 218 326\\n7 8\\n5 7\\n8 9\\n7 10\\n1 2\\n1 4\\n3 6\\n4 5\\n2 3\\n1 9 624\\n2 1\\n2 4\\n1 6 505\\n1 8 467\\n1 3 643\\n2 1\\n1 8 631\\n2 4\\n1 7 244\\n\"], \"outputs\": [\"3\\n3\\n0\\n\", \"45\\n1147\\n-119\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"31\\n1147\\n-119\\n\", \"137\\n768\\n137\\n137\\n\", \"197\\n768\\n137\\n768\\n\", \"137\\n768\\n780\\n125\\n\", \"146\\n768\\n789\\n125\\n\", \"44\\n1147\\n-119\\n\", \"44\\n1338\\n-119\\n\", \"197\\n768\\n137\\n1235\\n\", \"137\\n768\\n137\\n1235\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"31\\n1147\\n-119\\n\", \"197\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"31\\n1147\\n-119\\n\", \"137\\n768\\n780\\n125\\n\", \"197\\n768\\n137\\n768\\n\", \"137\\n768\\n780\\n125\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n137\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n780\\n125\\n\", \"197\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"197\\n768\\n137\\n768\\n\", \"44\\n1147\\n-119\\n\", \"44\\n1147\\n-119\\n\", \"44\\n1147\\n-119\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n137\\n\", \"137\\n768\\n780\\n125\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n780\\n125\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\", \"137\\n768\\n137\\n768\\n\"]}", "source": "primeintellect"}
|
Iahub likes trees very much. Recently he discovered an interesting tree named propagating tree. The tree consists of n nodes numbered from 1 to n, each node i having an initial value ai. The root of the tree is node 1.
This tree has a special property: when a value val is added to a value of node i, the value -val is added to values of all the children of node i. Note that when you add value -val to a child of node i, you also add -(-val) to all children of the child of node i and so on. Look an example explanation to understand better how it works.
This tree supports two types of queries:
* "1 x val" — val is added to the value of node x;
* "2 x" — print the current value of node x.
In order to help Iahub understand the tree better, you must answer m queries of the preceding type.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 200000). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1000). Each of the next n–1 lines contains two integers vi and ui (1 ≤ vi, ui ≤ n), meaning that there is an edge between nodes vi and ui.
Each of the next m lines contains a query in the format described above. It is guaranteed that the following constraints hold for all queries: 1 ≤ x ≤ n, 1 ≤ val ≤ 1000.
Output
For each query of type two (print the value of node x) you must print the answer to the query on a separate line. The queries must be answered in the order given in the input.
Examples
Input
5 5
1 2 1 1 2
1 2
1 3
2 4
2 5
1 2 3
1 1 2
2 1
2 2
2 4
Output
3
3
0
Note
The values of the nodes are [1, 2, 1, 1, 2] at the beginning.
Then value 3 is added to node 2. It propagates and value -3 is added to it's sons, node 4 and node 5. Then it cannot propagate any more. So the values of the nodes are [1, 5, 1, - 2, - 1].
Then value 2 is added to node 1. It propagates and value -2 is added to it's sons, node 2 and node 3. From node 2 it propagates again, adding value 2 to it's sons, node 4 and node 5. Node 3 has no sons, so it cannot propagate from there. The values of the nodes are [3, 3, - 1, 0, 1].
You can see all the definitions about the tree at the following link: http://en.wikipedia.org/wiki/Tree_(graph_theory)
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"4 5 2\\n\", \"3 3 2\\n\", \"3 3 3\\n\", \"4 3 2\\n\", \"10 13 6\\n\", \"90 97 24\\n\", \"28 74 2\\n\", \"8 11 4\\n\", \"9 17 14\\n\", \"98 98 64\\n\", \"86 69 62\\n\", \"40 77 77\\n\", \"31 8 8\\n\", \"100 100 100\\n\", \"2 100 1\\n\", \"78 90 38\\n\", \"52 46 4\\n\", \"3 2 2\\n\", \"41 98 76\\n\", \"50 50 1\\n\", \"35 95 9\\n\", \"11 6 2\\n\", \"1 1 1\\n\", \"47 5 1\\n\", \"74 41 28\\n\", \"89 75 59\\n\", \"100 50 50\\n\", \"100 100 1\\n\", \"90 100 30\\n\", \"89 73 32\\n\", \"96 9 6\\n\", \"54 60 16\\n\", \"100 90 80\\n\", \"2 100 2\\n\", \"1 100 1\\n\", \"1 100 100\\n\", \"73 72 12\\n\", \"5 26 17\\n\", \"45 5 3\\n\", \"70 6 1\\n\", \"100 50 3\\n\", \"50 6 3\\n\", \"28 6 3\\n\", \"1 100 2\\n\", \"35 47 42\\n\", \"31 8 4\\n\", \"20 16 14\\n\", \"99 99 5\\n\", \"100 45 8\\n\", \"16 5 4\\n\", \"1 10 1\\n\", \"1 5 5\\n\", \"5 100 1\\n\", \"100 13 11\\n\", \"10 25 6\\n\", \"90 97 34\\n\", \"1 17 14\\n\", \"86 69 17\\n\", \"31 8 2\\n\", \"3 100 1\\n\", \"52 73 4\\n\", \"50 74 1\\n\", \"35 9 9\\n\", \"6 6 2\\n\", \"84 5 1\\n\", \"93 75 59\\n\", \"100 50 25\\n\", \"89 73 18\\n\", \"51 60 16\\n\", \"73 72 9\\n\", \"45 8 3\\n\", \"50 6 5\\n\", \"28 7 3\\n\", \"99 99 7\\n\", \"100 12 8\\n\", \"16 5 1\\n\", \"1 15 1\\n\", \"100 23 11\\n\", \"4 4 2\\n\", \"7 3 2\\n\", \"28 8 2\\n\", \"52 73 2\\n\", \"23 74 1\\n\", \"35 12 9\\n\", \"6 6 4\\n\", \"93 75 60\\n\", \"100 74 25\\n\", \"89 73 4\\n\", \"73 100 9\\n\", \"53 7 3\\n\", \"23 99 5\\n\", \"100 12 10\\n\", \"8 3 1\\n\", \"12 33 6\\n\", \"8 73 2\\n\", \"35 23 9\\n\", \"10 6 4\\n\", \"100 74 43\\n\", \"89 73 6\\n\", \"73 100 3\\n\", \"53 4 3\\n\", \"100 16 10\\n\", \"21 33 6\\n\", \"13 73 2\\n\", \"35 23 8\\n\", \"94 4 3\\n\", \"6 99 5\\n\", \"100 16 13\\n\", \"22 73 2\\n\", \"22 23 8\\n\", \"25 4 3\\n\", \"100 16 15\\n\", \"22 23 11\\n\", \"16 4 3\\n\", \"5 99 2\\n\", \"100 16 12\\n\", \"13 41 28\\n\", \"2 100 100\\n\", \"5 47 42\\n\", \"1 5 2\\n\", \"4 3 1\\n\", \"3 3 4\\n\", \"10 33 6\\n\", \"1 27 14\\n\", \"84 1 1\\n\", \"11 41 28\\n\", \"4 5 1\\n\", \"1 6 1\\n\", \"4 7 2\\n\", \"3 5 4\\n\", \"1 4 14\\n\", \"11 62 28\\n\", \"5 99 5\\n\", \"1 3 1\\n\", \"4 8 2\\n\", \"3 7 4\\n\", \"1 5 14\\n\", \"11 62 21\\n\", \"1 3 2\\n\", \"4 8 4\\n\", \"3 4 4\\n\", \"21 50 6\\n\", \"11 62 40\\n\", \"6 99 2\\n\", \"1 2 2\\n\", \"5 8 4\\n\", \"1 4 4\\n\", \"21 42 6\\n\", \"11 36 40\\n\", \"2 2 2\\n\"], \"outputs\": [\"7\\n\", \"3\\n\", \"1\\n\", \"6\\n\", \"48\\n\", \"413496885\\n\", \"134217727\\n\", \"47\\n\", \"0\\n\", \"237643149\\n\", \"217513984\\n\", \"0\\n\", \"52532592\\n\", \"1\\n\", \"2\\n\", \"744021655\\n\", \"27907693\\n\", \"2\\n\", \"0\\n\", \"949480669\\n\", \"927164672\\n\", \"975\\n\", \"1\\n\", \"164058640\\n\", \"806604424\\n\", \"179807625\\n\", \"661237556\\n\", \"988185646\\n\", \"697322870\\n\", \"152673180\\n\", \"362487247\\n\", \"931055544\\n\", \"11531520\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"426374014\\n\", \"0\\n\", \"252804490\\n\", \"592826579\\n\", \"494224664\\n\", \"295630102\\n\", \"110682188\\n\", \"0\\n\", \"0\\n\", \"924947104\\n\", \"236\\n\", \"700732369\\n\", \"367847193\\n\", \"16175\\n\", \"1\\n\", \"0\\n\", \"16\\n\", \"883875774\\n\", \"48\\n\", \"845170219\\n\", \"0\\n\", \"460087654\\n\", \"23897192\\n\", \"4\\n\", \"27907805\\n\", \"949480669\\n\", \"476668976\\n\", \"31\\n\", \"701656691\\n\", \"236397965\\n\", \"364354424\\n\", \"406267081\\n\", \"594862363\\n\", \"965369259\\n\", \"605817233\\n\", \"202386195\\n\", \"122381755\\n\", \"739765266\\n\", \"67155203\\n\", \"26784\\n\", \"1\\n\", \"282973508\\n\", \"7\\n\", \"43\\n\", \"128752120\\n\", \"797922654\\n\", \"4194304\\n\", \"876849664\\n\", \"8\\n\", \"322609126\\n\", \"623126487\\n\", \"333678399\\n\", \"965369260\\n\", \"141611452\\n\", \"2160676\\n\", \"12597920\\n\", \"81\\n\", \"255\\n\", \"127\\n\", \"927151360\\n\", \"218\\n\", \"23871346\\n\", \"275523651\\n\", \"544271138\\n\", \"507773568\\n\", \"314363005\\n\", \"262008\\n\", \"4095\\n\", \"886303005\\n\", \"546833437\\n\", \"3\\n\", \"301765085\\n\", \"2097151\\n\", \"129952\\n\", \"7434542\\n\", \"814615878\\n\", \"13311\\n\", \"18972\\n\", \"15\\n\", \"927435567\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"7\\n\", \"0\\n\", \"48\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"8\\n\", \"1\\n\", \"7\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"7\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"262008\\n\", \"0\\n\", \"31\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"262008\\n\", \"0\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
Quite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a k-tree.
A k-tree is an infinite rooted tree where:
* each vertex has exactly k children;
* each edge has some weight;
* if we look at the edges that goes from some vertex to its children (exactly k edges), then their weights will equal 1, 2, 3, ..., k.
The picture below shows a part of a 3-tree.
<image>
As soon as Dima, a good friend of Lesha, found out about the tree, he immediately wondered: "How many paths of total weight n (the sum of all weights of the edges in the path) are there, starting from the root of a k-tree and also containing at least one edge of weight at least d?".
Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109 + 7).
Input
A single line contains three space-separated integers: n, k and d (1 ≤ n, k ≤ 100; 1 ≤ d ≤ k).
Output
Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).
Examples
Input
3 3 2
Output
3
Input
3 3 3
Output
1
Input
4 3 2
Output
6
Input
4 5 2
Output
7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"2 2\\n\", \"1 1\\n\", \"1000 1000\\n\", \"3 10000000\\n\", \"9253578 1799941\\n\", \"666666 666666\\n\", \"3505377 9167664\\n\", \"7319903 9017051\\n\", \"191919 123123\\n\", \"123456 123456\\n\", \"6407688 3000816\\n\", \"2 9999999\\n\", \"4108931 211273\\n\", \"9900111 1082917\\n\", \"7835126 9883365\\n\", \"346169 367216\\n\", \"3 4\\n\", \"9999999 9999999\\n\", \"999999 1000000\\n\", \"9998486 9998486\\n\", \"4 3\\n\", \"7054221 7251088\\n\", \"6340794 6874449\\n\", \"4410236 9316955\\n\", \"1001 1500126\\n\", \"1 10000000\\n\", \"10000000 10000\\n\", \"9999999 2\\n\", \"9999997 9999998\\n\", \"4 4\\n\", \"9832578 8599931\\n\", \"413703 2850203\\n\", \"2926377 2367675\\n\", \"2 10000000\\n\", \"7672285 753250\\n\", \"999999 92321\\n\", \"861392 6200826\\n\", \"888888 888888\\n\", \"123456 234567\\n\", \"6351267 7966789\\n\", \"3895014 8450640\\n\", \"1897562 4766779\\n\", \"8995251 5966331\\n\", \"10000000 2\\n\", \"10000 10000000\\n\", \"1000023 1000043\\n\", \"31623 10000000\\n\", \"1000000 1000000\\n\", \"1 4\\n\", \"8348718 6683355\\n\", \"4 1\\n\", \"2 4\\n\", \"10000000 9999999\\n\", \"10000000 10000000\\n\", \"9243243 432434\\n\", \"999999 999999\\n\", \"1507925 5483803\\n\", \"4 2\\n\", \"9956532 1084240\\n\", \"1000 1001\\n\", \"3 10010000\\n\", \"8869097 1799941\\n\", \"666666 815299\\n\", \"3505377 9272738\\n\", \"13469847 9017051\\n\", \"375713 123123\\n\", \"123456 242674\\n\", \"6407688 2250280\\n\", \"2 16246560\\n\", \"4108931 59365\\n\", \"9900111 1551596\\n\", \"7835126 13688526\\n\", \"346169 551022\\n\", \"2 1\\n\", \"5517575 9999999\\n\", \"999999 1000010\\n\", \"12520154 9998486\\n\", \"4 5\\n\", \"7054221 11167092\\n\", \"7491097 6874449\\n\", \"3075779 9316955\\n\", \"1001 2258427\\n\", \"10000000 10100\\n\", \"9775627 2\\n\", \"9255432 9999998\\n\", \"5 2\\n\", \"9832578 6346116\\n\", \"413703 4756780\\n\", \"4162438 2367675\\n\", \"2 10010000\\n\", \"7672285 1033344\\n\", \"999999 134247\\n\", \"441023 6200826\\n\", \"1407527 888888\\n\", \"155537 234567\\n\", \"6351267 2542636\\n\", \"3895014 11599021\\n\", \"883880 4766779\\n\", \"8995251 3188395\\n\", \"1000023 309544\\n\", \"31623 10000010\\n\", \"1000000 1000010\\n\", \"10313077 6683355\\n\", \"10000000 11383836\\n\", \"10000100 10000000\\n\", \"9689526 432434\\n\", \"999999 1551794\\n\", \"1587725 5483803\\n\", \"2301152 1084240\\n\", \"2 3\\n\", \"1001 1001\\n\", \"6 10010000\\n\", \"9901859 1799941\\n\", \"1296884 815299\\n\", \"3505377 12991871\\n\", \"6044172 9017051\\n\", \"553671 123123\\n\", \"234126 242674\\n\", \"6407688 927246\\n\", \"1 16246560\\n\", \"4108931 17629\\n\", \"6928153 1551596\\n\", \"7835126 11314306\\n\", \"346169 139095\\n\", \"5517575 1850711\\n\", \"1447374 1000010\\n\", \"12520154 17573427\\n\", \"4 7\\n\", \"7054221 13999616\\n\", \"7491097 10066192\\n\", \"3075779 5699585\\n\", \"1001 4343617\\n\", \"10000000 11100\\n\", \"9255432 14511743\\n\", \"5 4\\n\", \"18337486 6346116\\n\", \"413703 7962926\\n\", \"5610258 2367675\\n\", \"2 10010001\\n\", \"6088184 1033344\\n\", \"999999 77978\\n\", \"441023 9087067\\n\", \"1407527 528254\\n\", \"155537 395447\\n\", \"6351267 1251875\\n\", \"3895014 13617131\\n\", \"883880 8099122\\n\", \"10900563 3188395\\n\", \"00100 10000000\\n\", \"1000023 597857\\n\", \"25848 10000010\\n\", \"1000000 1001010\\n\", \"2647052 6683355\\n\", \"7 2\\n\", \"10000001 11383836\\n\", \"10000100 10001000\\n\", \"9689526 402096\\n\", \"551981 1551794\\n\", \"697907 5483803\\n\"], \"outputs\": [\"8\\n\", \"0\\n\", \"247750000\\n\", \"986197007\\n\", \"868664771\\n\", \"869302791\\n\", \"80435138\\n\", \"975259203\\n\", \"358196438\\n\", \"417111819\\n\", \"895399645\\n\", \"48573499\\n\", \"142398939\\n\", \"539539383\\n\", \"119844544\\n\", \"358144298\\n\", \"162\\n\", \"957764103\\n\", \"725921292\\n\", \"988877388\\n\", \"102\\n\", \"7849970\\n\", \"930977735\\n\", \"602743722\\n\", \"45074025\\n\", \"995024507\\n\", \"723127969\\n\", \"999300006\\n\", \"946983076\\n\", \"264\\n\", \"428281878\\n\", \"76966774\\n\", \"395740917\\n\", \"990423507\\n\", \"461773059\\n\", \"286549418\\n\", \"180835815\\n\", \"456888843\\n\", \"93010021\\n\", \"683811063\\n\", \"627604019\\n\", \"148050609\\n\", \"451718548\\n\", \"19300000\\n\", \"372369289\\n\", \"175442768\\n\", \"382702377\\n\", \"249917764\\n\", \"30\\n\", \"275994807\\n\", \"0\\n\", \"84\\n\", \"930564389\\n\", \"425362313\\n\", \"203891513\\n\", \"691690639\\n\", \"727607740\\n\", \"24\\n\", \"554368769\", \"248994743\\n\", \"773163548\\n\", \"446785399\\n\", \"894705471\\n\", \"401744947\\n\", \"322144878\\n\", \"790044144\\n\", \"877474335\\n\", \"105721837\\n\", \"511392764\\n\", \"494925096\\n\", \"514596851\\n\", \"896847250\\n\", \"542060552\\n\", \"0\\n\", \"675415133\\n\", \"402269306\\n\", \"254384064\\n\", \"540\\n\", \"439775020\\n\", \"88400078\\n\", \"209807020\\n\", \"7750086\\n\", \"479941562\\n\", \"902125449\\n\", \"776973478\\n\", \"35\\n\", \"855981893\\n\", \"330437164\\n\", \"137828835\\n\", \"408903924\\n\", \"390438365\\n\", \"116152113\\n\", \"741207526\\n\", \"825527838\\n\", \"319568982\\n\", \"510623263\\n\", \"800590732\\n\", \"432167416\\n\", \"412005655\\n\", \"236319867\\n\", \"32923429\\n\", \"385286558\\n\", \"744601418\\n\", \"113242098\\n\", \"778965806\\n\", \"241789821\\n\", \"931138986\\n\", \"837449023\\n\", \"347866402\\n\", \"33\\n\", \"750992236\\n\", \"505173054\\n\", \"731217028\\n\", \"690270865\\n\", \"844514001\\n\", \"396624679\\n\", \"835875160\\n\", \"817467635\\n\", \"429879574\\n\", \"619420822\\n\", \"275112987\\n\", \"362451640\\n\", \"374011537\\n\", \"26469754\\n\", \"584941521\\n\", \"776271795\\n\", \"525729623\\n\", \"1554\\n\", \"845457729\\n\", \"589352651\\n\", \"41905693\\n\", \"513406875\\n\", \"989498919\\n\", \"404827659\\n\", \"390\\n\", \"487366036\\n\", \"635332636\\n\", \"886229547\\n\", \"890782624\\n\", \"678861244\\n\", \"351073376\\n\", \"903127367\\n\", \"575998035\\n\", \"904986803\\n\", \"707942765\\n\", \"805120804\\n\", \"453763624\\n\", \"348805207\\n\", \"356224993\\n\", \"389745406\\n\", \"140989497\\n\", \"72491388\\n\", \"707431044\\n\", \"63\\n\", \"737147366\\n\", \"521653481\\n\", \"799911050\\n\", \"441761832\\n\", \"833243809\\n\"]}", "source": "primeintellect"}
|
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n00100\\n\", \"6\\n111010\\n\", \"5\\n10001\\n\", \"7\\n1100010\\n\", \"18\\n110100000000000000\\n\", \"70\\n0010011001010100000110011001011111101011010110110101110101111011101010\\n\", \"7\\n0000000\\n\", \"17\\n00100000000000000\\n\", \"16\\n1101010010000000\\n\", \"3\\n111\\n\", \"4\\n0000\\n\", \"4\\n0110\\n\", \"3\\n010\\n\", \"4\\n1001\\n\", \"337\\n0000000000000000000000000000000000000010000000000000000000000000000000010000000000001000000000100100000000000000000000000000000000000000000000000000000000100000000000000010000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000001000100000000000000000000000000000000000100010000000100\\n\", \"2\\n11\\n\", \"6\\n110011\\n\", \"4\\n1100\\n\", \"15\\n110101101111111\\n\", \"3\\n101\\n\", \"6\\n111111\\n\", \"10\\n1000000000\\n\", \"8\\n10011001\\n\", \"10\\n1000101001\\n\", \"100\\n1111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111\\n\", \"7\\n0100011\\n\", \"12\\n101101010010\\n\", \"1\\n0\\n\", \"14\\n00101111111111\\n\", \"100\\n1001001000011010001101000011100101101110101001110110010001110011011100111000010010011011101000011101\\n\", \"149\\n11110101110111101111110110001111110101111011111111111111101111110000101101110110111101011111011111111000111011011110111111001011111111111010110111110\\n\", \"35\\n11111111111111111111111111111111110\\n\", \"8\\n00000110\\n\", \"14\\n10101001101010\\n\", \"6\\n000000\\n\", \"23\\n10010101010101010101001\\n\", \"100\\n0000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\\n\", \"18\\n111100000000000000\\n\", \"70\\n0010011001010100000110011001011110101011010110110101110101111011101010\\n\", \"7\\n0000010\\n\", \"17\\n01100000000000000\\n\", \"3\\n001\\n\", \"337\\n0000000000000000000000000000000000000010000000000000000000000000000000010000000000001000000000100100000000000000000000000000000000000000000000000000000000100000000001000010000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000001000100000000000000000000000000000000000100010000000100\\n\", \"15\\n110001101111111\\n\", \"10\\n1010000000\\n\", \"10\\n1100101001\\n\", \"100\\n1111111111111111111111111111111111111111111111111111111111111111011111111111101111111111111111111111\\n\", \"12\\n101111010010\\n\", \"100\\n1001001000011010001101000011100101101110101001110110010001110011011100111000010010011011101000011100\\n\", \"149\\n11110101110111101111110110001111110101111011111111111111101111110000101101110110111101011111011111111000111011011110111110001011111111111010110111110\\n\", \"35\\n11110111111111111111111111111111110\\n\", \"70\\n0010011001010100000110011001011110101011010110111101110101111011101010\\n\", \"4\\n0101\\n\", \"337\\n0000000000000000000000000000000000000010000000000000000000000000000000010000000000001000000000100100000000000000000000000000000000000000000000000000000000100000000001000010000000000000000000000000000000000000000000000000000000000000000100000010000000000000000000000000000000000000001000100000000000000000000000000000000000100010000000100\\n\", \"100\\n1111111111111111111111111111111111111111111111111111111111111111011111111111101111111111111111101111\\n\", \"12\\n111111010010\\n\", \"100\\n1001001000011010001101000011100101101110101001110110010001110011011000111000010010011011101000011100\\n\", \"35\\n11110111111111111111111101111111110\\n\", \"16\\n1100010010000000\\n\", \"4\\n0010\\n\", \"4\\n0100\\n\", \"3\\n110\\n\", \"4\\n1000\\n\", \"6\\n110010\\n\", \"4\\n0001\\n\", \"3\\n100\\n\", \"6\\n101111\\n\", \"8\\n10011011\\n\", \"7\\n0000011\\n\", \"14\\n00101101111111\\n\", \"8\\n00000111\\n\", \"14\\n10101011101010\\n\", \"6\\n100000\\n\", \"23\\n10010100010101010101001\\n\", \"100\\n0000000000100000000000000000000000000000000000000000000000000000010000000000000000000000000000000000\\n\", \"5\\n10100\\n\", \"6\\n011010\\n\", \"5\\n10011\\n\", \"7\\n1100011\\n\", \"18\\n111100000000010000\\n\", \"7\\n1000000\\n\", \"17\\n01100010000000000\\n\", \"16\\n1100110010000000\\n\", \"3\\n011\\n\", \"4\\n0011\\n\", \"3\\n000\\n\", \"4\\n1101\\n\", \"6\\n111000\\n\", \"4\\n1110\\n\", \"15\\n110001101111110\\n\", \"6\\n100111\\n\", \"10\\n1010000100\\n\", \"8\\n10011010\\n\", \"10\\n1100101101\\n\", \"7\\n0100001\\n\", \"14\\n00101101111101\\n\", \"149\\n11110101110111101111110110001111110101111011111111111111101111110000101101110110111001011111011111111000111011011110111110001011111111111010110111110\\n\", \"8\\n00000011\\n\", \"14\\n10001011101010\\n\", \"6\\n100010\\n\", \"23\\n10010100010111010101001\\n\", \"100\\n0000000000100000000000000000000000000010000000000000000000000000010000000000000000000000000000000000\\n\", \"5\\n00000\\n\", \"6\\n011011\\n\", \"5\\n10000\\n\", \"7\\n1101011\\n\", \"18\\n111100000010010000\\n\", \"70\\n0000011001010100000110011001011110101011010110111101110101111011101010\\n\", \"7\\n1001000\\n\", \"17\\n01000010000000000\\n\", \"16\\n1100110010000100\\n\", \"4\\n0111\\n\"], \"outputs\": [\"2\", \"1\", \"1\", \"2\", \"8\", \"32\", \"3\", \"8\", \"7\", \"1\", \"2\", \"2\", \"0\", \"2\", \"160\", \"1\", \"3\", \"2\", \"7\", \"0\", \"3\", \"4\", \"4\", \"3\", \"49\", \"2\", \"6\", \"0\", \"6\", \"49\", \"73\", \"17\", \"4\", \"2\", \"3\", \"4\", \"49\", \"9\\n\", \"33\\n\", \"2\\n\", \"8\\n\", \"1\\n\", \"161\\n\", \"7\\n\", \"3\\n\", \"4\\n\", \"50\\n\", \"5\\n\", \"48\\n\", \"74\\n\", \"16\\n\", \"34\\n\", \"0\\n\", \"162\\n\", \"49\\n\", \"6\\n\", \"47\\n\", \"15\\n\", \"8\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"7\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"5\\n\", \"50\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"8\\n\", \"3\\n\", \"8\\n\", \"7\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"7\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"6\\n\", \"74\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"6\\n\", \"49\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"9\\n\", \"33\\n\", \"3\\n\", \"8\\n\", \"8\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
Vasya and Petya have invented a new game. Vasya takes a stripe consisting of 1 × n square and paints the squares black and white. After that Petya can start moves — during a move he may choose any two neighboring squares of one color and repaint these two squares any way he wants, perhaps in different colors. Petya can only repaint the squares in white and black colors. Petya’s aim is to repaint the stripe so that no two neighboring squares were of one color. Help Petya, using the given initial coloring, find the minimum number of moves Petya needs to win.
Input
The first line contains number n (1 ≤ n ≤ 1000) which represents the stripe’s length. The second line contains exactly n symbols — the line’s initial coloring. 0 corresponds to a white square, 1 corresponds to a black one.
Output
If Petya cannot win with such an initial coloring, print -1. Otherwise print the minimum number of moves Petya needs to win.
Examples
Input
6
111010
Output
1
Input
5
10001
Output
1
Input
7
1100010
Output
2
Input
5
00100
Output
2
Note
In the first sample Petya can take squares 1 and 2. He repaints square 1 to black and square 2 to white.
In the second sample Petya can take squares 2 and 3. He repaints square 2 to white and square 3 to black.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n1 2 3\\n\", \"4\\n2 1 3 2\\n\", \"20\\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\\n\", \"25\\n1 2 3 4 4 4 4 4 4 4 2 3 5 5 7 9 8 5 10 12 15 12 100500 800600 228228228\\n\", \"5\\n1 5 3 5 2\\n\", \"10\\n17 18 19 19 18 17 100 500 100 100\\n\", \"10\\n1 1 1 1 5 5 1 1 1 1\\n\", \"4\\n2 2 1 1\\n\", \"17\\n1 45 22 39 28 23 23 100 500 778 777 778 1001 1002 1005 1003 1005\\n\", \"1\\n1\\n\", \"101\\n1 50 170 148 214 153 132 234 181 188 180 225 226 200 197 122 181 168 87 220 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 246 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 149 104 72 303 291 124 237 112 165 183 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n1 1 1 1 2 2 2 2 4 3\\n\", \"10\\n1 2 2 2 2 2 2 2 2 1\\n\", \"20\\n1 2 2 2 5 6 6 6 7 7 8 9 15 15 16 16 17 18 19 19\\n\", \"25\\n1 2 3 4 4 6 4 4 4 4 2 3 5 5 7 9 8 5 10 12 15 12 100500 800600 228228228\\n\", \"5\\n1 5 1 5 2\\n\", \"10\\n17 18 19 19 18 17 100 500 100 101\\n\", \"17\\n1 45 22 39 28 12 23 100 500 778 777 778 1001 1002 1005 1003 1005\\n\", \"1\\n2\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 87 220 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 246 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 149 104 72 303 291 124 237 112 165 183 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n1 1 1 1 2 2 2 4 4 3\\n\", \"20\\n1 3 2 2 5 6 6 6 7 7 8 9 15 15 16 16 17 18 19 19\\n\", \"25\\n1 2 3 4 4 6 4 4 4 4 2 3 5 5 7 9 8 8 10 12 15 12 100500 800600 228228228\\n\", \"17\\n1 45 22 39 28 12 23 100 500 778 1245 778 1001 1002 1005 1003 1005\\n\", \"20\\n1 3 2 2 5 6 6 6 7 7 8 9 15 15 27 16 17 18 19 19\\n\", \"10\\n0 0 1 1 5 5 1 1 1 2\\n\", \"20\\n1 3 2 2 2 6 6 6 7 7 8 9 15 15 27 16 17 18 19 19\\n\", \"10\\n1 1 1 2 1 2 2 6 4 3\\n\", \"10\\n1 0 1 1 5 5 1 1 1 1\\n\", \"4\\n2 2 1 2\\n\", \"10\\n1 3 2 2 2 2 2 2 2 1\\n\", \"3\\n0 2 3\\n\", \"4\\n3 1 3 2\\n\", \"5\\n1 1 1 5 2\\n\", \"10\\n17 18 19 29 18 17 100 500 100 101\\n\", \"10\\n1 0 1 1 5 5 1 1 1 2\\n\", \"4\\n2 2 1 0\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 87 220 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 246 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 145 104 72 303 291 124 237 112 165 183 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n1 1 1 1 2 2 2 6 4 3\\n\", \"10\\n1 3 2 2 2 2 2 2 2 0\\n\", \"3\\n0 3 3\\n\", \"4\\n3 2 3 2\\n\", \"25\\n1 2 3 4 4 6 4 4 6 4 2 3 5 5 7 9 8 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n1 1 1 5 3\\n\", \"10\\n17 18 19 29 18 17 100 500 100 001\\n\", \"4\\n2 2 2 0\\n\", \"17\\n1 45 22 65 28 12 23 100 500 778 1245 778 1001 1002 1005 1003 1005\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 87 220 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 246 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 145 104 72 303 291 124 237 112 165 108 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n1 1 1 2 2 2 2 6 4 3\\n\", \"10\\n1 3 4 2 2 2 2 2 2 0\\n\", \"3\\n0 4 3\\n\", \"4\\n6 2 3 2\\n\", \"25\\n1 2 3 4 4 6 4 4 6 4 2 5 5 5 7 9 8 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n1 1 1 7 3\\n\", \"10\\n17 18 35 29 18 17 100 500 100 001\\n\", \"10\\n0 0 2 1 5 5 1 1 1 2\\n\", \"17\\n1 45 22 65 28 4 23 100 500 778 1245 778 1001 1002 1005 1003 1005\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 87 220 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 106 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 145 104 72 303 291 124 237 112 165 108 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n1 3 4 2 2 1 2 2 2 0\\n\", \"20\\n1 3 2 2 2 6 6 6 7 7 8 9 15 15 27 16 17 18 19 0\\n\", \"3\\n0 5 3\\n\", \"4\\n6 0 3 2\\n\", \"25\\n1 2 3 4 4 6 4 4 6 1 2 5 5 5 7 9 8 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n1 1 1 9 3\\n\", \"10\\n17 18 35 29 19 17 100 500 100 001\\n\", \"10\\n0 0 2 1 10 5 1 1 1 2\\n\", \"17\\n1 45 22 65 28 4 23 100 500 778 30 778 1001 1002 1005 1003 1005\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 160 220 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 106 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 145 104 72 303 291 124 237 112 165 108 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n1 1 1 2 1 2 2 6 1 3\\n\", \"10\\n1 3 4 2 2 1 3 2 2 0\\n\", \"20\\n1 3 2 2 2 6 6 6 7 7 8 9 0 15 27 16 17 18 19 0\\n\", \"3\\n1 5 3\\n\", \"4\\n6 0 2 2\\n\", \"25\\n1 2 3 5 4 6 4 4 6 1 2 5 5 5 7 9 8 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n0 1 1 9 3\\n\", \"10\\n17 18 35 29 19 17 100 500 110 001\\n\", \"10\\n0 0 2 1 17 5 1 1 1 2\\n\", \"17\\n1 45 22 65 28 4 23 100 500 746 30 778 1001 1002 1005 1003 1005\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 160 132 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 106 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 304 259 135 145 104 72 303 291 124 237 112 165 108 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n0 1 1 2 1 2 2 6 1 3\\n\", \"20\\n1 3 2 2 2 6 6 6 7 7 8 9 0 15 27 11 17 18 19 0\\n\", \"3\\n1 5 6\\n\", \"4\\n11 0 2 2\\n\", \"25\\n1 2 3 5 4 6 4 4 6 1 2 5 5 5 7 9 9 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n0 1 1 9 2\\n\", \"10\\n17 18 35 40 19 17 100 500 110 001\\n\", \"10\\n0 0 1 1 17 5 1 1 1 2\\n\", \"17\\n1 45 22 65 28 4 23 100 500 746 30 77 1001 1002 1005 1003 1005\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 160 132 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 106 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 179 285 104 99 139 122 188 184 215 242 244 115 197 259 135 145 104 72 303 291 124 237 112 165 108 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n0 1 1 2 1 2 2 8 1 3\\n\", \"20\\n0 3 2 2 2 6 6 6 7 7 8 9 0 15 27 11 17 18 19 0\\n\", \"3\\n2 5 3\\n\", \"4\\n11 0 2 4\\n\", \"25\\n1 2 0 5 4 6 4 4 6 1 2 5 5 5 7 9 9 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n0 1 1 8 2\\n\", \"10\\n27 18 35 40 19 17 100 500 110 001\\n\", \"10\\n0 0 1 1 17 5 1 1 1 1\\n\", \"17\\n1 45 22 65 28 4 23 100 500 746 21 77 1001 1002 1005 1003 1005\\n\", \"101\\n1 50 170 269 214 153 132 234 181 188 180 225 226 200 197 122 181 168 160 132 223 160 235 94 257 145 199 235 102 146 119 60 109 134 209 260 210 191 180 271 236 195 155 169 166 143 106 102 208 137 278 269 156 251 198 165 111 198 151 213 256 121 276 163 72 285 104 99 139 122 188 184 215 242 244 115 197 259 135 145 104 72 303 291 124 237 112 165 108 168 71 139 85 131 137 107 120 267 235 337 69\\n\", \"10\\n0 1 1 2 1 2 2 14 1 3\\n\", \"20\\n0 3 2 2 2 6 6 6 5 7 8 9 0 15 27 11 17 18 19 0\\n\", \"3\\n1 6 3\\n\", \"4\\n11 0 2 3\\n\", \"25\\n1 2 0 5 4 6 4 4 4 1 2 5 5 5 7 9 9 8 10 12 15 12 100500 800600 228228228\\n\", \"5\\n0 1 1 16 2\\n\", \"10\\n27 18 35 40 19 17 100 500 111 001\\n\", \"10\\n0 1 1 1 17 5 1 1 1 2\\n\"], \"outputs\": [\"3\\n\", \"2\\n\", \"20\\n\", \"12\\n\", \"2\\n\", \"4\\n\", \"5\\n\", \"1\\n\", \"10\\n\", \"1\\n\", \"3\\n\", \"9\\n\", \"2\\n\", \"20\\n\", \"9\\n\", \"2\\n\", \"4\\n\", \"10\\n\", \"1\\n\", \"3\\n\", \"8\\n\", \"18\\n\", \"11\\n\", \"6\\n\", \"13\\n\", \"5\\n\", \"12\\n\", \"7\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"8\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"11\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"6\\n\", \"3\\n\", \"8\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"11\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"6\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"10\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"7\\n\", \"3\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"10\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"7\\n\", \"3\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"10\\n\", \"4\\n\", \"1\\n\", \"5\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"9\\n\", \"4\\n\", \"1\\n\", \"5\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"9\\n\", \"4\\n\", \"1\\n\", \"5\\n\"]}", "source": "primeintellect"}
|
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi ≤ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks — groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 ≤ hi ≤ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"10 15\\n\", \"1 3\\n\", \"222145 353252\\n\", \"1 100\\n\", \"192 200\\n\", \"213 221442\\n\", \"100 10000\\n\", \"1000000 1000000\\n\", \"1 1000000\\n\", \"1 999999\\n\", \"2 1000000\\n\", \"111 200\\n\", \"371 221442\\n\", \"100 11000\\n\", \"15 15\\n\", \"2 3\\n\", \"110 200\\n\", \"443 221442\\n\", \"100 11001\\n\", \"15 28\\n\", \"110 114\\n\", \"179 221442\\n\", \"15 35\\n\", \"010 114\\n\", \"259 221442\\n\", \"15 23\\n\", \"011 114\\n\", \"45 221442\\n\", \"011 37\\n\", \"55 221442\\n\", \"010 37\\n\", \"61 221442\\n\", \"71 221442\\n\", \"71 330037\\n\", \"68 330037\\n\", \"68 364259\\n\", \"68 51105\\n\", \"68 91491\\n\", \"2 91491\\n\", \"1 91491\\n\", \"188883 353252\\n\", \"1 110\\n\", \"124 200\\n\", \"90 221442\\n\", \"110 10000\\n\", \"371 265465\\n\", \"111 10000\\n\", \"1 1\\n\", \"011 200\\n\", \"443 390308\\n\", \"110 11001\\n\", \"18 28\\n\", \"119 221442\\n\", \"7 35\\n\", \"110 139\\n\", \"259 220246\\n\", \"011 224\\n\", \"51 221442\\n\", \"55 125960\\n\", \"61 304788\\n\", \"3 221442\\n\", \"4 330037\\n\", \"58 330037\\n\", \"68 36212\\n\", \"68 101722\\n\", \"68 140887\\n\", \"2 14774\\n\", \"1 90095\\n\", \"188883 240204\\n\", \"168 221442\\n\", \"1 4\\n\", \"371 199916\\n\", \"101 10000\\n\", \"111 367\\n\", \"426 390308\\n\", \"1 2\\n\"], \"outputs\": [\"39\\n\", \"12\\n\", \"3860750\\n\", \"928\\n\", \"122\\n\", \"5645356\\n\", \"188446\\n\", \"38\\n\", \"28733372\\n\", \"28733334\\n\", \"28733370\\n\", \"1058\\n\", \"5643032\\n\", \"211142\\n\", \"7\\n\", \"10\\n\", \"1068\\n\", \"5642016\\n\", \"211160\\n\", \"125\\n\", \"42\\n\", \"5645828\\n\", \"193\\n\", \"1042\\n\", \"5644701\\n\", \"75\\n\", \"1034\\n\", \"5647291\\n\", \"236\\n\", \"5647197\\n\", \"244\\n\", \"5647133\\n\", \"5647027\\n\", \"8851907\\n\", \"8851941\\n\", \"9857076\\n\", \"1160849\\n\", \"2164367\\n\", \"2164947\\n\", \"2164949\\n\", \"4803878\\n\", \"1053\\n\", \"933\\n\", \"5646838\\n\", \"188317\\n\", \"6939290\\n\", \"188307\\n\", \"2\\n\", \"2060\\n\", \"10631342\\n\", \"211031\\n\", \"105\\n\", \"5646521\\n\", \"241\\n\", \"327\\n\", \"5609776\\n\", \"2393\\n\", \"5647233\\n\", \"3050982\\n\", \"8126744\\n\", \"5647636\\n\", \"8852511\\n\", \"8852048\\n\", \"801248\\n\", \"2429117\\n\", \"3450308\\n\", \"289877\\n\", \"2129996\\n\", \"1479377\\n\", \"5645945\\n\", \"16\\n\", \"5026239\\n\", \"188432\\n\", \"3509\\n\", \"10631576\\n\", \"7\\n\"]}", "source": "primeintellect"}
|
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then — 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 ≤ a ≤ b ≤ 106) — the first and the last number typed by Max.
Output
Print the only integer a — the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"4\\n1 1 1 1\\n\", \"3\\n1 2 3\\n\", \"7\\n1 3 5 15 3 105 35\\n\", \"1\\n1\\n\", \"5\\n10 8 6 4 6\\n\", \"5\\n5 1 3 5 4\\n\", \"10\\n9 6 8 5 5 2 8 9 2 2\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 781 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 455 746 950 41 585 549 892 687 264 41 487 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 559 405 851 919 128 318 698 820 409 547 43 777 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 6 86 11 33 19 46 70 79 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 81 81 8 25 87 23 76 100 53 11 36 19 87 89 53 65 97 67 3 65 88 87\\n\", \"5\\n5 1 6 6 6\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 143 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 191 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 107 137 99 55 189 2 118 55 27 4 198 23 79 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 98 42 179 166 99 192 1 185 114 173 152 187 57 21 132 88 152 55 110 51 1 30 147 153 34 115 59 3 78 16 19 136 188 134 28 48 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"10\\n2 2 16 16 14 1 9 12 15 13\\n\", \"1\\n100000\\n\", \"5\\n20 8 6 4 6\\n\", \"5\\n5 1 1 5 4\\n\", \"10\\n9 6 8 5 5 2 8 2 2 2\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 781 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 455 746 950 41 585 549 892 687 264 41 487 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 777 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 6 86 11 33 19 46 70 79 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 81 81 8 22 87 23 76 100 53 11 36 19 87 89 53 65 97 67 3 65 88 87\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 143 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 107 137 99 55 189 2 118 55 27 4 198 23 79 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 132 88 152 55 110 51 1 30 147 153 34 115 59 3 78 16 19 136 188 134 28 48 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"10\\n2 2 16 16 14 1 9 12 3 13\\n\", \"3\\n1 2 5\\n\", \"7\\n1 3 5 4 3 105 35\\n\", \"5\\n7 8 6 4 6\\n\", \"10\\n9 6 8 5 9 2 8 2 2 2\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 781 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 187 746 950 41 585 549 892 687 264 41 487 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 777 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 6 86 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 81 81 8 22 87 23 76 100 53 11 36 19 87 89 53 65 97 67 3 65 88 87\\n\", \"5\\n5 1 10 1 6\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 256 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 107 137 99 55 189 2 118 55 27 4 198 23 79 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 80 88 152 55 110 51 1 30 147 153 34 115 59 3 78 16 19 136 188 134 28 48 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"3\\n1 1 5\\n\", \"7\\n1 3 5 4 3 93 35\\n\", \"10\\n9 6 8 5 9 2 8 2 3 2\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 781 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 187 746 950 41 585 549 892 687 264 41 551 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 777 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 5 86 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 81 81 8 22 87 23 76 100 53 11 36 19 87 89 53 65 97 67 3 65 88 87\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 256 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 107 137 99 55 189 2 118 55 27 4 198 16 79 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 80 88 152 55 110 51 1 30 147 153 34 115 59 3 143 16 19 136 188 134 28 48 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"3\\n1 1 1\\n\", \"7\\n1 4 5 4 3 93 35\\n\", \"5\\n7 14 6 4 12\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 635 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 187 746 950 41 585 549 892 687 264 41 551 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 777 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 5 86 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 81 81 8 22 87 23 76 100 53 16 36 19 87 89 53 65 97 67 3 65 88 87\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 256 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 107 137 99 55 189 2 118 55 27 4 198 16 102 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 80 88 152 55 110 51 1 30 147 153 34 115 59 3 143 16 19 136 188 134 28 17 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"10\\n9 6 8 5 18 4 8 2 3 2\\n\", \"5\\n5 1 15 1 1\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 80 88 152 55 110 51 1 30 142 153 34 115 59 3 143 16 19 136 188 134 28 17 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"5\\n7 14 6 4 5\\n\", \"10\\n15 6 8 5 18 4 8 2 3 2\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 635 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 187 2 950 41 585 549 892 687 264 41 551 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 730 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 5 86 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 141 81 8 22 87 23 76 100 53 16 36 19 87 110 53 65 97 67 3 65 88 87\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 256 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 132 137 99 55 189 4 118 55 27 4 198 16 102 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 80 88 152 55 110 51 1 30 142 153 34 115 59 3 143 16 19 136 123 134 28 17 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 635 434 307 164 154 241 381 38 942 680 906 240 15 431 478 628 959 346 74 493 964 187 2 950 41 585 549 892 687 264 41 551 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 730 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 90 20 84 5 86 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 141 81 8 22 87 23 76 100 53 16 36 19 87 110 53 65 97 67 3 65 88 87\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 256 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 143 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 132 137 99 55 189 4 118 55 27 4 198 16 102 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"50\\n166 126 44 42 179 166 99 192 1 185 114 173 152 187 57 21 80 21 152 55 110 51 1 30 142 153 34 115 59 3 143 16 19 136 123 134 28 17 54 120 97 74 108 54 181 79 143 187 51 4\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 635 434 307 164 154 241 381 38 942 680 906 240 15 431 478 775 959 346 74 493 964 187 2 950 41 585 549 892 687 264 41 551 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 730 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 90 20 84 5 67 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 141 81 8 22 87 23 76 100 53 16 36 19 87 110 53 65 97 67 3 65 88 87\\n\", \"5\\n5 1 6 1 6\\n\", \"10\\n2 2 16 16 14 1 12 12 3 13\\n\", \"5\\n7 8 6 4 12\\n\", \"5\\n5 1 15 1 6\\n\", \"10\\n2 4 16 16 14 1 12 12 3 13\\n\", \"10\\n9 6 8 5 9 4 8 2 3 2\\n\", \"5\\n5 1 15 1 2\\n\", \"5\\n7 14 6 4 8\\n\", \"100\\n881 479 355 759 257 497 690 598 275 446 439 787 257 326 584 713 322 5 253 635 434 307 164 154 241 381 38 942 680 906 240 11 431 478 628 959 346 74 493 964 187 2 950 41 585 549 892 687 264 41 551 676 63 453 861 980 477 901 80 907 285 506 619 748 773 743 56 925 651 685 845 313 419 504 770 324 2 430 405 851 919 128 318 698 820 409 547 43 777 496 925 918 162 725 481 83 220 203 609 617\\n\", \"50\\n17 81 20 84 5 86 11 33 19 46 70 78 23 64 40 99 78 70 3 10 32 42 18 73 35 36 69 90 141 81 8 22 87 23 76 100 53 16 36 19 87 89 53 65 97 67 3 65 88 87\\n\", \"100\\n154 163 53 13 186 87 143 114 17 111 256 108 102 111 158 171 69 74 67 18 87 43 80 104 63 109 19 113 86 52 119 91 15 154 9 153 140 91 19 19 70 193 76 84 50 128 173 27 120 83 6 59 65 5 135 59 162 121 15 110 146 107 137 99 55 189 4 118 55 27 4 198 16 102 167 125 72 30 74 163 44 184 166 43 198 116 68 5 47 138 121 146 98 103 89 75 137 36 146 195\\n\", \"5\\n7 14 8 4 5\\n\", \"10\\n15 6 8 5 18 7 8 2 3 2\\n\", \"5\\n7 14 8 2 5\\n\", \"10\\n14 6 8 5 18 7 8 2 3 2\\n\"], \"outputs\": [\"15\", \"5\", \"100\", \"1\", \"0\", \"26\", \"951\", \"934190491\", \"896338157\", \"23\", \"363088732\", \"763698643\", \"953\", \"0\", \"0\\n\", \"27\\n\", \"891\\n\", \"908853756\\n\", \"894241999\\n\", \"339716574\\n\", \"763698419\\n\", \"953\\n\", \"5\\n\", \"113\\n\", \"15\\n\", \"889\\n\", \"910981622\\n\", \"889523658\\n\", \"26\\n\", \"293240606\\n\", \"764220850\\n\", \"6\\n\", \"116\\n\", \"945\\n\", \"910981600\\n\", \"894240970\\n\", \"200279978\\n\", \"831590579\\n\", \"7\\n\", \"118\\n\", \"14\\n\", \"908886498\\n\", \"890046698\\n\", \"424456921\\n\", \"865275443\\n\", \"883\\n\", \"28\\n\", \"831786555\\n\", \"21\\n\", \"882\\n\", \"866617891\\n\", \"881656143\\n\", \"872806828\\n\", \"865275451\\n\", \"849841731\\n\", \"864875343\\n\", \"244640919\\n\", \"881921839\\n\", \"879544818\\n\", \"881652557\\n\", \"27\\n\", \"891\\n\", \"15\\n\", \"26\\n\", \"891\\n\", \"945\\n\", \"27\\n\", \"14\\n\", \"908886498\\n\", \"890046698\\n\", \"424456921\\n\", \"21\\n\", \"945\\n\", \"21\\n\", \"889\\n\"]}", "source": "primeintellect"}
|
Let's call a non-empty sequence of positive integers a1, a2... ak coprime if the greatest common divisor of all elements of this sequence is equal to 1.
Given an array a consisting of n positive integers, find the number of its coprime subsequences. Since the answer may be very large, print it modulo 109 + 7.
Note that two subsequences are considered different if chosen indices are different. For example, in the array [1, 1] there are 3 different subsequences: [1], [1] and [1, 1].
Input
The first line contains one integer number n (1 ≤ n ≤ 100000).
The second line contains n integer numbers a1, a2... an (1 ≤ ai ≤ 100000).
Output
Print the number of coprime subsequences of a modulo 109 + 7.
Examples
Input
3
1 2 3
Output
5
Input
4
1 1 1 1
Output
15
Input
7
1 3 5 15 3 105 35
Output
100
Note
In the first example coprime subsequences are:
1. 1
2. 1, 2
3. 1, 3
4. 1, 2, 3
5. 2, 3
In the second example all subsequences are coprime.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"3\\n111\\n\", \"8\\n11010111\\n\", \"10\\n1000010110\\n\", \"9\\n001011001\\n\", \"10\\n0011011111\\n\", \"11\\n00010000011\\n\", \"10\\n0100000000\\n\", \"15\\n100000100000011\\n\", \"18\\n110010101101111111\\n\", \"3\\n011\\n\", \"45\\n011010001100001111110001011100000001101100111\\n\", \"11\\n00001000100\\n\", \"13\\n0001000011010\\n\", \"19\\n0000011111111100000\\n\", \"2\\n01\\n\", \"65\\n11001000110001001011011110111100000000101001001010101111000100010\\n\", \"18\\n000001111111100000\\n\", \"12\\n110000110000\\n\", \"4\\n0101\\n\", \"14\\n01111101111111\\n\", \"12\\n000101011001\\n\", \"14\\n00000100101011\\n\", \"2\\n10\\n\", \"14\\n11111111111111\\n\", \"4\\n1110\\n\", \"3\\n110\\n\", \"14\\n11000011000000\\n\", \"3\\n001\\n\", \"18\\n011010101110111101\\n\", \"10\\n0011111000\\n\", \"13\\n1110000001110\\n\", \"10\\n1000010111\\n\", \"9\\n001111001\\n\", \"10\\n0011011110\\n\", \"11\\n00010000001\\n\", \"10\\n0101000000\\n\", \"18\\n010010101101111111\\n\", \"45\\n011010001101001111110001011100000001101100111\\n\", \"19\\n0000011110111100000\\n\", \"65\\n11001000110101001011011110111100000000101001001010101111000100010\\n\", \"18\\n000001111111100010\\n\", \"3\\n000\\n\", \"65\\n11001001110101001011011110111100000000101001001010101111000100010\\n\", \"18\\n011010001100111101\\n\", \"45\\n011010001101001011110001001100000001101100111\\n\", \"15\\n100000110000011\\n\", \"3\\n101\\n\", \"11\\n00011000100\\n\", \"13\\n0001100011010\\n\", \"12\\n110000111000\\n\", \"4\\n0100\\n\", \"14\\n01011101111111\\n\", \"12\\n000100011001\\n\", \"14\\n00000100001011\\n\", \"14\\n11111111011111\\n\", \"4\\n1100\\n\", \"3\\n010\\n\", \"14\\n10000011000000\\n\", \"18\\n011010101100111101\\n\", \"10\\n0111111000\\n\", \"13\\n1110000001100\\n\", \"3\\n100\\n\", \"8\\n11010110\\n\", \"10\\n1100010111\\n\", \"9\\n001110001\\n\", \"10\\n0111011111\\n\", \"11\\n10010000001\\n\", \"10\\n0101000010\\n\", \"15\\n100100110000011\\n\", \"18\\n010010101101111101\\n\", \"45\\n011010001101001111110001001100000001101100111\\n\", \"11\\n00011000110\\n\", \"13\\n0011100011010\\n\", \"19\\n0000111110111100000\\n\", \"18\\n000001110111100010\\n\", \"12\\n110001111000\\n\", \"4\\n0001\\n\", \"14\\n01010101111111\\n\", \"12\\n000100001001\\n\", \"14\\n00000100011011\\n\", \"14\\n11111101011111\\n\", \"4\\n0000\\n\", \"14\\n10000111000000\\n\", \"10\\n0011111010\\n\", \"13\\n1110000001010\\n\", \"8\\n10010110\\n\", \"10\\n1100110111\\n\", \"9\\n000110001\\n\", \"10\\n1111011111\\n\", \"11\\n10010000000\\n\", \"10\\n0111000010\\n\", \"15\\n100100110000111\\n\", \"18\\n010010101101110101\\n\", \"11\\n00011000010\\n\", \"13\\n0011101011010\\n\", \"19\\n0000111110011100000\\n\", \"65\\n11001001110101001011011110111100000000101001001010101111000100011\\n\", \"18\\n000000110111100010\\n\", \"12\\n100001111000\\n\", \"4\\n1010\\n\", \"14\\n01010001111111\\n\", \"12\\n000110001001\\n\", \"14\\n00000100001111\\n\", \"14\\n11101101011111\\n\", \"4\\n1001\\n\", \"14\\n10100011000000\\n\", \"18\\n011010011100111101\\n\", \"10\\n0011101010\\n\", \"13\\n1110010001010\\n\", \"8\\n01010110\\n\", \"10\\n1100110101\\n\", \"9\\n000110101\\n\", \"10\\n1110011111\\n\", \"11\\n10010000100\\n\", \"10\\n0111000110\\n\", \"15\\n100110110000111\\n\", \"18\\n010010111101110101\\n\", \"45\\n011010001101001011110001001100000001100100111\\n\", \"11\\n00011010010\\n\", \"13\\n0011111011010\\n\", \"19\\n0000111110011101000\\n\", \"65\\n11001001100101001011011110111100000000101001001010101111000100011\\n\", \"18\\n010000110111100010\\n\", \"12\\n000001111000\\n\", \"4\\n0010\\n\", \"14\\n01011001111111\\n\"], \"outputs\": [\"0\\n\", \"4\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"10\\n\", \"2\\n\", \"44\\n\", \"2\\n\", \"6\\n\", \"18\\n\", \"2\\n\", \"48\\n\", \"16\\n\", \"8\\n\", \"4\\n\", \"2\\n\", \"10\\n\", \"10\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"8\\n\", \"2\\n\", \"8\\n\", \"10\\n\", \"12\\n\", \"10\\n\", \"8\\n\", \"6\\n\", \"2\\n\", \"4\\n\", \"12\\n\", \"44\\n\", \"16\\n\", \"56\\n\", \"18\\n\", \"0\\n\", \"60\\n\", \"14\\n\", \"28\\n\", \"4\\n\", \"2\\n\", \"6\\n\", \"10\\n\", \"10\\n\", \"2\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"4\\n\", \"12\\n\", \"6\\n\", \"6\\n\", \"2\\n\", \"6\\n\", \"8\\n\", \"8\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"8\\n\", \"12\\n\", \"44\\n\", \"8\\n\", \"12\\n\", \"18\\n\", \"16\\n\", \"12\\n\", \"2\\n\", \"8\\n\", \"4\\n\", \"10\\n\", \"4\\n\", \"0\\n\", \"8\\n\", \"4\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"6\\n\", \"2\\n\", \"4\\n\", \"8\\n\", \"12\\n\", \"12\\n\", \"4\\n\", \"8\\n\", \"16\\n\", \"60\\n\", \"14\\n\", \"10\\n\", \"4\\n\", \"10\\n\", \"6\\n\", \"10\\n\", \"6\\n\", \"4\\n\", \"8\\n\", \"12\\n\", \"10\\n\", \"12\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"4\\n\", \"4\\n\", \"10\\n\", \"14\\n\", \"8\\n\", \"28\\n\", \"8\\n\", \"6\\n\", \"18\\n\", \"56\\n\", \"16\\n\", \"8\\n\", \"2\\n\", \"8\\n\"]}", "source": "primeintellect"}
|
You are given a string s consisting only of characters 0 and 1. A substring [l, r] of s is a string slsl + 1sl + 2... sr, and its length equals to r - l + 1. A substring is called balanced if the number of zeroes (0) equals to the number of ones in this substring.
You have to determine the length of the longest balanced substring of s.
Input
The first line contains n (1 ≤ n ≤ 100000) — the number of characters in s.
The second line contains a string s consisting of exactly n characters. Only characters 0 and 1 can appear in s.
Output
If there is no non-empty balanced substring in s, print 0. Otherwise, print the length of the longest balanced substring.
Examples
Input
8
11010111
Output
4
Input
3
111
Output
0
Note
In the first example you can choose the substring [3, 6]. It is balanced, and its length is 4. Choosing the substring [2, 5] is also possible.
In the second example it's impossible to find a non-empty balanced substring.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"3\\n1 1 1\\n\", \"4\\n1 1 2 1\\n\", \"2\\n2 2\\n\", \"7\\n2 2 2 1 1 1 1\\n\", \"10\\n1 2 2 1 2 2 1 2 1 1\\n\", \"3\\n1 2 2\\n\", \"10\\n2 2 1 1 1 1 1 1 1 1\\n\", \"4\\n1 1 1 1\\n\", \"3\\n2 2 2\\n\", \"247\\n2 2 1 2 1 2 2 2 2 2 2 1 1 2 2 1 2 1 1 1 2 1 1 1 1 2 1 1 2 2 1 2 1 1 1 2 2 2 1 1 2 1 1 2 1 1 1 2 1 2 1 2 2 1 1 2 1 2 2 1 2 1 2 1 1 2 1 1 1 2 2 1 1 2 2 1 1 2 1 1 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 2 2 1 2 2 2 1 1 2 2 1 1 1 2 1 1 1 1 2 2 1 2 2 1 1 1 2 1 2 2 1 2 1 1 1 2 2 2 2 2 1 2 2 2 1 1 1 2 1 2 1 1 2 2 2 2 1 1 2 2 2 1 2 2 2 1 2 1 1 2 2 2 2 1 2 2 1 1 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 1 1 1 2 1 1 1 1 2 2 1 2 1 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 1 1 2 2 2\\n\", \"4\\n2 2 2 2\\n\", \"2\\n2 1\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 1 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"5\\n1 1 1 1 2\\n\", \"7\\n1 1 2 2 1 2 1\\n\", \"2\\n1 1\\n\", \"4\\n1 1 1 2\\n\", \"26\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2\\n\", \"64\\n2 2 1 1 1 2 1 1 1 2 2 1 2 2 2 1 2 2 2 1 1 1 1 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 2 1 2 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 2\\n\", \"20\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"20\\n1 1 1 1 2 1 2 2 2 1 2 1 2 1 2 1 1 2 1 2\\n\", \"3\\n2 2 1\\n\", \"5\\n2 2 2 1 2\\n\", \"72\\n1 2 1 2 2 1 2 1 1 1 1 2 2 1 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 2 1 1 1 2 2 2\\n\", \"14\\n1 2 2 2 2 2 2 2 2 2 2 2 2 2\\n\", \"4\\n2 1 1 1\\n\", \"3\\n2 1 1\\n\", \"5\\n2 1 1 1 1\\n\", \"3\\n1 2 1\\n\", \"6\\n1 1 1 2 2 2\\n\", \"4\\n1 2 2 2\\n\", \"38\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"30\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"3\\n2 1 2\\n\", \"5\\n2 2 1 1 1\\n\", \"43\\n1 2 2 2 1 1 2 2 1 1 2 2 2 2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2\\n\", \"2\\n1 2\\n\", \"4\\n1 1 2 2\\n\", \"3\\n1 1 2\\n\", \"6\\n1 1 1 1 1 1\\n\", \"9\\n1 1 1 1 1 1 2 2 2\\n\", \"23\\n1 1 1 1 2 1 2 1 1 1 2 2 2 2 2 2 1 2 1 2 2 1 1\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"5\\n2 1 2 1 1\\n\", \"9\\n2 1 1 1 1 1 2 2 2\\n\", \"23\\n2 1 1 1 2 1 2 1 1 1 2 2 2 2 2 2 1 2 1 2 2 1 1\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 1 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"38\\n2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"26\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n\", \"20\\n1 1 1 1 2 1 2 2 2 1 2 2 2 1 2 1 1 2 1 2\\n\", \"72\\n1 2 1 2 2 1 2 1 1 1 1 2 1 1 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 2 1 1 1 2 2 2\\n\", \"6\\n1 2 2 2 2 2\\n\", \"20\\n1 1 1 1 2 2 2 2 2 1 2 2 2 1 2 1 1 2 1 2\\n\", \"247\\n2 2 1 2 1 2 2 2 2 2 2 1 1 2 2 1 2 1 1 1 2 1 1 1 1 2 1 1 2 2 1 2 1 1 1 2 2 2 1 1 2 1 1 2 1 1 1 2 1 2 1 2 2 1 1 2 1 2 2 1 2 1 2 1 1 2 1 1 1 2 2 1 1 2 2 1 1 2 1 1 1 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 2 2 1 2 2 2 1 1 2 2 1 1 1 2 1 1 1 1 2 2 1 2 2 1 1 1 2 1 2 2 1 2 1 1 1 2 2 2 2 2 1 2 2 2 1 1 1 2 1 2 1 1 2 2 2 2 1 1 2 2 2 1 2 2 2 1 2 1 1 2 2 2 2 1 2 2 1 1 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 1 1 1 2 1 1 1 1 2 2 1 2 1 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 1 1 2 2 2\\n\", \"64\\n2 2 1 1 1 2 1 1 1 2 2 1 2 2 2 1 2 2 2 1 1 1 1 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 2 1 1 2 1 2 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 2\\n\", \"72\\n1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 1 1 1 1 2 2 2\\n\", \"72\\n1 2 1 2 2 1 2 1 1 1 1 2 2 1 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 2 2 1 1 2 2 2\\n\", \"6\\n1 2 1 2 2 2\\n\", \"38\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"6\\n2 1 1 1 1 1\\n\", \"6\\n2 1 1 1 1 2\\n\", \"10\\n2 2 2 1 2 2 1 2 1 1\\n\", \"7\\n1 1 1 2 1 2 1\\n\", \"4\\n1 2 2 1\\n\", \"5\\n2 2 2 1 1\\n\", \"6\\n1 1 1 1 2 1\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 1 1 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"5\\n2 1 2 2 1\\n\", \"6\\n1 1 2 2 2 2\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 1 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 1 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"38\\n2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1\\n\", \"6\\n1 2 2 2 1 2\\n\", \"5\\n2 1 2 2 2\\n\", \"6\\n2 1 2 2 2 2\\n\", \"10\\n2 1 1 1 1 1 1 1 1 1\\n\", \"4\\n2 2 2 1\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 2 2 2 1 1 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"5\\n1 1 1 1 1\\n\", \"20\\n2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1\\n\", \"72\\n1 2 1 2 2 1 2 1 1 1 1 2 2 1 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 1 1 1 1 2 2 2\\n\", \"14\\n1 2 2 2 1 2 2 2 2 2 2 2 2 2\\n\", \"4\\n2 1 2 1\\n\", \"4\\n2 1 2 2\\n\", \"6\\n2 2 1 2 2 2\\n\", \"38\\n2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"6\\n2 1 1 1 2 1\\n\", \"23\\n2 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 2 1 2 2 1 1\\n\", \"6\\n1 1 1 1 1 2\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 1 1 1 2 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"201\\n1 1 1 2 2 2 1 1 1 2 2 1 2 1 1 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 1 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"20\\n1 1 1 1 2 1 1 2 2 1 2 2 2 1 2 1 1 2 1 2\\n\", \"6\\n2 2 2 2 1 2\\n\", \"10\\n2 1 1 1 2 1 1 1 1 1\\n\", \"14\\n2 2 2 2 1 2 2 2 2 2 2 2 2 2\\n\", \"23\\n2 1 1 1 2 2 1 1 1 1 2 2 2 2 2 2 1 2 1 2 2 1 1\\n\", \"6\\n1 1 1 1 2 2\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 1 1 1 2 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 1 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"14\\n2 2 2 2 1 2 2 1 2 2 2 2 2 2\\n\", \"23\\n2 1 1 1 2 2 1 2 1 1 2 2 2 2 2 2 1 2 1 2 2 1 1\\n\", \"14\\n2 2 2 2 1 2 2 1 2 2 2 2 1 2\\n\", \"14\\n2 2 2 2 1 1 2 1 2 2 2 2 1 2\\n\", \"10\\n1 2 2 1 2 2 1 2 1 2\\n\", \"201\\n1 1 2 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 1 2 2 2 1 1 1 2 1 1 2 1 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 2\\n\", \"4\\n1 2 1 2\\n\", \"64\\n2 2 1 1 1 2 1 1 1 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 2 1 2 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 2\\n\", \"20\\n2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1\\n\", \"14\\n1 2 1 2 2 2 2 2 2 2 2 2 2 2\\n\", \"38\\n2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\", \"30\\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1\\n\"], \"outputs\": [\"1\", \"1\", \"0\", \"3\", \"5\", \"1\", \"4\", \"1\", \"0\", \"123\", \"0\", \"1\", \"100\", \"2\", \"3\", \"0\", \"1\", \"1\", \"32\", \"1\", \"9\", \"1\", \"1\", \"34\", \"1\", \"1\", \"1\", \"2\", \"1\", \"3\", \"1\", \"1\", \"1\", \"1\", \"2\", \"10\", \"1\", \"2\", \"1\", \"2\", \"4\", \"11\", \"99\\n\", \"2\\n\", \"4\\n\", \"11\\n\", \"100\\n\", \"3\\n\", \"0\\n\", \"10\\n\", \"35\\n\", \"1\\n\", \"9\\n\", \"123\\n\", \"31\\n\", \"36\\n\", \"33\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"100\\n\", \"2\\n\", \"2\\n\", \"100\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"99\\n\", \"1\\n\", \"2\\n\", \"35\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"10\\n\", \"2\\n\", \"99\\n\", \"100\\n\", \"9\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"11\\n\", \"2\\n\", \"100\\n\", \"2\\n\", \"10\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"100\\n\", \"2\\n\", \"31\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\"]}", "source": "primeintellect"}
|
There were n groups of students which came to write a training contest. A group is either one person who can write the contest with anyone else, or two people who want to write the contest in the same team.
The coach decided to form teams of exactly three people for this training. Determine the maximum number of teams of three people he can form. It is possible that he can't use all groups to form teams. For groups of two, either both students should write the contest, or both should not. If two students from a group of two will write the contest, they should be in the same team.
Input
The first line contains single integer n (2 ≤ n ≤ 2·105) — the number of groups.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 2), where ai is the number of people in group i.
Output
Print the maximum number of teams of three people the coach can form.
Examples
Input
4
1 1 2 1
Output
1
Input
2
2 2
Output
0
Input
7
2 2 2 1 1 1 1
Output
3
Input
3
1 1 1
Output
1
Note
In the first example the coach can form one team. For example, he can take students from the first, second and fourth groups.
In the second example he can't make a single team.
In the third example the coach can form three teams. For example, he can do this in the following way:
* The first group (of two people) and the seventh group (of one person),
* The second group (of two people) and the sixth group (of one person),
* The third group (of two people) and the fourth group (of one person).
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"6\\n10 8 5 3 50 45\\n\", \"5\\n10 3 1 10 11\\n\", \"7\\n10 4 6 3 2 8 15\\n\", \"13\\n16 14 12 9 11 28 30 21 35 30 32 31 43\\n\", \"13\\n18 9 8 9 23 20 18 18 33 25 31 37 36\\n\", \"2\\n1 1000000000\\n\", \"2\\n1000000000 1\\n\", \"15\\n18 6 18 21 14 20 13 9 18 20 28 13 19 25 21\\n\", \"12\\n5 1 2 5 100 1 1000 100 10000 20000 10000 20000\\n\", \"10\\n15 21 17 22 27 21 31 26 32 30\\n\", \"15\\n14 4 5 12 6 19 14 19 12 22 23 17 14 21 27\\n\", \"11\\n15 17 18 18 26 22 23 33 33 21 29\\n\", \"10\\n18 20 18 17 17 13 22 20 34 29\\n\", \"5\\n15 1 8 15 3\\n\", \"13\\n16 14 12 9 11 28 30 21 35 30 32 31 86\\n\", \"13\\n18 9 8 9 23 20 18 18 33 10 31 37 36\\n\", \"2\\n1 1001000000\\n\", \"2\\n1000000000 0\\n\", \"15\\n18 6 33 21 14 20 13 9 18 20 28 13 19 25 21\\n\", \"12\\n5 1 2 7 100 1 1000 100 10000 20000 10000 20000\\n\", \"10\\n15 21 17 22 27 21 31 11 32 30\\n\", \"15\\n14 4 5 15 6 19 14 19 12 22 23 17 14 21 27\\n\", \"11\\n15 17 18 18 8 22 23 33 33 21 29\\n\", \"10\\n18 17 18 17 17 13 22 20 34 29\\n\", \"5\\n2 1 8 15 3\\n\", \"6\\n10 8 5 0 50 45\\n\", \"5\\n10 3 1 5 11\\n\", \"7\\n10 2 6 3 2 8 15\\n\", \"13\\n16 14 12 9 11 28 37 21 35 30 32 31 86\\n\", \"15\\n18 6 33 21 14 20 20 9 18 20 28 13 19 25 21\\n\", \"12\\n5 1 2 7 100 1 1000 100 10000 32052 10000 20000\\n\", \"10\\n15 21 17 22 27 21 31 21 32 30\\n\", \"15\\n14 4 5 15 6 19 14 19 12 22 23 17 14 8 27\\n\", \"11\\n15 17 18 18 8 22 23 33 33 21 38\\n\", \"10\\n18 17 18 17 17 13 22 20 34 7\\n\", \"5\\n0 1 8 15 3\\n\", \"13\\n16 14 12 9 0 28 37 21 35 30 32 31 86\\n\", \"13\\n18 9 8 9 23 20 18 31 33 6 31 37 36\\n\", \"15\\n18 6 33 21 14 17 20 9 18 20 28 13 19 25 21\\n\", \"15\\n14 4 5 15 6 19 14 1 12 22 23 17 14 8 27\\n\", \"6\\n10 8 5 0 50 4\\n\", \"7\\n10 1 2 3 2 8 15\\n\", \"15\\n18 6 33 21 14 17 20 9 18 20 0 13 19 25 21\\n\", \"6\\n10 8 0 0 50 4\\n\", \"7\\n10 1 2 1 2 8 15\\n\", \"15\\n18 6 33 21 14 17 20 9 18 20 0 13 3 25 21\\n\", \"15\\n14 4 5 15 12 19 15 1 12 22 23 17 14 8 27\\n\", \"11\\n15 18 21 18 8 22 23 33 33 18 38\\n\", \"6\\n1 8 0 0 50 4\\n\", \"13\\n16 14 12 12 0 28 37 21 40 30 32 31 15\\n\", \"12\\n5 1 3 1 100 2 1000 101 10000 32052 10000 20000\\n\", \"10\\n15 21 17 27 27 21 66 40 32 30\\n\", \"11\\n15 18 21 18 8 22 23 53 33 18 38\\n\", \"5\\n17 2 2 9 22\\n\", \"7\\n20 1 2 1 3 8 15\\n\", \"13\\n18 9 8 9 23 33 18 26 33 4 31 47 36\\n\", \"10\\n15 21 17 27 27 29 66 40 32 30\\n\", \"15\\n14 4 5 15 12 3 15 1 12 22 23 17 14 8 28\\n\", \"11\\n15 18 21 18 16 22 23 53 33 18 38\\n\", \"13\\n18 9 8 9 23 20 18 31 33 10 31 37 36\\n\", \"2\\n0 1001000000\\n\", \"2\\n1000001000 0\\n\", \"6\\n10 8 5 0 50 20\\n\", \"5\\n10 3 1 5 22\\n\", \"7\\n10 1 6 3 2 8 15\\n\", \"2\\n0 1001000001\\n\", \"2\\n1001001000 0\\n\", \"12\\n5 1 3 7 100 1 1000 100 10000 32052 10000 20000\\n\", \"10\\n15 21 17 27 27 21 31 21 32 30\\n\", \"11\\n15 18 18 18 8 22 23 33 33 21 38\\n\", \"10\\n18 17 18 17 17 13 22 37 34 7\\n\", \"5\\n1 1 8 15 3\\n\", \"5\\n10 3 2 5 22\\n\", \"13\\n16 14 12 9 0 28 37 21 40 30 32 31 86\\n\", \"13\\n18 9 8 9 23 20 18 26 33 6 31 37 36\\n\", \"2\\n0 1001000101\\n\", \"12\\n5 1 3 7 100 1 1000 101 10000 32052 10000 20000\\n\", \"10\\n15 21 17 27 27 21 34 21 32 30\\n\", \"15\\n14 4 5 15 6 19 15 1 12 22 23 17 14 8 27\\n\", \"11\\n15 18 21 18 8 22 23 33 33 21 38\\n\", \"10\\n18 17 18 17 17 13 22 61 34 7\\n\", \"5\\n1 2 8 15 3\\n\", \"5\\n10 3 2 9 22\\n\", \"13\\n16 14 12 12 0 28 37 21 40 30 32 31 86\\n\", \"13\\n18 9 8 9 23 20 18 26 33 6 31 47 36\\n\", \"2\\n0 1011000101\\n\", \"12\\n5 1 3 7 100 2 1000 101 10000 32052 10000 20000\\n\", \"10\\n15 21 17 27 27 21 66 21 32 30\\n\", \"10\\n18 17 18 17 31 13 22 61 34 7\\n\", \"5\\n1 2 9 15 3\\n\", \"5\\n17 3 2 9 22\\n\", \"7\\n10 1 2 1 3 8 15\\n\", \"13\\n18 9 8 9 23 20 18 26 33 4 31 47 36\\n\", \"2\\n1 1011000101\\n\", \"15\\n18 6 33 21 14 17 20 9 18 20 0 13 3 32 21\\n\", \"15\\n14 4 5 15 12 19 15 1 12 22 23 17 14 8 28\\n\", \"10\\n18 17 18 17 31 13 22 61 53 7\\n\", \"5\\n1 2 9 15 4\\n\", \"13\\n16 6 12 12 0 28 37 21 40 30 32 31 15\\n\", \"2\\n1 1001000101\\n\", \"15\\n18 6 33 13 14 17 20 9 18 20 0 13 3 32 21\\n\", \"12\\n5 1 3 1 100 2 1000 101 10000 32052 10010 20000\\n\", \"10\\n10 17 18 17 31 13 22 61 53 7\\n\", \"5\\n0 2 9 15 4\\n\"], \"outputs\": [\"2 1 0 -1 0 -1 \", \"1 0 -1 -1 -1 \", \"4 2 1 0 -1 -1 -1 \", \"3 2 1 -1 -1 1 0 -1 2 -1 0 -1 -1 \", \"2 0 -1 -1 2 1 -1 -1 1 -1 -1 0 -1 \", \"-1 -1 \", \"0 -1 \", \"10 -1 8 8 6 6 0 -1 2 2 3 -1 -1 0 -1 \", \"4 -1 2 1 0 -1 0 -1 -1 0 -1 -1 \", \"-1 0 -1 1 2 -1 2 -1 0 -1 \", \"7 -1 -1 0 -1 6 1 4 -1 3 2 0 -1 -1 -1 \", \"-1 -1 -1 -1 4 3 2 2 1 -1 -1 \", \"4 3 2 1 0 -1 0 -1 0 -1 \", \"3 -1 1 0 -1 \", \"3 2 1 -1 -1 1 0 -1 2 -1 0 -1 -1 \", \"8 0 -1 -1 4 3 2 1 1 -1 -1 0 -1 \", \"-1 -1 \", \"0 -1 \", \"10 -1 11 8 6 6 0 -1 2 2 3 -1 -1 0 -1 \", \"4 -1 2 1 0 -1 0 -1 -1 0 -1 -1 \", \"6 5 4 3 2 1 2 -1 0 -1 \", \"7 -1 -1 8 -1 6 1 4 -1 3 2 0 -1 -1 -1 \", \"3 2 1 0 -1 3 2 2 1 -1 -1 \", \"4 3 2 1 0 -1 0 -1 0 -1 \", \"0 -1 1 0 -1 \", \"2 1 0 -1 0 -1 \", \"2 0 -1 -1 -1 \", \"4 -1 1 0 -1 -1 -1 \", \"3 2 1 -1 -1 1 4 -1 2 -1 0 -1 -1 \", \"10 -1 11 8 6 6 5 -1 2 2 3 -1 -1 0 -1 \", \"4 -1 2 1 0 -1 0 -1 -1 1 -1 -1 \", \"-1 0 -1 3 2 -1 2 -1 0 -1 \", \"12 -1 -1 9 -1 7 6 5 4 3 2 1 0 -1 -1 \", \"3 2 1 0 -1 3 2 1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 0 -1 \", \"-1 -1 1 0 -1 \", \"3 2 1 0 -1 1 4 -1 2 -1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 1 -1 -1 0 -1 \", \"10 -1 11 8 6 5 5 -1 2 2 3 -1 -1 0 -1 \", \"12 5 4 9 2 7 6 -1 4 3 2 1 0 -1 -1 \", \"4 3 2 -1 0 -1 \", \"4 -1 -1 0 -1 -1 -1 \", \"10 8 11 8 6 5 5 2 2 2 -1 -1 -1 0 -1 \", \"4 3 -1 -1 0 -1 \", \"4 -1 0 -1 -1 -1 -1 \", \"11 10 11 8 7 6 5 4 3 2 -1 0 -1 0 -1 \", \"12 5 4 9 8 7 6 -1 4 3 2 1 0 -1 -1 \", \"3 2 6 0 -1 3 2 1 0 -1 -1 \", \"2 3 -1 -1 0 -1 \", \"11 2 1 0 -1 6 5 4 3 2 1 0 -1 \", \"4 -1 2 -1 0 -1 0 -1 -1 1 -1 -1 \", \"-1 0 -1 1 0 -1 2 1 0 -1 \", \"3 2 6 0 -1 3 2 2 0 -1 -1 \", \"2 -1 -1 -1 -1 \", \"5 -1 0 -1 -1 -1 -1 \", \"8 7 6 5 4 4 2 1 1 -1 -1 0 -1 \", \"-1 0 -1 -1 -1 -1 2 1 0 -1 \", \"12 5 4 9 8 1 6 -1 4 3 2 1 0 -1 -1 \", \"-1 2 6 0 -1 3 2 2 0 -1 -1 \", \"8 0 -1 -1 4 3 2 1 1 -1 -1 0 -1 \", \"-1 -1 \", \"0 -1 \", \"2 1 0 -1 0 -1 \", \"2 0 -1 -1 -1 \", \"4 -1 1 0 -1 -1 -1 \", \"-1 -1 \", \"0 -1 \", \"4 -1 2 1 0 -1 0 -1 -1 1 -1 -1 \", \"-1 0 -1 3 2 -1 2 -1 0 -1 \", \"3 2 1 0 -1 3 2 1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 0 -1 \", \"-1 -1 1 0 -1 \", \"2 0 -1 -1 -1 \", \"3 2 1 0 -1 1 4 -1 2 -1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 1 -1 -1 0 -1 \", \"-1 -1 \", \"4 -1 2 1 0 -1 0 -1 -1 1 -1 -1 \", \"-1 0 -1 3 2 -1 2 -1 0 -1 \", \"12 5 4 9 2 7 6 -1 4 3 2 1 0 -1 -1 \", \"3 2 1 0 -1 3 2 1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 0 -1 \", \"-1 -1 1 0 -1 \", \"2 0 -1 -1 -1 \", \"3 2 1 0 -1 1 4 -1 2 -1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 1 -1 -1 0 -1 \", \"-1 -1 \", \"4 -1 2 1 0 -1 0 -1 -1 1 -1 -1 \", \"-1 0 -1 3 2 -1 2 -1 0 -1 \", \"8 7 6 5 4 3 2 1 0 -1 \", \"-1 -1 1 0 -1 \", \"2 0 -1 -1 -1 \", \"4 -1 0 -1 -1 -1 -1 \", \"8 7 6 5 4 3 2 1 1 -1 -1 0 -1 \", \"-1 -1 \", \"11 10 11 8 7 6 5 4 3 2 -1 0 -1 0 -1 \", \"12 5 4 9 8 7 6 -1 4 3 2 1 0 -1 -1 \", \"8 7 6 5 4 3 2 1 0 -1 \", \"-1 -1 1 0 -1 \", \"11 2 1 0 -1 6 5 4 3 2 1 0 -1 \", \"-1 -1 \", \"11 10 11 8 7 6 5 4 3 2 -1 0 -1 0 -1 \", \"4 -1 2 -1 0 -1 0 -1 -1 1 -1 -1 \", \"8 7 6 5 4 3 2 1 0 -1 \", \"-1 -1 1 0 -1 \"]}", "source": "primeintellect"}
|
There are n walruses standing in a queue in an airport. They are numbered starting from the queue's tail: the 1-st walrus stands at the end of the queue and the n-th walrus stands at the beginning of the queue. The i-th walrus has the age equal to ai.
The i-th walrus becomes displeased if there's a younger walrus standing in front of him, that is, if exists such j (i < j), that ai > aj. The displeasure of the i-th walrus is equal to the number of walruses between him and the furthest walrus ahead of him, which is younger than the i-th one. That is, the further that young walrus stands from him, the stronger the displeasure is.
The airport manager asked you to count for each of n walruses in the queue his displeasure.
Input
The first line contains an integer n (2 ≤ n ≤ 105) — the number of walruses in the queue. The second line contains integers ai (1 ≤ ai ≤ 109).
Note that some walruses can have the same age but for the displeasure to emerge the walrus that is closer to the head of the queue needs to be strictly younger than the other one.
Output
Print n numbers: if the i-th walrus is pleased with everything, print "-1" (without the quotes). Otherwise, print the i-th walrus's displeasure: the number of other walruses that stand between him and the furthest from him younger walrus.
Examples
Input
6
10 8 5 3 50 45
Output
2 1 0 -1 0 -1
Input
7
10 4 6 3 2 8 15
Output
4 2 1 0 -1 -1 -1
Input
5
10 3 1 10 11
Output
1 0 -1 -1 -1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"2\\n2\\n1 1\\n2\\n1 2\\n\\nSAMPLE\", \"2\\n2\\n1 1\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n1 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n1 2\\n2\\n1 1\\n\\nSAMOLE\", \"2\\n2\\n0 0\\n2\\n0 0\\n\\nSAPEKM\", \"2\\n2\\n2 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n4 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n0 2\\n2\\n1 1\\n\\nSAMOLE\", \"2\\n2\\n1 2\\n1\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n1 2\\n2\\n1 2\\n\\nSLMOAE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nSOMALE\", \"2\\n2\\n1 3\\n2\\n1 1\\n\\nSAMOLE\", \"2\\n2\\n0 3\\n2\\n1 1\\n\\nSAMOLE\", \"2\\n2\\n1 3\\n2\\n1 2\\n\\nSLMOAE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nSOEALM\", \"2\\n2\\n1 3\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n2\\n0 3\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n1 3\\n2\\n1 3\\n\\nSLMOAE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nMOEALS\", \"2\\n1\\n1 3\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n2\\n0 1\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n-1 1\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n0 1\\n2\\n1 2\\n\\nRAMOLE\", \"2\\n2\\n0 1\\n2\\n0 2\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n0 2\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n1 4\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n2 4\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n2 7\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n1 7\\n\\nRAMOLE\", \"2\\n2\\n1 1\\n2\\n1 2\\n\\nSAMPLD\", \"2\\n2\\n1 1\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n2\\n-1 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n1\\n1 2\\n2\\n1 1\\n\\nSAMOLE\", \"2\\n2\\n8 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n0 1\\n2\\n1 1\\n\\nSAMOLE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nSLMOAE\", \"2\\n2\\n1 3\\n2\\n1 1\\n\\nELOMAS\", \"2\\n2\\n1 3\\n2\\n0 2\\n\\nSLMOAE\", \"2\\n2\\n1 6\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n2\\n1 3\\n2\\n0 3\\n\\nSLMOAE\", \"2\\n2\\n0 2\\n2\\n1 3\\n\\nMOEALS\", \"2\\n1\\n1 3\\n2\\n1 0\\n\\nSAMOKE\", \"2\\n2\\n0 2\\n2\\n2 2\\n\\nRAMOLE\", \"2\\n2\\n-1 2\\n2\\n1 4\\n\\nRAMOLE\", \"2\\n2\\n-1 2\\n2\\n2 7\\n\\nRAMOLE\", \"2\\n2\\n-1 2\\n2\\n1 3\\n\\nSAMOLE\", \"2\\n1\\n1 2\\n2\\n2 1\\n\\nSAMOLE\", \"2\\n2\\n0 1\\n2\\n1 2\\n\\nSAMOEL\", \"2\\n2\\n0 2\\n2\\n1 3\\n\\nSLMOAE\", \"2\\n2\\n1 2\\n2\\n1 1\\n\\nELOMAS\", \"2\\n2\\n1 1\\n2\\n0 2\\n\\nSLMOAE\", \"2\\n2\\n1 8\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n2\\n0 2\\n2\\n1 3\\n\\nSLAEOM\", \"2\\n1\\n1 3\\n2\\n1 0\\n\\nSAMPKE\", \"2\\n2\\n0 1\\n2\\n2 2\\n\\nRAMOLE\", \"2\\n2\\n-1 2\\n2\\n1 4\\n\\nSAMOLE\", \"2\\n1\\n1 2\\n1\\n2 1\\n\\nSAMOLE\", \"2\\n2\\n0 1\\n2\\n1 2\\n\\nLEOMAS\", \"2\\n2\\n1 2\\n2\\n1 3\\n\\nSLMOAE\", \"2\\n2\\n1 0\\n2\\n0 2\\n\\nSLMOAE\", \"2\\n2\\n1 4\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n1\\n1 3\\n2\\n1 1\\n\\nSAMPKE\", \"2\\n2\\n0 1\\n2\\n2 1\\n\\nRAMOLE\", \"2\\n2\\n0 1\\n2\\n1 2\\n\\nMEOMAS\", \"2\\n2\\n1 2\\n1\\n1 3\\n\\nSLMOAE\", \"2\\n2\\n1 1\\n2\\n0 2\\n\\nRLMOAE\", \"2\\n2\\n1 14\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n1\\n1 0\\n2\\n1 0\\n\\nSAMPKE\", \"2\\n2\\n1 1\\n2\\n1 2\\n\\nMEOMAS\", \"2\\n2\\n1 14\\n2\\n1 0\\n\\nELOMAS\", \"2\\n2\\n1 0\\n2\\n1 0\\n\\nSAMPKE\", \"2\\n2\\n1 1\\n2\\n1 2\\n\\nOEMMAS\", \"2\\n2\\n1 0\\n2\\n2 0\\n\\nSAMPKE\", \"2\\n2\\n1 0\\n2\\n2 0\\n\\nSAPMKE\", \"2\\n2\\n1 0\\n2\\n0 0\\n\\nSAPMKE\", \"2\\n2\\n1 0\\n2\\n0 0\\n\\nSAPEKM\", \"2\\n2\\n0 0\\n1\\n0 0\\n\\nSAPEKM\", \"2\\n2\\n1 1\\n2\\n1 0\\n\\nSAMPLE\", \"2\\n2\\n1 1\\n1\\n1 2\\n\\nSAMOLE\", \"2\\n1\\n3 2\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n4 1\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n0 2\\n2\\n1 1\\n\\nSALOLE\", \"2\\n2\\n1 4\\n1\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n1 2\\n2\\n2 2\\n\\nSLMOAE\", \"2\\n2\\n1 2\\n2\\n1 2\\n\\nSOMALE\", \"2\\n2\\n1 3\\n2\\n1 0\\n\\nSLMOAE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nSOEAMM\", \"2\\n2\\n0 3\\n2\\n1 2\\n\\nSANOLE\", \"2\\n2\\n1 0\\n2\\n1 3\\n\\nSLMOAE\", \"2\\n1\\n1 4\\n2\\n1 0\\n\\nSAMOLE\", \"2\\n2\\n0 3\\n2\\n1 2\\n\\nSAMPLE\", \"2\\n2\\n-1 0\\n2\\n1 2\\n\\nSAMOLE\", \"2\\n2\\n0 1\\n2\\n0 2\\n\\nRAMOME\", \"2\\n2\\n0 2\\n2\\n1 1\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n2\\n1 2\\n\\nRBMOLE\", \"2\\n2\\n0 2\\n2\\n1 6\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n1\\n2 4\\n\\nRAMOLE\", \"2\\n2\\n0 2\\n1\\n1 7\\n\\nRAMOLE\", \"2\\n2\\n1 1\\n2\\n1 4\\n\\nSAMPLD\"], \"outputs\": [\"Andrew\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Andrew\\nAndrew\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAndrew\\n\", \"Andrew\\nAndrew\\n\", \"Andrew\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAndrew\\n\", \"Aniruddha\\nAniruddha\\n\", \"Aniruddha\\nAniruddha\\n\", \"Andrew\\nAniruddha\\n\"]}", "source": "primeintellect"}
|
Aniruddha and Andrew are playing a Game on Christmas Eve named "Christmas-Gamecon". In this they are given a list of numbers.
In each turn alternatively one will select any one number from the list and decrease it by 1,2,3 or 4.
The last person who is unable to decrease the number loses the game.
At last all the numbers would become zero.
Aniruddha takes the first chance.
Input
The first line contains the T, the number of test cases. Each testcase consist of two lines. First line consist of single integer N — size of the list.
Next line consists of N non negative space separated integers.
Output
For each testcase you need to output the answer to the following query whether Andrew will win or Aniruddha will win. Output "Andrew" if Andrew wins otherwise output "Aniruddha" (without quotes).
Constraints
1 ≤ T ≤ 10
1 ≤ N ≤ 10^5
0 ≤ A[i] ≤ 10^9,where i ranges from 1 to N
SAMPLE INPUT
2
2
1 1
2
1 2
SAMPLE OUTPUT
Andrew
Aniruddha
Explanation
In 1st testcase Aniruddha will pick 1 from 1st list then Andrew will pick 1 from 2nd list.
Hence Andrew will win the game in 1st testcase.
In 2nd testcase to play optimally ,Aniruddha will pick 1 from 2nd list,then Andrew will pick 1 from any list hence 1 will be left from the remaining list which Aniruddha will pick hence Aniruddha will win the game.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 9\\n001\\n1 2\\n1 3\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 3\\n\\nSAMPLE\", \"55 6\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n41 33\\n2 34\\n11 5\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n41 33\\n2 34\\n11 5\", \"3 9\\n001\\n1 2\\n1 3\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 2\\n\\nSAMPLE\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n41 33\\n2 34\\n11 5\", \"55 6\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n37 33\\n2 34\\n11 5\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n46 46\\n48 24\\n43 45\\n41 33\\n2 34\\n11 5\", \"55 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 35\\n14 15\\n2 13\\n11 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n7 24\\n1 1\\n26 1\\n2 12\\n2 7\", \"3 9\\n001\\n1 2\\n1 1\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 3\\n\\nSAMPLE\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n46 46\\n48 10\\n43 45\\n41 33\\n2 34\\n11 5\", \"79 4\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n7 24\\n2 1\\n26 1\\n2 12\\n2 7\", \"79 1\\n0001100110100100111011001111001111100010010110110100001\\n37 42\\n7 5\\n1 1\\n26 0\\n2 12\\n2 7\", \"3 3\\n001\\n1 2\\n1 1\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 3\\n\\nSAMPLE\", \"79 5\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n7 24\\n2 1\\n26 1\\n2 12\\n2 7\", \"76 3\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n10 1\\n14 1\\n2 12\\n2 0\", \"55 5\\n0001100110100100111011001111001111101010010110100100001\\n37 46\\n21 24\\n43 35\\n21 15\\n2 34\\n11 10\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n26 37\\n43 10\\n41 10\\n2 34\\n11 5\", \"244 2\\n0001100110100100111011001111001111100010010110100100101\\n15 24\\n12 24\\n1 1\\n28 2\\n4 -2\\n4 12\", \"176 3\\n0001100110100100111011001111100111100010010110110100001\\n37 36\\n15 6\\n1 1\\n38 2\\n1 11\\n0 7\", \"244 2\\n0001100110100100111011001111001111100010010110100100101\\n15 24\\n12 5\\n1 1\\n28 2\\n4 -4\\n4 12\", \"3 9\\n000\\n2 2\\n1 3\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 3\\n\\nSAMPLE\", \"76 3\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n2 24\\n10 1\\n14 1\\n2 18\\n2 0\", \"79 1\\n0001100110100100111011001111001111100010010110100100001\\n6 15\\n4 24\\n12 1\\n31 1\\n2 12\\n12 7\", \"42 5\\n0001100110100100111011001111011111110010010110100100001\\n37 7\\n35 24\\n43 35\\n2 15\\n2 33\\n19 13\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 35\\n41 33\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n48 24\\n43 35\\n41 33\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n41 19\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n21 19\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n30 24\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n15 24\\n43 35\\n21 15\\n2 34\\n11 5\", \"3 9\\n001\\n2 2\\n1 3\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 3\\n\\nSAMPLE\", \"3 9\\n001\\n1 1\\n1 3\\n3 2\\n2 1\\n2 3\\n3 1\\n1 1\\n2 2\\n3 2\\n\\nSAMPLE\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 24\\n43 35\\n41 33\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n48 24\\n43 35\\n41 33\\n2 34\\n11 1\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n41 3\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 51\\n21 19\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 10\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n30 24\\n43 35\\n21 15\\n2 34\\n11 7\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n15 24\\n43 35\\n32 15\\n2 34\\n11 5\", \"55 6\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n37 33\\n2 34\\n5 5\", \"3 9\\n001\\n1 1\\n1 3\\n3 2\\n2 1\\n2 3\\n3 1\\n2 1\\n2 2\\n3 2\\n\\nSAMPLE\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 24\\n43 12\\n41 33\\n2 34\\n11 5\", \"55 4\\n0011100110100100111011001111011111100010010110100100001\\n37 46\\n48 24\\n43 35\\n41 33\\n2 34\\n11 1\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n41 3\\n2 34\\n15 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 51\\n38 19\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 11\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n30 24\\n7 35\\n21 15\\n2 34\\n11 7\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n15 24\\n43 10\\n32 15\\n2 34\\n11 5\", \"55 6\\n0011100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n37 33\\n2 34\\n5 5\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 24\\n43 20\\n41 33\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001011011111100010010110100100001\\n37 46\\n30 11\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n30 24\\n7 35\\n14 15\\n2 34\\n11 7\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n15 24\\n43 10\\n32 15\\n2 34\\n11 9\", \"55 6\\n0011100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n37 33\\n2 34\\n7 5\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 24\\n43 20\\n41 46\\n2 34\\n11 5\", \"55 4\\n0001100110110100111011001011011111100010010110100100001\\n37 46\\n30 11\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n30 24\\n7 35\\n14 15\\n2 13\\n11 7\", \"55 6\\n0011100110100100011011001111011111100010010110100100001\\n18 46\\n48 24\\n43 45\\n37 33\\n2 34\\n7 5\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 12\\n43 20\\n41 46\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 35\\n14 15\\n2 13\\n11 7\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 12\\n43 20\\n41 46\\n3 34\\n11 5\", \"55 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 50\\n14 15\\n2 13\\n11 7\", \"55 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 50\\n14 15\\n2 12\\n11 7\", \"55 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 1\\n14 15\\n2 12\\n11 7\", \"55 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 1\\n14 1\\n2 12\\n11 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 1\\n14 1\\n2 12\\n11 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n7 1\\n14 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n4 24\\n10 1\\n14 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n4 24\\n10 1\\n14 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n4 24\\n10 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n4 24\\n1 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n7 24\\n2 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110100100001\\n37 24\\n7 5\\n2 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110110100001\\n37 24\\n7 5\\n2 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110110100001\\n37 42\\n7 5\\n2 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110110100001\\n37 42\\n7 5\\n1 1\\n26 1\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110110100001\\n37 42\\n7 5\\n1 1\\n26 0\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111001111100010010110110100001\\n37 36\\n7 5\\n1 1\\n26 0\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 5\\n1 1\\n26 0\\n2 12\\n2 7\", \"79 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 6\\n1 1\\n26 0\\n2 12\\n2 7\", \"113 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 6\\n1 1\\n26 0\\n2 12\\n2 7\", \"113 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 6\\n1 1\\n26 0\\n2 4\\n2 7\", \"113 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 6\\n1 1\\n26 0\\n2 1\\n2 7\", \"113 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 6\\n0 1\\n26 0\\n2 1\\n2 7\", \"113 2\\n0001100110100100111011001111000111100010010110110100001\\n37 36\\n7 6\\n0 1\\n26 0\\n2 1\\n2 10\", \"113 2\\n0001100110100100111011001111000111100010010110110100001\\n37 48\\n7 6\\n0 1\\n26 0\\n2 1\\n2 10\", \"55 2\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n41 33\\n2 34\\n11 5\", \"3 9\\n001\\n1 2\\n1 3\\n3 2\\n2 1\\n2 3\\n3 2\\n1 1\\n2 2\\n3 2\\n\\nSAMPLE\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n30 35\\n41 33\\n2 34\\n11 5\", \"69 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n41 19\\n2 34\\n11 5\", \"55 4\\n0001000110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 35\\n21 19\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n42 35\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n30 24\\n43 51\\n21 15\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111001111100010010110100100001\\n37 46\\n21 24\\n43 35\\n21 15\\n2 34\\n11 5\", \"55 2\\n0001100110100100011011001111011111100010010110100100001\\n37 46\\n48 24\\n43 45\\n37 33\\n2 34\\n11 5\", \"3 9\\n001\\n1 1\\n1 3\\n3 2\\n2 1\\n2 3\\n3 2\\n1 1\\n2 2\\n3 2\\n\\nSAMPLE\", \"55 4\\n0001100110100100011011001111011111100010010110100100001\\n37 30\\n48 24\\n43 35\\n41 33\\n2 29\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n48 24\\n43 35\\n44 33\\n2 34\\n11 1\", \"55 4\\n0001100110100100111011001111011111100010010110101100001\\n37 46\\n30 24\\n43 35\\n41 3\\n2 34\\n11 5\", \"55 4\\n0001100110100100111011001111011111100010010110100100001\\n37 46\\n30 24\\n43 51\\n21 19\\n2 34\\n3 5\"], \"outputs\": [\"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\n\", \"No\\nYes\\n\", \"Yes\\nYes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nYes\\nNo\\n\", \"No\\n\", \"Yes\\nYes\\nNo\\n\", \"No\\nYes\\nYes\\nNo\\nYes\\n\", \"No\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nYes\\n\", \"Yes\\nYes\\n\", \"No\\nYes\\nYes\\n\", \"Yes\\nNo\\n\", \"Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\n\", \"No\\nYes\\nNo\\n\", \"Yes\\n\", \"No\\nNo\\nNo\\nYes\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nYes\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nNo\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"No\\nYes\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nYes\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\n\"]}", "source": "primeintellect"}
|
Nandu is stuck in a maze consisting of N rooms. Each room with room number x has a door leading into room number 2x (if 2x ≤ N) and another door leading into room number 2x+1 (if 2x+1 ≤ N). All these doors are 2-way doors ie. they can be opened from both the sides.
Some of these N rooms have monsters living in them.
Nandu is currently in room number i . Nandu's only escape from this maze is to somehow reach room number j which contains the magical Wish-Granting Well. The Well will only grant a wish to Nandu if he offers it a single golden coin. Nandu presently has only a single golden coin in his possession. However, if while going from room number i to j he meets a monster, the monster will take away the only golden coin Nandu has and Nandu will never be able to escape from the maze.
You will be given information about every room telling you whether a monster resides in it or not. You will then be given Q scenarios, each scenario describing the locations i (the room currently Nandu is present in) and j (the room where the wishing well is present), i and j will vary over different scenarios but the locations of the monsters will remain fixed for all these scenarios. For each of these scenarios, you have to find out whether Nandu can escape from the maze or not.
Input :
The first line consists on N and Q denoting the number of rooms in the maze and the number of different scenarios that will be given to you. The next line consists of N non-space separated integers such that if the kth integer is '0' , there is no monster present in room number k and if the kth integer is '1' , there is a monster present in room number k. The next Q lines are such that each line consists of two space separated integers i and j denoting Nandu's current location and the location of the Wishing Well for this particular scenario respectively.
Output :
For every scenario print on a new line 'Yes' if Nandu can escape from the maze and 'No' if he cannot escape from the maze. (Quotes for clarity).
Constraints :
1 ≤ N ≤ 100000
1 ≤ Q ≤ 100000
1 ≤ i,j ≤ N
Author : Shreyans
Tester : Sayan
(By IIT Kgp HackerEarth Programming Club)
SAMPLE INPUT
3 9
001
1 2
1 3
3 2
2 1
2 3
3 1
1 1
2 2
3 3
SAMPLE OUTPUT
Yes
No
No
Yes
No
No
Yes
Yes
No
Explanation
A monster is present only in room number 3.
Scenario 1 : Nandu is initially present in room number 1 and the Wish-Granting Well is present in room number 2 . Since there is no monster in either of the rooms Nandu goes from 1 -> 2 without losing his golden coin. Hence Nandu can escape the maze by making a wish to the Wish-Granting Well
Scenario 2 : Nandu goes from 1 -> 3. However, there is a monster present in room number 3, which takes away his only golden coin before he can make a wish to the Wish-Granting Well. Hence Nandu cannot escape the maze.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"2\\n5 2\\n1 1 1 1 1 1\\n5 1\\n1 3 2 4 3 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n5 1\\n1 3 2 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n5 1\\n2 3 2 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 1 1 1\\n5 1\\n2 3 2 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 0\\n5 1\\n1 3 2 4 2 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 2 1 1\\n5 1\\n1 3 2 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 2 1 1\\n5 1\\n1 3 3 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 1 1 1\\n7 1\\n3 3 2 8 4 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n4 1\\n2 4 1 6 1 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n4 2\\n2 4 1 6 1 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n5 1\\n1 3 1 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 1 1 1\\n7 1\\n2 3 4 4 2 5\\n\\nSAMPLD\", \"2\\n5 2\\n1 1 1 1 0 1\\n4 1\\n2 3 2 4 1 5\\n\\nSAMPLE\", \"2\\n1 3\\n1 1 1 1 2 1\\n7 1\\n2 3 2 1 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 2 1 1 1\\n7 1\\n2 3 2 8 4 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 2 1 1 1 1\\n4 1\\n2 4 2 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 1 2 0\\n4 1\\n2 3 2 1 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n4 1\\n2 4 4 4 1 5\\n\\nSANPLE\", \"2\\n1 2\\n1 1 1 1 1 0\\n7 1\\n3 6 2 8 4 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 2\\n4 1\\n2 4 2 6 1 5\\n\\nSANPLE\", \"2\\n1 2\\n1 1 1 1 1 1\\n4 1\\n2 4 1 6 1 5\\n\\nSANPLE\", \"2\\n2 2\\n1 2 1 1 3 1\\n4 1\\n2 3 2 0 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 1 1 2\\n5 1\\n2 3 2 4 1 5\\n\\nELPMAS\", \"2\\n5 2\\n1 1 1 1 1 1\\n5 1\\n1 3 3 1 2 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 2 1 2\\n5 1\\n1 3 2 4 0 5\\n\\nSAMPLE\", \"2\\n1 4\\n1 1 1 1 2 1\\n7 1\\n2 3 2 8 2 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 2 2 1 1 1\\n4 1\\n2 4 2 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 1 1 1 0\\n7 1\\n1 6 2 8 4 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 2 2 1 1\\n5 1\\n1 3 1 4 1 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 2 1 1 2\\n5 1\\n2 3 2 4 1 5\\n\\nELPMAS\", \"2\\n1 2\\n1 1 1 1 0 0\\n5 1\\n2 3 1 4 0 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 0 1 1 1\\n4 1\\n2 4 4 4 2 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n5 3\\n2 4 1 9 1 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 2 2 1 1\\n5 1\\n2 3 1 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 0 1 1 1\\n4 2\\n2 4 4 4 2 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 1 2 2 2\\n5 1\\n1 3 1 4 0 5\\n\\nSAMPME\", \"2\\n1 4\\n1 1 1 1 2 1\\n7 1\\n2 3 4 8 2 8\\n\\nSAMOLE\", \"2\\n5 2\\n1 1 0 1 1 1\\n4 2\\n2 4 1 4 2 5\\n\\nSANPLE\", \"2\\n1 2\\n1 1 1 1 2 0\\n7 1\\n2 6 4 8 4 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 0 2 2\\n8 1\\n1 4 2 6 1 5\\n\\nSANPLE\", \"2\\n2 2\\n2 2 0 1 2 1\\n4 1\\n2 3 2 0 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 2 2 1\\n5 1\\n2 3 1 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n2 1 1 2 2 2\\n5 1\\n1 3 1 4 0 5\\n\\nSAMPME\", \"2\\n1 4\\n1 1 1 1 2 2\\n7 1\\n2 3 4 8 2 8\\n\\nSAMOLE\", \"2\\n1 3\\n1 1 -1 1 2 1\\n7 1\\n2 3 2 -1 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 0 1 1 1\\n4 2\\n2 4 2 4 2 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 0 0 2 2\\n8 1\\n1 4 2 6 1 5\\n\\nSANPLE\", \"2\\n1 4\\n1 1 1 1 2 1\\n4 1\\n1 4 2 8 2 4\\n\\nSAMPLE\", \"2\\n3 2\\n1 1 0 1 1 1\\n4 2\\n2 4 2 4 2 10\\n\\nSANPLE\", \"2\\n3 2\\n1 1 1 1 0 0\\n5 1\\n2 3 1 13 0 2\\n\\nTAMPLE\", \"2\\n1 3\\n1 1 -1 1 2 1\\n7 1\\n2 5 4 -1 1 5\\n\\nELPMAS\", \"2\\n3 2\\n1 1 1 1 0 0\\n5 2\\n2 3 1 13 0 2\\n\\nTAMPLE\", \"2\\n1 4\\n1 1 0 1 2 2\\n7 1\\n2 3 4 11 2 12\\n\\nSAMOLE\", \"2\\n3 2\\n1 1 1 1 1 1\\n4 2\\n2 4 2 4 0 10\\n\\nSANPLE\", \"2\\n1 7\\n1 1 0 1 2 2\\n7 1\\n2 3 4 11 2 12\\n\\nSAMOLE\", \"2\\n1 3\\n1 1 -1 1 2 1\\n7 1\\n3 5 4 -1 1 8\\n\\nELPMAS\", \"2\\n3 2\\n1 1 1 1 0 0\\n10 3\\n2 3 1 13 0 2\\n\\nTAMPLE\", \"2\\n3 2\\n1 1 1 1 0 0\\n10 3\\n2 3 1 13 -1 2\\n\\nTAMPLE\", \"2\\n1 4\\n1 1 1 1 2 1\\n4 2\\n1 4 2 8 4 1\\n\\nSBMOLE\", \"2\\n1 3\\n1 1 -1 1 2 1\\n7 1\\n3 5 7 -2 2 8\\n\\nELPMAS\", \"2\\n1 7\\n1 1 0 1 2 2\\n11 1\\n2 3 1 3 3 12\\n\\nSAMOLF\", \"2\\n3 2\\n1 1 1 1 0 0\\n9 3\\n1 3 1 13 -2 2\\n\\nTEMPLA\", \"2\\n3 2\\n1 1 1 1 0 0\\n9 3\\n1 3 1 13 -3 2\\n\\nTEMPLA\", \"2\\n1 7\\n1 1 1 0 2 2\\n11 1\\n2 3 1 3 3 12\\n\\nSAMOLF\", \"2\\n5 2\\n1 1 1 1 1 1\\n4 1\\n3 3 2 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n4 2\\n2 4 2 6 1 5\\n\\nSANPLE\", \"2\\n8 2\\n1 1 1 0 1 1\\n5 1\\n1 3 2 4 3 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 2 1 1 1 1\\n5 1\\n1 3 2 1 2 5\\n\\nSAMPLE\", \"2\\n1 2\\n1 1 4 1 1 1\\n7 1\\n2 3 2 8 4 5\\n\\nSAMPLE\", \"2\\n2 2\\n1 2 1 1 3 2\\n4 1\\n2 3 2 0 1 5\\n\\nSAMPLE\", \"2\\n8 1\\n1 1 1 1 1 1\\n5 1\\n1 3 3 4 3 5\\n\\nSAMPLE\", \"2\\n5 1\\n1 1 1 2 1 1\\n5 1\\n1 3 1 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 2\\n5 1\\n1 3 3 1 2 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 0 2 1 2\\n5 1\\n1 3 2 4 0 5\\n\\nSAMPLE\", \"2\\n1 4\\n1 1 1 1 2 2\\n7 1\\n2 3 2 8 2 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 2 2 1 2\\n5 1\\n1 3 2 4 0 5\\n\\nSAMPME\", \"2\\n5 2\\n1 1 2 1 1 1\\n4 2\\n2 4 2 4 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 1 1 1 1\\n5 3\\n2 4 1 9 0 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 2 2 2 1\\n5 1\\n2 3 1 4 1 5\\n\\nSAMPLE\", \"2\\n1 4\\n1 1 1 1 2 1\\n7 1\\n2 3 1 8 2 8\\n\\nSAMOLE\", \"2\\n5 2\\n2 1 0 1 1 1\\n4 2\\n2 4 4 4 2 5\\n\\nSANPLE\", \"2\\n8 1\\n1 1 1 1 1 1\\n9 1\\n1 4 4 4 3 5\\n\\nELPMAS\", \"2\\n1 2\\n1 1 1 1 2 1\\n4 2\\n1 4 2 4 2 4\\n\\nSAMPLE\", \"2\\n5 2\\n1 2 1 2 2 2\\n5 1\\n1 3 1 4 0 5\\n\\nSAMPME\", \"2\\n1 4\\n1 1 1 1 2 0\\n7 1\\n2 3 4 8 2 8\\n\\nSAMOLE\", \"2\\n5 2\\n1 1 0 1 1 1\\n4 2\\n2 4 1 1 2 5\\n\\nSANPLE\", \"2\\n1 3\\n1 1 -1 1 2 1\\n7 2\\n2 3 2 -1 1 5\\n\\nSAMPLE\", \"2\\n5 2\\n1 1 0 1 0 1\\n4 2\\n2 4 2 4 2 5\\n\\nSANPLE\", \"2\\n5 2\\n1 1 1 0 2 4\\n8 1\\n1 4 2 6 1 5\\n\\nSANPLE\", \"2\\n1 4\\n1 1 1 1 2 1\\n4 1\\n1 4 1 8 2 4\\n\\nSAMPLE\", \"2\\n3 2\\n1 1 0 1 1 1\\n4 4\\n2 4 2 4 2 5\\n\\nSANPLE\", \"2\\n3 2\\n2 1 0 1 1 1\\n4 2\\n2 4 2 4 2 10\\n\\nSANPLE\", \"2\\n5 4\\n1 1 0 0 2 2\\n8 1\\n1 4 2 6 4 5\\n\\nSANPLE\", \"2\\n1 4\\n1 1 2 1 2 1\\n4 1\\n1 4 2 8 2 0\\n\\nSAMPLE\", \"2\\n2 2\\n1 1 1 1 1 1\\n4 2\\n2 4 2 4 0 10\\n\\nSANPLE\", \"2\\n3 2\\n1 1 1 1 0 0\\n10 2\\n2 3 1 9 0 2\\n\\nTAMPLE\", \"2\\n3 2\\n1 1 1 1 -1 0\\n10 3\\n2 3 1 13 0 2\\n\\nTAMPLE\", \"2\\n1 7\\n1 1 0 1 2 4\\n11 1\\n2 3 4 11 3 12\\n\\nSAMOLE\", \"2\\n1 7\\n1 1 0 1 2 2\\n11 2\\n2 3 4 11 3 12\\n\\nSAMOLE\", \"2\\n1 4\\n1 1 1 1 2 1\\n4 2\\n1 2 2 8 4 1\\n\\nSBMOLE\", \"2\\n3 2\\n1 1 1 1 0 0\\n14 3\\n2 3 1 13 -1 2\\n\\nTAMPLE\"], \"outputs\": [\"3 2\\n1 2\\n\", \"3 2\\n1 2\\n\", \"3 2\\n2 2\\n\", \"1 3\\n2 2\\n\", \"1 1\\n1 2\\n\", \"1 3\\n1 2\\n\", \"1 3\\n1 3\\n\", \"1 3\\n3 2\\n\", \"3 2\\n2 1\\n\", \"3 2\\n2 7\\n\", \"3 2\\n1 1\\n\", \"1 3\\n2 4\\n\", \"2 2\\n2 2\\n\", \"1 6\\n2 2\\n\", \"1 5\\n2 2\\n\", \"4 2\\n2 2\\n\", \"1 2\\n2 2\\n\", \"3 2\\n2 4\\n\", \"1 2\\n3 2\\n\", \"3 3\\n2 2\\n\", \"1 3\\n2 1\\n\", \"2 3\\n2 2\\n\", \"1 4\\n2 2\\n\", \"3 2\\n1 3\\n\", \"3 3\\n1 2\\n\", \"1 10\\n2 2\\n\", \"4 3\\n2 2\\n\", \"1 2\\n1 2\\n\", \"3 3\\n1 1\\n\", \"1 7\\n2 2\\n\", \"1 2\\n2 1\\n\", \"3 1\\n2 4\\n\", \"3 2\\n2 38\\n\", \"3 3\\n2 1\\n\", \"3 1\\n2 25\\n\", \"4 3\\n1 1\\n\", \"1 10\\n2 4\\n\", \"3 1\\n2 7\\n\", \"1 2\\n2 4\\n\", \"2 3\\n1 2\\n\", \"1 1\\n2 2\\n\", \"4 2\\n2 1\\n\", \"1 3\\n1 1\\n\", \"1 26\\n2 4\\n\", \"1 1000000\\n2 2\\n\", \"3 1\\n2 13\\n\", \"2 1\\n1 2\\n\", \"1 10\\n1 2\\n\", \"3 1\\n2 23\\n\", \"1 1\\n2 1\\n\", \"1 1000000\\n2 4\\n\", \"1 1\\n3 4\\n\", \"1 11\\n2 4\\n\", \"3 2\\n2 23\\n\", \"1 120\\n2 4\\n\", \"1 1000000\\n3 4\\n\", \"1 1\\n4 10\\n\", \"1 1\\n1 7\\n\", \"1 10\\n1 5\\n\", \"1 1000000\\n3 7\\n\", \"1 120\\n2 1\\n\", \"1 1\\n5 10\\n\", \"1 1\\n6 10\\n\", \"1 247\\n2 1\\n\", \"3 2\\n3 2\\n\", \"3 2\\n2 13\\n\", \"2 2\\n1 2\\n\", \"4 2\\n1 2\\n\", \"1 9\\n2 2\\n\", \"2 4\\n2 2\\n\", \"1 1\\n1 3\\n\", \"1 1\\n1 1\\n\", \"3 3\\n1 3\\n\", \"3 1\\n1 2\\n\", \"1 26\\n2 2\\n\", \"3 5\\n1 2\\n\", \"3 3\\n2 13\\n\", \"3 2\\n3 38\\n\", \"4 3\\n2 1\\n\", \"1 10\\n2 1\\n\", \"4 1\\n2 25\\n\", \"1 1\\n1 4\\n\", \"1 3\\n1 11\\n\", \"1 4\\n1 1\\n\", \"1 4\\n2 4\\n\", \"3 1\\n3 7\\n\", \"1 1000000\\n2 13\\n\", \"2 1\\n2 13\\n\", \"2 5\\n1 2\\n\", \"1 10\\n1 1\\n\", \"3 1\\n1 292\\n\", \"1 1\\n2 23\\n\", \"2 11\\n1 2\\n\", \"1 14\\n1 2\\n\", \"1 3\\n2 23\\n\", \"1 1\\n2 4\\n\", \"1 2\\n4 10\\n\", \"1 1818\\n2 4\\n\", \"1 120\\n2 53\\n\", \"1 10\\n2 5\\n\", \"1 1\\n3 11\\n\"]}", "source": "primeintellect"}
|
Shantam is very rich , even richer than Richie Rich. He is extremely talented in almost everything except one , mathematics. So one day, he pays a visit to a temple (to pray for his upcoming mathematics exams) and decides to donate some amount of money to the poor people ( everyone is poor on a relative scale to Shantam). He order N people to sit in a linear arrangement and indexes them from 1 to N , to ease the process of donating money.
As with all rich people , their way of doing things is completely eerie and different. Shantam donates his money in M steps , each of his step being to choose two indices L and R , and an amount of money C and then he donates C currencies to each and every person whose index lies in [L,R]. In other words he donates C currencies to every index i such L ≤ i ≤ R.
Luckily, you too were among the N people selected and somehow you know all the M steps in advance. Figure out the maximum amount of money you can obtain and at what position you should sit to get this maximum amount of money. If multiple positions guarantee the maximum amount of money , output the minimum index out of all these possibilities.
You will be given initial L , R and C (which points to first query) as well as P , Q and S. Each subsequent query is generated as :
L[i] = (L[i-1] * P + R[i-1]) % N + 1;
R[i] = (R[i-1] * Q + L[i-1]) % N + 1;
if(L[i] > R[i])
swap(L[i] , R[i]);
C[i] = (C[i-1] * S) % 1000000 + 1;
Input Format :
The first line contains T , the number of test cases. The first line of each test case contains two space separated integers N and M , which denotes the number of people and the number of steps, respectively. The next line contains integers L , R , C , P , Q and S , which are used to generate the queries using the method specified above.
Output Format :
For each test case , output one line containing two space separated integers, the first being the optimal position and the second being the highest amount of money that can be obtained.
Constraints :
1 ≤ T ≤ 200
1 ≤ N ≤ 10^5
1 ≤ M ≤ 10^5
1 ≤ L ≤ R ≤ N
1 ≤ C ≤ 10^6
1 ≤ P,Q,S ≤ 10^4
SAMPLE INPUT
2
5 2
1 1 1 1 1 1
5 1
1 3 2 4 3 5
SAMPLE OUTPUT
3 2
1 2
Explanation
Sample Case 2 :
Initially all have 0 money, and can be represented as [ 0 , 0 , 0 , 0 , 0].
After first update , [2, 2, 2, 0, 0]
The maximum amount is 2 and the minimum position with this maximum amount is 1.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"90081 33447 90629 6391049189\", \"2 5 6 0\", \"4 1 2 5\", \"90081 33447 66380 6391049189\", \"2 5 6 1\", \"90081 33447 77758 6391049189\", \"2 9 7 0\", \"4 1 3 5\", \"90081 33447 77758 2284871002\", \"6 1 2 17\", \"121980 33447 90629 11295524182\", \"4 1 1 5\", \"111605 33447 77758 2284871002\", \"11 1 2 17\", \"4 1 1 7\", \"111605 33447 14069 2284871002\", \"42470 60074 125620 6171829514\", \"11 1 4 17\", \"42470 50231 61801 2995288065\", \"1 2 2 2\", \"42470 92623 71757 2078437598\", \"6 1 1 7\", \"111605 33447 27166 2284871002\", \"11 1 4 1\", \"42470 92623 43227 2078437598\", \"4 2 2 5\", \"2 9 6 1\", \"4 2 2 9\", \"90081 33447 71757 6391049189\", \"2 9 7 1\", \"6 2 2 9\", \"42470 33447 71757 6391049189\", \"6 2 2 17\", \"42470 50231 71757 6391049189\", \"0 9 7 0\", \"0 2 2 17\", \"42470 50231 71757 8937709765\", \"0 9 7 1\", \"0 2 2 3\", \"42470 50231 71757 12775405687\", \"0 14 7 1\", \"1 2 2 3\", \"42470 65861 71757 12775405687\", \"-1 14 7 1\", \"1 2 1 3\", \"42470 65861 110679 12775405687\", \"-1 14 11 1\", \"30652 65861 110679 12775405687\", \"-1 24 11 1\", \"30652 65861 151601 12775405687\", \"-1 24 13 1\", \"30652 65861 151601 17634240489\", \"-1 24 25 1\", \"30652 65861 151601 33146475924\", \"-2 24 25 1\", \"26422 65861 151601 33146475924\", \"-2 24 40 1\", \"26422 82427 151601 33146475924\", \"-2 24 56 1\", \"26422 82427 151601 46823749253\", \"-2 24 56 0\", \"26422 80620 151601 46823749253\", \"-1 24 56 0\", \"26422 80620 151601 88095724507\", \"-1 1 56 0\", \"26422 13352 151601 88095724507\", \"-1 1 8 0\", \"26422 18932 151601 88095724507\", \"26422 11485 151601 88095724507\", \"26422 11485 151601 128745938646\", \"26422 2698 151601 128745938646\", \"26422 2698 151601 218994886226\", \"26422 759 151601 218994886226\", \"26422 786 151601 218994886226\", \"26422 786 228496 218994886226\", \"26422 786 303944 218994886226\", \"26422 786 303944 255531414857\", \"26422 786 303944 29921263322\", \"26422 786 238528 29921263322\", \"26422 602 238528 29921263322\", \"26422 602 259348 29921263322\", \"26422 597 259348 29921263322\", \"26422 597 437351 29921263322\", \"26422 597 437351 23555325000\", \"26422 597 148807 23555325000\", \"26422 46 148807 23555325000\", \"32289 46 148807 23555325000\", \"32289 46 124751 23555325000\", \"32289 46 26552 23555325000\", \"5933 46 26552 23555325000\", \"5933 72 26552 23555325000\", \"5933 72 32909 23555325000\", \"3572 72 32909 23555325000\", \"3572 72 2217 23555325000\", \"5117 72 2217 23555325000\", \"6818 72 2217 23555325000\", \"6818 72 3183 23555325000\", \"6818 78 3183 23555325000\", \"6818 78 5327 23555325000\", \"4541 78 5327 23555325000\", \"4541 44 5327 23555325000\", \"2021 44 5327 23555325000\", \"184 44 5327 23555325000\"], \"outputs\": [\"577742975\", \"1\", \"40\", \"108311950\\n\", \"0\\n\", \"61698994\\n\", \"1\\n\", \"24\\n\", \"792830587\\n\", \"6\\n\", \"643972230\\n\", \"56\\n\", \"762328834\\n\", \"440484\\n\", \"8\\n\", \"815838636\\n\", \"334199188\\n\", \"82885\\n\", \"1130130\\n\", \"2\\n\", \"510905963\\n\", \"792\\n\", \"927401872\\n\", \"11\\n\", \"914919326\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Takahashi has a tower which is divided into N layers. Initially, all the layers are uncolored. Takahashi is going to paint some of the layers in red, green or blue to make a beautiful tower. He defines the beauty of the tower as follows:
* The beauty of the tower is the sum of the scores of the N layers, where the score of a layer is A if the layer is painted red, A+B if the layer is painted green, B if the layer is painted blue, and 0 if the layer is uncolored.
Here, A and B are positive integer constants given beforehand. Also note that a layer may not be painted in two or more colors.
Takahashi is planning to paint the tower so that the beauty of the tower becomes exactly K. How many such ways are there to paint the tower? Find the count modulo 998244353. Two ways to paint the tower are considered different when there exists a layer that is painted in different colors, or a layer that is painted in some color in one of the ways and not in the other.
Constraints
* 1 ≤ N ≤ 3×10^5
* 1 ≤ A,B ≤ 3×10^5
* 0 ≤ K ≤ 18×10^{10}
* All values in the input are integers.
Input
Input is given from Standard Input in the following format:
N A B K
Output
Print the number of the ways to paint tiles, modulo 998244353.
Examples
Input
4 1 2 5
Output
40
Input
2 5 6 0
Output
1
Input
90081 33447 90629 6391049189
Output
577742975
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red gaMenta Green Blue\\nnayC Yellow Red Magenta Green Blue\\nRed Yellow eagMnta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow eagMnta Blue Green Cyan\\n0\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCy`n Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yeklow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG ayCn\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow eagMnta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow eagMnta Blue Green Cyan\\n4\\nRed Lagenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellnw Magenta Blue Green Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neeqG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cybn\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Ydllow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow eagMnta Blue Green Cyan\\n4\\nRed Lagenta Blue Hreen Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Zellow Cybn\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yemlow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Hreen wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yeklow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Ydllow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Grene Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Gredn Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG nayC\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyna Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yeklow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Grefn Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yeklow Magenta Blue Green Cyan\\n4\\nRed Magenua Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neerG Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow ayCn\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neeqG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cayn\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Ydllow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Maaentg Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yemlow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Gneer Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Hreen wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Gredn Yellow Blue Lagenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yelolw Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyna Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Grefn Cyan\\n4\\nRed Magenua Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellox Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neerG Cyan\\n4\\nRed Magenta Blue Green Yellpw Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yelolw Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nanyC Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellox Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Grfen Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yelolw Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nanyC Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Ylelow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Mnheata Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Green Cyan\\n4\\nRed Magenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow eahMnta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yemlow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellwo Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yelmow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyna Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neeqG nayC\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cyan\\n4\\nRed Mahfnta Blue Green Yellox Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Grfen Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyao\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nnayC Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Gqeen Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCzan Green Yemlow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue Green Czan\\n4\\nRed Magenta Blue Green Yeklow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green wolleY Cyna\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yelolw Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Gredn Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG nayC\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue tagenMa Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yemlow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyna Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cyan\\n4\\nRed Mahemta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow ayBn\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Gneer Yellow yCan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Hreen wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Grefn Cyan\\n4\\nRed Magenua Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magentb Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yelolw Magenta Blue Greeo Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nanyC Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Green Cyan\\n4\\nRed Magenta Blue Green wollYe Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolkeY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cybn\\n4\\nRed Mahemta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed volleY Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellow ayBn\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow atnegaM Blue Grefn Cyan\\n4\\nRed Magenua Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan neerG wolkeY Blue Magentb Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mahensa Blue neerG Cybn\\n4\\nRed Mahemta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue ereGn Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG nCya\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow Cyam\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue gaMenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow eagMnta Blue Green Cyan\\n4\\nRed Lagenta Blue Green Yeklow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellnw Magenta Blue Gredn Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed wolleY Magenta Blue neeqG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellox Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellpv Magenta Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Zellow Cybn\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue Mahenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yeollw Magenta Blue nGeqe Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Gredn Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue neerG nayC\\n4\\nRed Mahenta Blue Green wolleY Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wloleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellov Magenta Blue neeqG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue aMgenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Mafenta Blue Green Cyan\\n4\\nRed Magenta Blue Gneer Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Hreen wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magensa Blue nereG Cyan\\n4\\nRed Mahenta Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yelolw Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue neesG Cyan\\n4\\nRed Magenta Blue Green Yellpw Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green wolleY Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed wolleY Mahensa Blue neerG Cyan\\n4\\nRed Mahenta Blue Green Yellox Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Grfen Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yelolw Magenta Blue Green Cyan\\n4\\nRed Magenta Blue Green Yellow nayC\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyna Green Yellow Blue Magenta Red\\n0\", \"3\\nCyan Yellow Red Magenta Green Blue\\nCyan Yellow Red Magenta Green Blue\\nRed Yellow Magenta Blue Green Cy`n\\n4\\nRed Mnheata Blue Green Yellow Cyan\\nRed Yellow Magenta Blue Green Cyan\\nMagenta Green Red Cyan Yellow Blue\\nCyan Green Yellow Blue Magenta Red\\n0\"], \"outputs\": [\"1\\n1\", \"1\\n1\\n\", \"0\\n1\\n\", \"1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\"]}", "source": "primeintellect"}
|
Artist Shinagawa was asked to exhibit n works. Therefore, I decided to exhibit the six sides of the cube colored with paint as a work. The work uses all six colors, Red, Yellow, Blue, Magenta, Green, and Cyan, and each side is filled with one color. Shinagawa changed the arrangement of colors even for cubic works with the same shape, and created n points as different works.
<image>
As a friend of mine, you, a friend of mine, allowed you to browse the work before exhibiting, and noticed that it was there. Even though they seemed to be colored differently, there were actually cubes with the same color combination. At this rate, it will not be possible to exhibit n works.
Please create a program that inputs the number of created works and the color information of each work and outputs how many more points you need to exhibit.
The color of each side of the cube is represented by the symbols from c1 to c6, and the arrangement is as follows. Also, each of c1 to c6 is one of Red, Yellow, Blue, Magenta, Green, and Cyan.
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
cube1
cube2
::
cuben
The first line gives the number of works n (1 ≤ n ≤ 30), and the following n lines give information on the i-th work. Information on each work is given in the following format.
c1 c2 c3 c4 c5 c6
The color arrangement ci of the work is given, separated by blanks.
The number of datasets does not exceed 100.
Output
For each dataset, output how many more works are needed to exhibit in one line.
Example
Input
3
Cyan Yellow Red Magenta Green Blue
Cyan Yellow Red Magenta Green Blue
Red Yellow Magenta Blue Green Cyan
4
Red Magenta Blue Green Yellow Cyan
Red Yellow Magenta Blue Green Cyan
Magenta Green Red Cyan Yellow Blue
Cyan Green Yellow Blue Magenta Red
0
Output
1
1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n1 2 -1\\n1 3 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -3\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 2 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n2 2 -1\\n1 3 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -6\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 4 2 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n0 2 0\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n1 3 5\\n2 2 -1\\n1 3 5\", \"3 5 1 1\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n2 3 0\\n1 2 -1\\n1 2 5\", \"3 5 4 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 0\\n1 2 8\", \"3 5 4 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 0\\n2 2 8\", \"3 5 4 2\\n0\\n4\\n1\\n7\\n2 0 2\\n1 2 -3\\n2 1 5\\n1 2 0\\n2 2 8\", \"3 5 4 2\\n0\\n4\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n1 2 0\\n2 2 8\", \"3 5 4 2\\n0\\n1\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n1 0 0\\n2 2 8\", \"3 5 4 4\\n0\\n1\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n2 0 0\\n2 2 8\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n1 3 5\\n1 2 -1\\n1 3 5\", \"3 5 2 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -3\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n3 2 2\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 0 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -6\\n2 3 3\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n2 2 2\\n1 0 -3\\n2 3 0\\n1 2 -1\\n1 2 5\", \"3 5 2 0\\n0\\n4\\n1\\n7\\n2 2 1\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 4 2 1\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 0\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n1 3 5\\n2 2 -1\\n1 3 5\", \"3 5 4 2\\n0\\n6\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 0\\n1 2 8\", \"3 5 1 2\\n0\\n7\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 3\\n0 2 0\\n1 2 5\", \"3 5 1 1\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n2 3 1\\n1 2 -1\\n1 2 2\", \"3 5 4 2\\n0\\n6\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n1 0 0\\n2 2 8\", \"3 5 4 2\\n0\\n1\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 2 5\\n1 0 0\\n2 2 8\", \"3 5 4 4\\n0\\n1\\n1\\n9\\n3 0 0\\n1 1 -3\\n2 1 5\\n2 0 0\\n2 1 8\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n3 2 2\\n1 1 -3\\n2 1 5\\n1 2 -2\\n1 2 5\", \"3 5 0 2\\n0\\n7\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 3 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n2 1 -1\\n1 3 5\", \"3 5 1 2\\n0\\n4\\n2\\n8\\n1 2 2\\n1 1 -6\\n2 3 3\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n2 2 4\\n1 0 -3\\n2 3 0\\n1 2 -1\\n1 2 5\", \"3 5 2 0\\n0\\n4\\n2\\n7\\n2 2 1\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 4 2 1\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n3 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 0\\n0\\n5\\n1\\n8\\n1 2 2\\n1 1 -2\\n1 3 5\\n2 2 -1\\n1 3 5\", \"3 5 4 2\\n0\\n6\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 2 5\\n1 2 0\\n1 2 8\", \"3 5 0 4\\n0\\n1\\n1\\n7\\n3 0 0\\n1 1 -3\\n2 1 5\\n2 1 0\\n2 1 16\", \"3 4 0 2\\n0\\n7\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 3 2\\n0\\n4\\n1\\n7\\n2 2 3\\n1 0 -3\\n2 1 5\\n1 2 0\\n1 2 5\", \"3 3 1 2\\n0\\n4\\n2\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n2 1 -1\\n1 3 5\", \"3 5 1 2\\n0\\n4\\n2\\n8\\n1 2 2\\n1 1 -6\\n2 3 3\\n1 2 -1\\n2 2 5\", \"3 5 2 2\\n0\\n4\\n2\\n10\\n2 0 1\\n1 1 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 4 2\\n0\\n6\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 2 6\\n1 2 0\\n1 2 8\", \"3 4 1 1\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n3 3 1\\n1 2 -1\\n1 2 2\", \"3 5 1 2\\n0\\n4\\n1\\n7\\n2 2 0\\n1 2 -3\\n2 1 3\\n0 -1 0\\n1 2 6\", \"3 5 4 2\\n0\\n6\\n1\\n7\\n2 0 0\\n1 1 -3\\n2 1 5\\n1 0 1\\n2 2 8\", \"3 5 4 2\\n0\\n1\\n1\\n7\\n2 -1 0\\n1 2 -5\\n2 2 5\\n1 0 0\\n2 2 8\", \"3 4 4 4\\n0\\n1\\n2\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n2 0 0\\n1 2 8\", \"3 5 0 4\\n0\\n1\\n1\\n7\\n3 0 0\\n1 1 -3\\n2 1 5\\n2 1 0\\n4 1 16\", \"3 4 1 2\\n0\\n7\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 3 2\\n0\\n4\\n1\\n7\\n2 2 5\\n1 0 -3\\n2 1 5\\n1 2 0\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n2\\n8\\n1 2 2\\n1 1 -3\\n2 3 3\\n1 2 -1\\n2 2 5\", \"3 5 2 0\\n0\\n4\\n2\\n7\\n2 2 0\\n1 1 -3\\n2 0 5\\n1 2 -1\\n1 2 5\", \"3 5 4 3\\n0\\n6\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 2 6\\n1 2 0\\n1 2 8\", \"3 4 1 1\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n3 3 2\\n1 2 -1\\n1 2 2\", \"3 5 4 2\\n0\\n6\\n1\\n7\\n2 0 0\\n1 1 -3\\n2 1 5\\n2 0 1\\n2 2 8\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n2 1 10\\n1 2 -2\\n1 2 5\", \"3 4 0 2\\n0\\n7\\n1\\n7\\n2 2 2\\n2 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 4 1 2\\n0\\n4\\n2\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n2 1 -1\\n1 0 5\", \"3 5 1 2\\n0\\n4\\n2\\n8\\n1 2 2\\n1 1 -3\\n2 3 3\\n1 2 0\\n2 2 5\", \"3 5 2 2\\n0\\n4\\n2\\n11\\n2 0 1\\n1 1 -3\\n2 1 7\\n1 2 -1\\n1 2 5\", \"3 5 4 3\\n0\\n6\\n1\\n7\\n2 2 2\\n1 2 -6\\n2 2 6\\n1 2 0\\n1 2 8\", \"3 5 4 2\\n0\\n0\\n1\\n7\\n2 0 0\\n1 1 -3\\n2 1 5\\n2 0 1\\n2 2 8\", \"3 5 1 2\\n0\\n4\\n1\\n10\\n1 2 2\\n1 1 -2\\n2 1 10\\n1 2 -2\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n2\\n8\\n2 2 2\\n1 1 -3\\n2 3 3\\n1 2 0\\n2 2 5\", \"3 5 1 2\\n0\\n4\\n0\\n15\\n2 2 4\\n1 0 -3\\n0 3 0\\n1 1 -1\\n1 2 5\", \"3 5 4 3\\n0\\n6\\n1\\n7\\n2 2 2\\n1 0 -6\\n2 2 6\\n1 2 0\\n1 2 8\", \"3 5 1 4\\n0\\n1\\n1\\n7\\n4 -1 0\\n1 2 -1\\n2 0 5\\n0 0 0\\n2 1 8\", \"3 5 0 2\\n0\\n4\\n2\\n8\\n2 2 2\\n1 1 -3\\n2 3 3\\n1 2 0\\n2 2 5\", \"3 5 4 3\\n0\\n10\\n1\\n7\\n2 2 2\\n1 0 -6\\n2 2 6\\n1 2 0\\n1 2 8\", \"3 5 4 2\\n0\\n0\\n1\\n7\\n2 1 0\\n1 1 -3\\n2 1 5\\n2 0 1\\n1 2 8\", \"3 5 4 2\\n0\\n0\\n1\\n6\\n2 1 0\\n1 1 -3\\n2 1 5\\n2 0 1\\n1 2 8\", \"3 5 1 1\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 3 2\\n1 1 -3\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n2 2 2\\n2 1 -3\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 1 -3\\n2 0 5\\n1 2 -1\\n1 2 5\", \"3 5 2 0\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -6\\n2 3 5\\n1 2 -1\\n1 2 10\", \"3 5 1 2\\n0\\n4\\n0\\n7\\n2 2 2\\n1 2 -3\\n2 1 5\\n0 2 0\\n1 2 5\", \"3 5 1 2\\n0\\n4\\n0\\n8\\n1 2 2\\n1 1 -2\\n1 3 5\\n2 2 -1\\n1 3 5\", \"3 4 2 2\\n0\\n4\\n1\\n7\\n2 3 4\\n1 2 -3\\n2 1 5\\n1 2 -1\\n1 2 5\", \"3 5 1 1\\n0\\n4\\n1\\n8\\n2 2 2\\n1 1 -3\\n2 3 0\\n1 2 -1\\n1 3 2\", \"3 5 4 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 1 -3\\n2 1 5\\n1 2 0\\n2 2 8\", \"3 5 2 3\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 3\\n0 2 0\\n1 2 5\", \"3 5 4 2\\n0\\n4\\n1\\n6\\n2 0 0\\n1 2 -3\\n2 1 5\\n1 2 0\\n2 2 8\", \"3 5 2 2\\n0\\n4\\n1\\n7\\n2 2 2\\n1 3 -3\\n2 1 3\\n0 -1 0\\n1 2 5\", \"3 5 2 4\\n0\\n4\\n1\\n7\\n2 2 2\\n1 2 -3\\n2 1 3\\n-1 -1 0\\n1 2 5\", \"3 5 4 1\\n0\\n1\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n1 0 0\\n2 2 8\", \"3 5 4 2\\n0\\n1\\n0\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n2 0 0\\n2 2 8\", \"3 5 4 5\\n0\\n1\\n1\\n7\\n2 0 0\\n1 2 -3\\n2 1 5\\n2 0 0\\n2 1 8\", \"3 5 4 6\\n0\\n1\\n1\\n7\\n3 0 0\\n1 2 -3\\n2 1 5\\n2 0 0\\n2 1 8\", \"3 5 1 4\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -2\\n1 3 5\\n1 2 -1\\n1 3 5\", \"3 5 1 2\\n0\\n8\\n1\\n8\\n2 2 2\\n1 1 -2\\n2 3 5\\n1 2 -1\\n1 2 5\", \"3 5 1 3\\n0\\n4\\n1\\n8\\n1 2 2\\n1 1 -3\\n2 3 5\\n1 2 -1\\n1 2 5\"], \"outputs\": [\"-5\\n-7\\n-13\\n-13\\n-18\", \"-5\\n-7\\n-13\\n-13\\n-13\\n\", \"-5\\n-8\\n-13\\n-13\\n-13\\n\", \"-7\\n-8\\n-13\\n-13\\n-13\\n\", \"-7\\n-8\\n-8\\n-8\\n-8\\n\", \"-6\\n-7\\n-7\\n-7\\n-7\\n\", \"-14\\n-14\\n-14\\n-14\\n-14\\n\", \"-5\\n-7\\n-13\\n-13\\n-18\\n\", \"-5\\n-8\\n-13\\n-12\\n-13\\n\", \"-14\\n-14\\n-14\\n-14\\n\", \"-6\\n-6\\n-6\\n-6\\n-6\\n\", \"-5\\n-7\\n-12\\n-11\\n-16\\n\", \"-8\\n-8\\n-8\\n-8\\n-8\\n\", \"-30\\n-30\\n-30\\n-30\\n-32\\n\", \"-30\\n-30\\n-30\\n-30\\n-30\\n\", \"-30\\n-32\\n-32\\n-32\\n-30\\n\", \"-34\\n-34\\n-34\\n-34\\n-28\\n\", \"-28\\n-32\\n-32\\n-32\\n-32\\n\", \"-28\\n-28\\n-28\\n-28\\n-28\\n\", \"-5\\n-7\\n-12\\n-12\\n-17\\n\", \"-16\\n-16\\n-26\\n-26\\n-26\\n\", \"-5\\n-8\\n-8\\n-8\\n-8\\n\", \"2\\n2\\n2\\n2\\n2\\n\", \"-5\\n-8\\n-11\\n-10\\n-11\\n\", \"-7\\n-7\\n-7\\n-7\\n-7\\n\", \"-18\\n-14\\n-14\\n-14\\n-14\\n\", \"-15\\n-15\\n-15\\n-15\\n\", \"-11\\n-9\\n-14\\n-15\\n-20\\n\", \"-34\\n-34\\n-34\\n-34\\n-36\\n\", \"-3\\n-3\\n-3\\n-3\\n-3\\n\", \"-8\\n-8\\n-9\\n-9\\n-9\\n\", \"-38\\n-38\\n-38\\n-38\\n-28\\n\", \"-28\\n-32\\n-32\\n-32\\n-40\\n\", \"-36\\n-36\\n-36\\n-36\\n-36\\n\", \"-5\\n-8\\n-8\\n-7\\n-8\\n\", \"8\\n8\\n8\\n8\\n8\\n\", \"-5\\n-7\\n-13\\n\", \"-6\\n-8\\n-11\\n-10\\n-11\\n\", \"-8\\n-8\\n-8\\n-8\\n-7\\n\", \"-16\\n-14\\n-14\\n-14\\n-14\\n\", \"-15\\n-15\\n-20\\n-20\\n\", \"-12\\n-10\\n-15\\n-16\\n-21\\n\", \"-34\\n-34\\n-28\\n-28\\n-40\\n\", \"0\\n8\\n8\\n8\\n8\\n\", \"8\\n8\\n8\\n8\\n\", \"-21\\n-21\\n-21\\n-21\\n-23\\n\", \"-6\\n-8\\n-13\\n\", \"-6\\n-8\\n-11\\n-10\\n-10\\n\", \"-20\\n-20\\n-20\\n-20\\n-20\\n\", \"-34\\n-34\\n-28\\n-28\\n-42\\n\", \"-8\\n-8\\n-9\\n-9\\n\", \"-4\\n-4\\n-4\\n-4\\n-4\\n\", \"-38\\n-32\\n-32\\n-32\\n-32\\n\", \"-28\\n-36\\n-36\\n-36\\n-40\\n\", \"-28\\n-28\\n-28\\n-28\\n\", \"0\\n8\\n8\\n8\\n60\\n\", \"-3\\n-3\\n-3\\n-3\\n\", \"-21\\n-21\\n-21\\n-21\\n-25\\n\", \"-6\\n-8\\n-11\\n-11\\n-11\\n\", \"-18\\n-14\\n-22\\n-24\\n-14\\n\", \"-31\\n-31\\n-28\\n-28\\n-35\\n\", \"-8\\n-8\\n-10\\n-10\\n\", \"-38\\n-32\\n-32\\n-30\\n-32\\n\", \"-5\\n-7\\n-7\\n-7\\n-7\\n\", \"8\\n14\\n14\\n14\\n\", \"-6\\n-8\\n-13\\n-13\\n\", \"-6\\n-8\\n-11\\n-11\\n-10\\n\", \"-22\\n-22\\n-22\\n-22\\n-22\\n\", \"-31\\n-31\\n-28\\n-28\\n-32\\n\", \"-28\\n-34\\n-34\\n-36\\n-40\\n\", \"-7\\n-9\\n-9\\n-9\\n-9\\n\", \"-8\\n-8\\n-11\\n-11\\n-10\\n\", \"-15\\n-15\\n-15\\n-15\\n-15\\n\", \"-31\\n-31\\n-30\\n-30\\n-38\\n\", \"-7\\n-7\\n8\\n8\\n8\\n\", \"0\\n0\\n0\\n0\\n2\\n\", \"-35\\n-35\\n-31\\n-31\\n-39\\n\", \"-28\\n-34\\n-34\\n-36\\n-32\\n\", \"-24\\n-30\\n-30\\n-32\\n-30\\n\", \"-8\\n-8\\n-13\\n-13\\n-13\\n\", \"-7\\n-10\\n-15\\n-15\\n-15\\n\", \"-7\\n-7\\n-13\\n-13\\n-13\\n\", \"-6\\n-7\\n-3\\n-2\\n-7\\n\", \"-16\\n-16\\n-16\\n-16\\n-16\\n\", \"-5\\n-8\\n-13\\n-12\\n-9\\n\", \"-5\\n-5\\n-5\\n-5\\n-5\\n\", \"-4\\n-6\\n-11\\n-10\\n-15\\n\", \"-22\\n-22\\n-22\\n-22\\n\", \"-8\\n-8\\n-8\\n-8\\n-10\\n\", \"-30\\n-28\\n-28\\n-28\\n-36\\n\", \"-13\\n-13\\n-13\\n-13\\n-13\\n\", \"-30\\n-30\\n-30\\n-30\\n-24\\n\", \"-14\\n-8\\n-8\\n-8\\n-8\\n\", \"-12\\n-12\\n-12\\n-12\\n-12\\n\", \"-28\\n-34\\n-34\\n-34\\n-34\\n\", \"-30\\n-34\\n-34\\n-34\\n-32\\n\", \"-28\\n-26\\n-26\\n-26\\n-26\\n\", \"-28\\n-24\\n-24\\n-24\\n-24\\n\", \"1\\n-5\\n-10\\n-10\\n-15\\n\", \"-3\\n-5\\n-13\\n-13\\n-13\\n\", \"-2\\n-8\\n-13\\n-13\\n-13\\n\"]}", "source": "primeintellect"}
|
In the Kingdom of IOI, the wind always blows from sea to land. There are $N + 1$ spots numbered from $0$ to $N$. The wind from Spot $0$ to Spot $N$ in order. Mr. JOI has a house at Spot $N$. The altitude of Spot $0$ is $A_0 = 0$, and the altitude of Spot $i$ ($1 \leq i \leq N$) is $A_i$.
The wind blows on the surface of the ground. The temperature of the wind changes according to the change of the altitude. The temperature of the wind at Spot $0$, which is closest to the sea, is $0$ degree. For each $i$ ($0 \leq i \leq N - 1$), the change of the temperature of the wind from Spot $i$ to Spot $i + 1$ depends only on the values of $A_i$ and $A_{i+1}$ in the following way:
* If $A_i < A_{i+1}$, the temperature of the wind decreases by $S$ degrees per altitude.
* If $A_i \geq A_{i+1}$, the temperature of the wind increases by $T$ degrees per altitude.
The tectonic movement is active in the land of the Kingdom of IOI. You have the data of tectonic movements for $Q$ days. In the $j$-th ($1 \leq j \leq Q$) day, the change of the altitude of Spot $k$ for $L_j \leq k \leq R_j$ ($1 \leq L_j \leq R_j \leq N$) is described by $X_j$. If $X_j$ is not negative, the altitude increases by $X_j$. If $X_j$ is negative, the altitude decreases by $|X_j|$.
Your task is to calculate the temperature of the wind at the house of Mr. JOI after each tectonic movement.
Task
Given the data of tectonic movements, write a program which calculates, for each $j$ ($1 \leq j \leq Q$), the temperature of the wind at the house of Mr. JOI after the tectonic movement on the $j$-th day.
Input
Read the following data from the standard input.
* The first line of input contains four space separated integers $N$, $Q$, $S$, $T$. This means there is a house of Mr. JOI at Spot $N$, there are $Q$ tectonic movements, the temperature of the wind decreases by $S$ degrees per altitude if the altitude increases, and the temperature of the wind increases by $T$ degrees per altitude if the altitude decreases.
* The $i$-th line ($1 \leq i \leq N +1$) of the following $N +1$ lines contains an integer $A_{i-1}$, which is the initial altitude at Spot ($i - 1$) before tectonic movements.
* The $j$-th line ($1 \leq j \leq Q$) of the following $Q$ lines contains three space separated integers $L_j$, $R_j$, $X_j$. This means, for the tectonic movement on the $j$-th day, the change of the altitude at the spots from $L_j$ to $R_j$ is described by $X_j$.
Output
Write $Q$ lines to the standard output. The $j$-th line ($1 \leq j \leq Q$) of output contains the temperature of the wind at the house of Mr. JOI after the tectonic movement on the $j$-th day.
Constraints
All input data satisfy the following conditions.
* $1 \leq N \leq 200 000．$
* $1 \leq Q \leq 200 000．$
* $1 \leq S \leq 1 000 000．$
* $1 \leq T \leq 1 000 000．$
* $A_0 = 0．$
* $-1 000 000 \leq A_i \leq 1 000 000 (1 \leq i \leq N)．$
* $1 \leq L_j \leq R_j \leq N (1 \leq j \leq Q)．$
* $ -1 000 000 \leq X_j \leq 1 000 000 (1 \leq j \leq Q)．$
Sample Input and Output
Sample Input 1
3 5 1 2
0
4
1
8
1 2 2
1 1 -2
2 3 5
1 2 -1
1 3 5
Sample Output 1
-5
-7
-13
-13
-18
Initially, the altitudes of the Spot 0, 1, 2, 3 are 0, 4, 1, 8, respectively. After the tectonic movement on the first day, the altitudes become 0, 6, 3, 8, respectively. At that moment, the temperatures of the wind are 0, -6, 0, -5,respectively.
Sample Input 2
2 2 5 5
0
6
-1
1 1 4
1 2 8
Sample Output 2
5
-35
Sample Input 3
7 8 8 13
0
4
-9
4
-2
3
10
-9
1 4 8
3 5 -2
3 3 9
1 7 4
3 5 -1
5 6 3
4 4 9
6 7 -10
Sample output 3
277
277
322
290
290
290
290
370
Creatie Commons License
The 16th Japanese Olympiad in Informatics (JOI 2016/2017) Final Round
Example
Input
3 5 1 2
0
4
1
8
1 2 2
1 1 -2
2 3 5
1 2 -1
1 3 5
Output
-5
-7
-13
-13
-18
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"6 3\\n1 3 4 2 6 5\", \"6 3\\n1 5 4 2 6 5\", \"2 1\\n0 1 -1 1 -1 -1\", \"6 3\\n1 5 4 2 0 5\", \"6 3\\n1 5 4 2 0 2\", \"6 3\\n1 5 4 2 0 3\", \"6 3\\n1 5 4 4 0 3\", \"6 3\\n1 5 4 1 0 3\", \"6 3\\n1 5 1 1 0 3\", \"6 3\\n1 5 1 1 0 0\", \"11 3\\n1 5 4 2 0 5\", \"6 3\\n1 5 7 2 0 2\", \"6 3\\n1 5 4 0 0 3\", \"6 3\\n0 5 4 4 0 3\", \"6 3\\n1 5 2 1 0 3\", \"6 2\\n1 5 1 1 0 3\", \"6 3\\n1 5 1 1 0 1\", \"11 3\\n1 4 4 2 0 5\", \"6 3\\n0 5 7 2 0 2\", \"6 3\\n2 5 4 0 0 3\", \"6 3\\n0 5 6 4 0 3\", \"6 3\\n1 5 2 0 0 3\", \"6 2\\n0 5 1 1 0 3\", \"6 3\\n1 5 1 1 -1 1\", \"11 3\\n1 4 4 2 0 0\", \"6 3\\n0 5 7 2 -1 2\", \"6 0\\n2 5 4 0 0 3\", \"6 3\\n0 5 6 1 0 3\", \"6 3\\n2 5 2 0 0 3\", \"12 2\\n0 5 1 1 0 3\", \"6 3\\n1 5 1 1 -1 2\", \"11 3\\n1 4 4 2 1 0\", \"6 3\\n0 10 7 2 -1 2\", \"6 1\\n2 5 4 0 0 3\", \"11 3\\n0 5 6 1 0 3\", \"6 3\\n4 5 2 0 0 3\", \"12 2\\n0 5 0 1 0 3\", \"6 1\\n1 5 1 1 -1 2\", \"11 3\\n1 4 2 2 1 0\", \"6 6\\n0 10 7 2 -1 2\", \"6 1\\n2 10 4 0 0 3\", \"11 0\\n0 5 6 1 0 3\", \"6 3\\n4 10 2 0 0 3\", \"6 0\\n1 5 1 1 -1 2\", \"11 3\\n1 4 2 2 2 0\", \"6 6\\n0 10 7 3 -1 2\", \"6 1\\n2 10 8 0 0 3\", \"11 1\\n0 5 6 1 0 3\", \"6 3\\n2 10 2 0 0 3\", \"6 -1\\n1 5 1 1 -1 2\", \"11 3\\n1 4 2 2 2 -1\", \"6 6\\n1 10 7 3 -1 2\", \"7 1\\n2 10 8 0 0 3\", \"11 0\\n0 5 6 1 0 6\", \"6 3\\n0 10 2 0 0 3\", \"6 -1\\n1 5 1 1 0 2\", \"11 3\\n1 6 2 2 2 -1\", \"6 6\\n1 10 7 2 -1 2\", \"7 1\\n2 18 8 0 0 3\", \"11 0\\n0 5 8 1 0 6\", \"6 3\\n0 10 2 1 0 3\", \"6 -2\\n1 5 1 1 0 2\", \"11 3\\n1 6 2 2 3 -1\", \"6 6\\n1 10 7 2 -1 4\", \"7 1\\n0 18 8 0 0 3\", \"11 0\\n-1 5 8 1 0 6\", \"6 3\\n0 19 2 1 0 3\", \"6 6\\n1 10 6 2 -1 4\", \"7 1\\n0 18 0 0 0 3\", \"11 0\\n-1 5 8 1 0 4\", \"6 6\\n0 19 2 1 0 3\", \"6 3\\n1 10 6 2 -1 4\", \"7 1\\n0 18 0 0 1 3\", \"18 0\\n-1 5 8 1 0 4\", \"6 6\\n0 19 3 1 0 3\", \"6 2\\n1 10 6 2 -1 4\", \"7 1\\n0 18 0 0 1 1\", \"18 1\\n-1 5 8 1 0 4\", \"6 6\\n0 19 3 2 0 3\", \"6 2\\n1 10 7 2 -1 4\", \"7 1\\n0 18 0 1 1 1\", \"18 1\\n-2 5 8 1 0 4\", \"6 6\\n0 12 3 2 0 3\", \"7 2\\n0 18 0 1 1 1\", \"18 1\\n-2 5 8 1 1 4\", \"6 6\\n1 12 3 2 0 3\", \"7 2\\n0 18 -1 1 1 1\", \"18 2\\n-2 5 8 1 1 4\", \"6 6\\n1 12 3 2 0 0\", \"7 2\\n0 18 -1 2 1 1\", \"18 2\\n-2 5 9 1 1 4\", \"7 2\\n0 8 -1 2 1 1\", \"29 2\\n-2 5 9 1 1 4\", \"7 2\\n0 8 -1 2 1 0\", \"29 2\\n-2 5 9 1 0 4\", \"7 2\\n0 8 -1 1 1 1\", \"29 2\\n-2 5 1 1 0 4\", \"7 2\\n0 8 -1 0 1 1\", \"29 1\\n-2 5 1 1 0 4\", \"7 2\\n0 8 -1 0 1 0\", \"29 1\\n-2 5 1 0 0 4\"], \"outputs\": [\"4\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Reordering the Documents
Susan is good at arranging her dining table for convenience, but not her office desk.
Susan has just finished the paperwork on a set of documents, which are still piled on her desk. They have serial numbers and were stacked in order when her boss brought them in. The ordering, however, is not perfect now, as she has been too lazy to put the documents slid out of the pile back to their proper positions. Hearing that she has finished, the boss wants her to return the documents immediately in the document box he is sending her. The documents should be stowed in the box, of course, in the order of their serial numbers.
The desk has room just enough for two more document piles where Susan plans to make two temporary piles. All the documents in the current pile are to be moved one by one from the top to either of the two temporary piles. As making these piles too tall in haste would make them tumble, not too many documents should be placed on them. After moving all the documents to the temporary piles and receiving the document box, documents in the two piles will be moved from their tops, one by one, into the box. Documents should be in reverse order of their serial numbers in the two piles to allow moving them to the box in order.
For example, assume that the pile has six documents #1, #3, #4, #2, #6, and #5, in this order from the top, and that the temporary piles can have no more than three documents. Then, she can form two temporary piles, one with documents #6, #4, and #3, from the top, and the other with #5, #2, and #1 (Figure E.1). Both of the temporary piles are reversely ordered. Then, comparing the serial numbers of documents on top of the two temporary piles, one with the larger number (#6, in this case) is to be removed and stowed into the document box first. Repeating this, all the documents will be perfectly ordered in the document box.
<image>
Figure E.1. Making two temporary piles
Susan is wondering whether the plan is actually feasible with the documents in the current pile and, if so, how many different ways of stacking them to two temporary piles would do. You are asked to help Susan by writing a program to compute the number of different ways, which should be zero if the plan is not feasible.
As each of the documents in the pile can be moved to either of the two temporary piles, for $n$ documents, there are $2^n$ different choice combinations in total, but some of them may disturb the reverse order of the temporary piles and are thus inappropriate.
The example described above corresponds to the first case of the sample input. In this case, the last two documents, #5 and #6, can be swapped their destinations. Also, exchanging the roles of two temporary piles totally will be OK. As any other move sequences would make one of the piles higher than three and/or make them out of order, the total number of different ways of stacking documents to temporary piles in this example is $2 \times 2 = 4$.
Input
The input consists of a single test case of the following format.
$n$ $m$
$s_1$ ... $s_n$
Here, $n$ is the number of documents in the pile ($1 \leq n \leq 5000$), and $m$ is the number of documents that can be stacked in one temporary pile without committing risks of making it tumble down ($n/2 \leq m \leq n$). Numbers $s_1$ through $s_n$ are the serial numbers of the documents in the document pile, from its top to its bottom. It is guaranteed that all the numbers $1$ through $n$ appear exactly once.
Output
Output a single integer in a line which is the number of ways to form two temporary piles suited for the objective. When no choice will do, the number of ways is $0$, of course.
If the number of possible ways is greater than or equal to $10^9 + 7$, output the number of ways modulo $10^9 + 7$.
Sample Input 1
6 3
1 3 4 2 6 5
Sample Output 1
4
Sample Input 2
6 6
1 3 4 2 6 5
Sample Output 2
8
Sample Input 3
4 4
4 3 1 2
Sample Output 3
0
Example
Input
6 3
1 3 4 2 6 5
Output
4
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n(1+2)*3+3\\n2\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*1\\n721\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n1480\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n1\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1+1*1\\n911\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1+1*1\\n911\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n3\\n1*1*1+1*1*2\\n1480\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n2\\n1*1*1+1*1*2\\n1480\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(2+2)*3+3\\n3\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n1\\n1*1*1+1*1*1\\n721\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(2+2)*3+3\\n3\\n1*1*1+1*1+1\\n323\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n1\\n1*1*1+1+1*1\\n911\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n721\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+3+2\\n3\\n1+1*1+1*2*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+3+2\\n3\\n1+1+1+1*2*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n2\\n1*1*1+1*1*1\\n360\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+2\\n342\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(4+2)*1+3\\n1\\n1*1*1+1*1*1\\n721\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1*1*1\\n1046\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n3\\n1*1*1+1*1*2\\n7\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(2+2)*3+3\\n6\\n1*1*1+1*1+1\\n403\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+3+2\\n3\\n1+1*2+1*1*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+3)*2+3\\n3\\n1*1*1+1+1*1\\n1439\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(3+2)*3+1\\n1\\n1*1*1+1+1*1\\n1307\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*4+3\\n1\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*4+3\\n1\\n1*1*1+1*1*1\\n1108\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n1\\n1*1*1+1*2*2\\n430\\n1*(2*3*4)+5+((6+8*8))*(9)\\n0\", \"3\\n(1+4)+3+3\\n2\\n1*1*1+1*1*1\\n77\\n1*(2*3*4)+5+((6+8*8))*(9)\\n0\", \"3\\n(1+4)+3+3\\n2\\n1*1*1+1+1*1\\n77\\n1*(2*3*4)+5+((6+8*8))*(9)\\n0\", \"3\\n(2+2)*3+3\\n1\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*1\\n911\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*1\\n1480\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*2\\n1480\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n323\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1+1*1\\n911\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*2\\n1480\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n323\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1+1*1\\n911\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*1\\n911\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1+1*1\\n1046\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n342\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1+1+1*1*1\\n911\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n2\\n1*1*1+1*1*2\\n556\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1+1*1\\n1046\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(2+2)*3+3\\n3\\n1*1*1+1*1+1\\n403\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1+1+1*1*1\\n1654\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n721\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+3+3\\n3\\n1*1*1+1*1*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n955\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+3+3\\n3\\n1+1*1+1*1*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n334\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+3+2\\n3\\n1+1*1+1*1*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n180\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n78\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1*1+1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n6\\n1*1*1+1*1*1\\n721\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n4\\n1*1*1+1*1*1\\n911\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*2*1\\n1480\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n1480\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n3\\n1*1*1+1*1*2\\n1480\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1+1*1\\n1213\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1+1*1+1*1*1\\n323\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1+1*1\\n1439\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1+1*1\\n66\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n2\\n1*1*1+1*1*2\\n273\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n1\\n1*1*1+1+1*1\\n1307\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)+3+2\\n2\\n1*1*1+1*1*2\\n556\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1+1+1*1*1\\n539\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(1+2)+3+2\\n3\\n1+1*1+1*1*1\\n1343\\n1*(2+3*4)+5*((6+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n66\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n6\\n1*1*1+1*1+1\\n721\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n4\\n1*1*1+1*1*1\\n623\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n1480\\n1*(2*3*4)+5+((7+7+8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1+1*1\\n693\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1*1+1+1*1\\n106\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n2\\n1*1*1+1*1*1\\n273\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n1\\n1*1*1+1+1*1\\n902\\n1*(2*3*4)+5+((5+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n2+1*1+1*1*1\\n342\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n4\\n1*1*1+1*1*1\\n1046\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n3\\n1*1+1+1*1*1\\n837\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n38\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n4\\n1*1*1+1*1*1\\n800\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n2+1*1+1*1*1\\n214\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)+2+3\\n4\\n1*1*1+1*1*1\\n1046\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n4\\n1*1+1+1*1*1\\n837\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n57\\n1*(1*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n4\\n1*1*2+1*1*1\\n800\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)+2+3\\n4\\n1*1*1+1*1*1\\n823\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n6\\n1*1*1+1*1*1\\n587\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n4\\n1*1*1+1*1*1\\n911\\n2*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n5\\n1*1*1+1+1*1\\n911\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n622\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n633\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(3+2)*3+3\\n3\\n1*1*1+1*1+1\\n323\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*1*1+1*1+1\\n251\\n1*(2*3*4)+5+((6+7+8))*(9)\\n0\", \"3\\n(1+2)*2+3\\n4\\n1*1+1+1*1*1\\n911\\n1*(2*3*4)+5+((5+8*8))*(9)\\n0\", \"3\\n(1+2)*3+2\\n2\\n2*1*1+1*1*1\\n556\\n1*(2*3*4)+5+((7+7*8))*(9)\\n0\", \"3\\n(3+2)*1+3\\n1\\n1*1*1+1*1*1\\n1415\\n1*(2*3*4)+5+((6+7*8))*(9)\\n0\", \"3\\n(1+2)*3+3\\n3\\n1*2*1+1*1*1\\n1343\\n1*(2+3*4)+5+((6+7*8))*(9)\\n0\"], \"outputs\": [\"4\\n9\\n2\", \"4\\n0\\n2\\n\", \"4\\n0\\n0\\n\", \"4\\n3\\n0\\n\", \"4\\n12\\n2\\n\", \"4\\n6\\n0\\n\", \"3\\n6\\n0\\n\", \"3\\n3\\n0\\n\", \"3\\n9\\n0\\n\", \"2\\n0\\n2\\n\", \"4\\n12\\n0\\n\", \"2\\n3\\n0\\n\", \"4\\n10\\n0\\n\", \"2\\n12\\n0\\n\", \"3\\n5\\n0\\n\", \"3\\n4\\n0\\n\", \"4\\n9\\n0\\n\", \"4\\n2\\n0\\n\", \"1\\n12\\n0\\n\", \"3\\n0\\n0\\n\", \"3\\n3\\n2\\n\", \"2\\n0\\n0\\n\", \"3\\n7\\n0\\n\", \"2\\n6\\n0\\n\", \"2\\n10\\n0\\n\", \"3\\n12\\n2\\n\", \"3\\n12\\n0\\n\", \"4\\n7\\n0\\n\", \"2\\n9\\n0\\n\", \"2\\n5\\n0\\n\", \"2\\n12\\n2\\n\", \"4\\n0\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n3\\n0\\n\", \"4\\n3\\n0\\n\", \"4\\n6\\n0\\n\", \"4\\n3\\n0\\n\", \"4\\n3\\n0\\n\", \"3\\n6\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n6\\n0\\n\", \"4\\n3\\n0\\n\", \"3\\n6\\n0\\n\", \"3\\n9\\n0\\n\", \"4\\n0\\n0\\n\", \"3\\n6\\n0\\n\", \"2\\n3\\n0\\n\", \"3\\n6\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n0\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n3\\n0\\n\", \"2\\n12\\n0\\n\", \"3\\n3\\n0\\n\", \"2\\n12\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n0\\n2\\n\", \"4\\n0\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n6\\n0\\n\", \"4\\n3\\n0\\n\", \"3\\n3\\n0\\n\", \"4\\n6\\n0\\n\", \"4\\n3\\n0\\n\", \"3\\n6\\n0\\n\", \"3\\n6\\n0\\n\", \"3\\n9\\n0\\n\", \"4\\n10\\n0\\n\", \"3\\n9\\n0\\n\", \"3\\n6\\n0\\n\", \"3\\n3\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n3\\n0\\n\", \"4\\n6\\n0\\n\", \"3\\n6\\n0\\n\", \"3\\n9\\n0\\n\", \"4\\n10\\n0\\n\", \"4\\n2\\n0\\n\", \"3\\n0\\n0\\n\", \"3\\n6\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n2\\n0\\n\", \"3\\n0\\n0\\n\", \"3\\n0\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n0\\n0\\n\", \"3\\n0\\n0\\n\", \"4\\n0\\n2\\n\", \"4\\n0\\n0\\n\", \"4\\n0\\n0\\n\", \"4\\n3\\n0\\n\", \"4\\n3\\n0\\n\", \"3\\n3\\n0\\n\", \"4\\n3\\n0\\n\", \"3\\n0\\n0\\n\", \"3\\n9\\n0\\n\", \"2\\n12\\n0\\n\", \"4\\n6\\n0\\n\"]}", "source": "primeintellect"}
|
Expression Mining
Consider an arithmetic expression built by combining single-digit positive integers with addition symbols `+`, multiplication symbols `*`, and parentheses `(` `)`, defined by the following grammar rules with the start symbol `E`.
E ::= T | E '+' T
T ::= F | T '*' F
F ::= '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' | '(' E ')'
When such an arithmetic expression is viewed as a string, its substring, that is, a contiguous sequence of characters within the string, may again form an arithmetic expression. Given an integer n and a string s representing an arithmetic expression, let us count the number of its substrings that can be read as arithmetic expressions with values computed equal to n.
Input
The input consists of multiple datasets, each in the following format.
> n
> s
>
A dataset consists of two lines. In the first line, the target value n is given. n is an integer satisfying 1 ≤ n ≤ 109. The string s given in the second line is an arithmetic expression conforming to the grammar defined above. The length of s does not exceed 2×106. The nesting depth of the parentheses in the string is at most 1000.
The end of the input is indicated by a line containing a single zero. The sum of the lengths of s in all the datasets does not exceed 5×106.
Output
For each dataset, output in one line the number of substrings of s that conform to the above grammar and have the value n. The same sequence of characters appearing at different positions should be counted separately.
Sample Input
3
(1+2)*3+3
2
1*1*1+1*1*1
587
1*(2*3*4)+5+((6+7*8))*(9)
0
Output for the Sample Input
4
9
2
Example
Input
3
(1+2)*3+3
2
1*1*1+1*1*1
587
1*(2*3*4)+5+((6+7*8))*(9)
0
Output
4
9
2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1\\n2 3\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"2\\n4 4\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 3\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 5\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 5\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 1\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 1\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 1\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 3\\nRRGG\\nGGRB\\nBRRR\\nRRBR\", \"2\\n1 3\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 4\\n2 1\\nRRRR\\nRGRR\\nRBRR\\nRRRR\", \"1\\n2 1\\nRRGG\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"1\\n4 1\\nGRGR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 1\\nRRGG\\nGGRB\\nRRBR\\nBRRR\", \"2\\n1 4\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 3\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 2\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 4\\n1 1\\nRRRR\\nRGRR\\nRBRR\\nRRRR\", \"1\\n4 3\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n1 4\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 2\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n2 3\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 3\\nGGRR\\nBRGG\\nRRRB\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nRRBR\", \"1\\n4 2\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n5 4\\n2 1\\nRRRR\\nRGRR\\nRBRR\\nRRRR\", \"1\\n4 1\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 3\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"2\\n4 6\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n1 4\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 3\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 5\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 2\\n4 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 1\\nGGRR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 2\\nGRRG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n2 0\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 3\\nGGRR\\nBGRG\\nRRRB\\nBRRR\", \"1\\n2 4\\nRGGR\\nGGRB\\nBRRR\\nRRBR\", \"1\\n4 4\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 3\\nRRGG\\nBRGG\\nBRRR\\nRRRB\", \"2\\n4 6\\n1 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 1\\nGRGR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n1 3\\nGGRR\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 2\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"2\\n2 0\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n5 3\\nGGRR\\nBGRG\\nRRRB\\nBRRR\", \"1\\n1 1\\nRRGG\\nBRGG\\nBRRR\\nRRRB\", \"1\\n2 1\\nGRGR\\nGGRB\\nBRRR\\nBRRR\", \"2\\n2 0\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 1\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"2\\n4 4\\n1 0\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 5\\n0 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n4 2\\n1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 1\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n1 3\\nRRGG\\nGGRB\\nBRRR\\nRRBR\", \"2\\n1 3\\n2 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 4\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"1\\n2 2\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nBRRR\\nRBRR\", \"1\\n1 2\\nRRGG\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 1\\nRRGG\\nBRGG\\nRRRB\\nBRRR\", \"2\\n1 4\\n3 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 4\\nGGRR\\nBRGG\\nBRRR\\nBRRR\", \"1\\n2 4\\nRRGG\\nGGRB\\nRRRB\\nBRRR\", \"2\\n4 1\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"2\\n4 3\\n4 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nGGRR\\nGGRB\\nRRRB\\nBRRR\", \"1\\n2 1\\nGRRG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n4 3\\nRRGG\\nBGRG\\nRRRB\\nBRRR\", \"2\\n4 6\\n2 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nRRGG\\nGGRB\\nBRRR\\nRRRB\", \"1\\n5 3\\nGGRR\\nBGRG\\nRRRB\\nRRRB\", \"1\\n1 1\\nRRGG\\nBRGG\\nRRRB\\nRRRB\", \"1\\n2 1\\nGRGR\\nBRGG\\nBRRR\\nBRRR\", \"2\\n2 0\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n1 1\\nRRGG\\nGRGB\\nBRRR\\nBRRR\", \"1\\n3 2\\nRRGG\\nGGRB\\nBRRR\\nBRRR\", \"2\\n1 4\\n2 0\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 4\\nGGRR\\nGRGB\\nBRRR\\nBRRR\", \"2\\n2 4\\n3 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 4\\nGGRR\\nGRBG\\nBRRR\\nBRRR\", \"1\\n2 1\\nRRGG\\nRGGB\\nRRRB\\nBRRR\", \"1\\n2 1\\nGRRG\\nGGRB\\nRRRB\\nBRRR\", \"2\\n4 6\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nRRGG\\nGGRB\\nRRRB\\nRRRB\", \"1\\n4 1\\nGRGR\\nBRGG\\nBRRR\\nBRRR\", \"2\\n2 -1\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nRGRG\\nGGRB\\nBRRR\\nBRRR\", \"1\\n2 4\\nGGRR\\nGRGB\\nBRRR\\nRRRB\", \"2\\n2 4\\n0 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n3 1\\nRRGG\\nRGGB\\nRRRB\\nBRRR\", \"2\\n4 5\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n4 2\\nGGRR\\nGGRB\\nRRRB\\nRRRB\", \"2\\n3 -1\\n3 2\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nRGRG\\nGGRB\\nRRRB\\nBRRR\", \"2\\n2 4\\n-1 1\\nRRRR\\nRRGR\\nRBRR\\nRRRR\", \"1\\n2 2\\nGRGR\\nGGRB\\nRRRB\\nBRRR\", \"2\\n2 4\\n-1 1\\nRRRR\\nRRGR\\nRRBR\\nRRRR\", \"2\\n2 2\\n-1 1\\nRRRR\\nRRGR\\nRRBR\\nRRRR\"], \"outputs\": [\"5\", \"3\", \"6\\n\", \"3\\n\", \"5\\n\", \"12\\n\", \"9\\n\", \"16\\n\", \"8\\n\", \"10\\n\", \"4\\n\", \"13\\n\", \"7\\n\", \"11\\n\", \"14\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"3\\n\", \"5\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"8\\n\", \"9\\n\", \"3\\n\", \"6\\n\", \"5\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"8\\n\", \"16\\n\", \"8\\n\", \"9\\n\", \"5\\n\", \"9\\n\", \"5\\n\", \"12\\n\", \"9\\n\", \"9\\n\", \"10\\n\", \"8\\n\", \"16\\n\", \"11\\n\", \"7\\n\", \"16\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"4\\n\", \"16\\n\", \"10\\n\", \"8\\n\", \"9\\n\", \"8\\n\", \"8\\n\", \"11\\n\", \"11\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"6\\n\", \"10\\n\", \"8\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"16\\n\", \"10\\n\", \"6\\n\", \"16\\n\", \"7\\n\", \"8\\n\", \"7\\n\", \"5\\n\", \"7\\n\", \"11\\n\", \"11\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"8\\n\", \"7\\n\", \"6\\n\", \"10\\n\", \"6\\n\", \"4\\n\", \"6\\n\", \"8\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"7\\n\"]}", "source": "primeintellect"}
|
Training is indispensable for achieving good results at ICPC. Rabbit wants to win at ICPC, so he decided to practice today as well.
Today's training is to increase creativity by drawing pictures. Let's draw a pattern well using a square stamp.
I want to use stamps of various sizes to complete the picture of the red, green, and blue streets specified on the 4 x 4 squared paper. The stamp is rectangular and is used to fit the squares. The height and width of the stamp cannot be swapped.
The paper is initially uncolored. When you stamp on paper, the stamped part changes to the color of the stamp, and the color hidden underneath becomes completely invisible. Since the color of the stamp is determined by the ink to be applied, it is possible to choose the color of any stamp. The stamp can be stamped with a part protruding from the paper, and the protruding part is ignored.
It is possible to use one stamp multiple times. You may use the same stamp for different colors. Stamping is a rather nerve-wracking task, so I want to reduce the number of stamps as much as possible.
Input
N
H1 W1
...
HN WN
C1,1C1,2C1,3C1,4
C2,1C2,2C2,3C2,4
C3,1C3,2C3,3C3,4
C4,1C4,2C4,3C4,4
N is the number of stamps, and Hi and Wi (1 ≤ i ≤ N) are integers representing the vertical and horizontal lengths of the i-th stamp, respectively. Ci, j (1 ≤ i ≤ 4, 1 ≤ j ≤ 4) is a character that represents the color of the picture specified for the cells in the i-th row from the top and the j-th column from the left. Red is represented by `R`, green is represented by` G`, and blue is represented by `B`.
Satisfy 1 ≤ N ≤ 16, 1 ≤ Hi ≤ 4, 1 ≤ Wi ≤ 4. The same set as (Hi, Wi) does not appear multiple times.
Output
Print the minimum number of stamps that must be stamped to complete the picture on a single line.
Examples
Input
2
4 4
1 1
RRRR
RRGR
RBRR
RRRR
Output
3
Input
1
2 3
RRGG
BRGG
BRRR
BRRR
Output
5
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 1\\n0 0 0 4\\n0 2 2 2\\n1 2\\n0 1\\n0 3\", \"5 3\\n0 4 2 4\\n0 2 2 2\\n0 0 2 0\\n0 0 0 4\\n2 0 2 4\\n0 2\\n1 0\\n2 2\\n1 4\\n2 1\", \"1 2\\n0 0 10 0\\n1 0\\n9 0\\n0 0\\n5 0\", \"2 1\\n0 0 0 4\\n0 2 2 2\\n1 2\\n-1 1\\n0 3\", \"5 3\\n0 4 2 4\\n0 2 2 2\\n0 0 2 0\\n0 0 0 4\\n2 0 2 4\\n0 2\\n1 0\\n2 2\\n2 4\\n2 1\", \"1 2\\n0 -1 10 0\\n1 0\\n9 0\\n0 0\\n5 0\", \"2 1\\n0 0 0 4\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"2 1\\n0 0 0 7\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"2 1\\n0 1 0 7\\n0 2 2 3\\n1 2\\n-1 1\\n0 5\", \"2 1\\n0 1 0 3\\n0 2 2 3\\n1 2\\n-2 2\\n0 5\", \"2 1\\n0 1 1 3\\n0 2 2 3\\n1 2\\n-2 2\\n0 5\", \"2 1\\n0 1 2 3\\n0 2 2 3\\n1 2\\n-2 2\\n-1 7\", \"2 1\\n0 1 2 3\\n-1 2 2 3\\n1 2\\n-2 2\\n-1 7\", \"2 1\\n0 0 1 4\\n0 2 2 2\\n1 2\\n-1 1\\n0 3\", \"1 2\\n0 0 10 -1\\n1 0\\n9 0\\n0 0\\n5 0\", \"5 3\\n0 4 2 4\\n0 2 2 2\\n0 0 2 0\\n0 0 0 4\\n2 0 2 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 1\\n0 -1 0 4\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"1 2\\n0 -1 7 0\\n1 0\\n9 0\\n0 0\\n10 0\", \"2 1\\n-1 0 0 7\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"2 1\\n0 1 0 7\\n0 2 3 3\\n1 2\\n-2 1\\n0 5\", \"1 2\\n1 -1 10 0\\n1 0\\n3 -1\\n0 0\\n21 0\", \"2 1\\n0 1 3 3\\n-1 2 2 3\\n1 2\\n-2 2\\n-1 7\", \"2 1\\n0 -1 -1 4\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"2 1\\n-1 0 1 7\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"2 1\\n-1 0 0 6\\n0 2 2 3\\n1 2\\n-1 1\\n0 5\", \"1 2\\n0 -1 18 0\\n1 -1\\n3 -1\\n-1 0\\n10 0\", \"2 1\\n0 1 0 7\\n-1 2 3 3\\n1 2\\n-2 1\\n0 5\", \"2 1\\n1 2 0 3\\n0 2 2 3\\n1 2\\n-2 2\\n0 5\", \"2 1\\n1 1 4 3\\n0 2 2 3\\n1 2\\n-2 2\\n-1 7\", \"2 1\\n0 0 3 3\\n-1 2 2 3\\n1 2\\n-2 2\\n-1 7\", \"4 3\\n0 4 2 4\\n0 2 1 2\\n0 0 2 0\\n0 0 0 4\\n2 0 2 4\\n0 2\\n1 1\\n2 2\\n1 4\\n2 1\", \"2 1\\n0 0 0 4\\n0 2 4 2\\n2 2\\n-1 2\\n0 3\", \"2 1\\n-1 -1 1 7\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"1 0\\n0 -1 4 0\\n1 -1\\n9 0\\n0 0\\n10 0\", \"2 1\\n-1 0 0 6\\n0 2 0 3\\n1 2\\n-1 1\\n0 5\", \"2 0\\n0 1 -1 3\\n1 2 2 3\\n1 2\\n-2 2\\n0 5\", \"2 1\\n1 1 4 2\\n0 2 2 3\\n1 2\\n-2 2\\n-1 7\", \"2 1\\n1 1 1 4\\n0 2 2 2\\n1 2\\n-1 1\\n0 6\", \"4 3\\n0 4 2 4\\n0 2 1 2\\n0 0 2 0\\n-1 0 0 4\\n2 0 2 4\\n0 2\\n1 1\\n2 2\\n1 4\\n2 1\", \"2 1\\n-1 0 0 4\\n0 2 4 2\\n2 2\\n-1 2\\n0 3\", \"1 2\\n0 -1 12 0\\n1 -1\\n14 1\\n0 0\\n5 0\", \"2 0\\n0 -1 -1 4\\n0 2 2 0\\n1 2\\n-1 1\\n0 3\", \"2 1\\n0 -1 1 7\\n0 2 2 3\\n1 2\\n-1 1\\n0 3\", \"1 2\\n0 -1 32 0\\n1 -1\\n3 -2\\n-1 0\\n10 0\", \"2 0\\n0 1 0 7\\n-2 2 3 3\\n1 2\\n-2 1\\n0 5\", \"2 0\\n0 1 -2 3\\n1 2 2 3\\n1 2\\n-2 2\\n0 5\", \"2 1\\n0 1 2 1\\n0 0 2 3\\n1 3\\n-2 2\\n-1 2\", \"2 1\\n0 0 3 0\\n-1 2 2 3\\n1 2\\n0 2\\n-1 7\", \"4 3\\n0 4 2 4\\n0 2 1 2\\n0 0 2 -1\\n-1 0 0 4\\n2 0 2 4\\n0 2\\n1 1\\n2 2\\n1 4\\n2 1\", \"5 3\\n1 4 2 4\\n0 2 2 2\\n0 0 2 0\\n0 0 0 5\\n0 0 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"1 2\\n0 -1 15 0\\n1 -1\\n14 1\\n0 0\\n5 0\", \"2 0\\n0 -1 -1 4\\n0 0 2 0\\n1 2\\n-1 1\\n0 3\", \"2 0\\n-1 1 0 7\\n-2 2 3 3\\n1 2\\n-2 1\\n0 5\", \"2 1\\n0 0 0 7\\n0 2 1 1\\n1 2\\n-2 3\\n-1 5\", \"2 1\\n0 0 3 0\\n-1 2 3 3\\n1 2\\n0 2\\n-1 7\", \"2 1\\n-1 0 0 4\\n0 2 4 2\\n3 2\\n-1 0\\n0 3\", \"5 3\\n1 4 2 4\\n0 0 2 2\\n0 0 2 0\\n0 0 0 5\\n0 0 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 0\\n1 -1 -1 4\\n0 0 2 0\\n1 2\\n-1 1\\n0 3\", \"2 1\\n0 -1 1 7\\n0 2 2 0\\n1 2\\n-1 1\\n0 3\", \"2 1\\n-1 0 0 6\\n0 0 0 3\\n2 0\\n-1 1\\n0 5\", \"2 1\\n1 3 0 3\\n0 2 2 3\\n1 1\\n-2 3\\n1 5\", \"2 0\\n0 1 -2 3\\n1 1 2 0\\n1 2\\n-2 2\\n0 5\", \"1 1\\n0 0 2 3\\n-1 2 2 2\\n1 4\\n-2 2\\n-1 5\", \"1 0\\n1 1 4 2\\n0 2 2 3\\n2 2\\n-2 2\\n-1 7\", \"5 3\\n1 4 2 4\\n0 0 2 2\\n0 0 2 0\\n0 0 0 5\\n0 1 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 0\\n1 -1 -1 4\\n0 0 2 1\\n1 2\\n-1 1\\n0 3\", \"2 1\\n-1 0 0 6\\n1 0 0 3\\n2 0\\n-1 1\\n0 5\", \"1 0\\n-1 1 0 7\\n-2 2 3 1\\n1 2\\n-2 1\\n0 5\", \"2 1\\n1 3 0 3\\n-1 2 2 3\\n1 1\\n-2 3\\n1 5\", \"2 1\\n0 1 1 6\\n0 2 2 2\\n1 2\\n0 1\\n0 6\", \"5 3\\n1 4 2 4\\n0 0 2 2\\n0 0 2 0\\n0 0 0 7\\n0 1 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 0\\n1 -1 -2 4\\n0 0 2 1\\n1 2\\n-1 1\\n0 3\", \"2 1\\n1 3 0 3\\n0 2 0 3\\n1 1\\n-2 3\\n1 5\", \"2 1\\n-1 0 0 0\\n-1 2 3 3\\n1 2\\n0 4\\n-1 7\", \"5 3\\n1 4 2 4\\n0 0 2 2\\n0 0 2 1\\n0 0 0 7\\n0 1 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"1 0\\n1 -1 -2 4\\n0 0 2 1\\n1 2\\n-1 1\\n0 3\", \"2 1\\n0 -1 2 7\\n0 2 2 0\\n1 3\\n-1 1\\n1 3\", \"2 1\\n1 3 0 3\\n1 2 0 3\\n1 1\\n-2 3\\n1 5\", \"2 1\\n-1 1 1 6\\n0 2 1 2\\n1 2\\n0 1\\n0 6\", \"1 2\\n-1 0 10 -1\\n1 0\\n9 0\\n0 2\\n8 1\", \"5 3\\n1 4 2 4\\n0 0 2 2\\n0 0 2 1\\n0 -1 0 7\\n0 1 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 1\\n0 -1 2 7\\n-1 2 2 0\\n1 3\\n-1 1\\n1 3\", \"1 3\\n0 -1 48 0\\n1 -1\\n4 -2\\n-2 -1\\n13 0\", \"5 3\\n1 4 2 4\\n0 0 2 2\\n0 0 4 1\\n0 -1 0 7\\n0 1 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 1\\n0 -1 2 7\\n-2 2 2 0\\n1 3\\n-1 1\\n1 3\", \"2 0\\n-2 0 0 6\\n1 0 0 3\\n3 0\\n-1 0\\n0 5\", \"2 0\\n-1 1 -2 5\\n1 2 2 -1\\n1 0\\n-2 2\\n0 5\", \"2 1\\n0 -1 2 7\\n-2 3 2 0\\n1 3\\n-1 1\\n1 3\", \"2 0\\n-2 0 0 6\\n1 -1 0 3\\n3 0\\n-1 0\\n0 5\", \"2 1\\n1 1 1 7\\n1 4 2 3\\n1 4\\n0 3\\n1 6\", \"2 1\\n1 3 -1 3\\n1 2 0 3\\n0 0\\n-2 3\\n1 5\", \"2 0\\n-1 1 -3 5\\n1 2 2 -1\\n1 0\\n-2 2\\n0 5\", \"2 1\\n-1 1 1 6\\n0 2 1 2\\n0 2\\n-1 1\\n0 6\", \"5 3\\n1 6 2 4\\n0 0 3 2\\n0 0 4 1\\n0 -1 0 7\\n0 1 3 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"2 1\\n1 2 1 7\\n1 4 2 3\\n1 4\\n0 3\\n1 6\", \"2 0\\n-1 1 -3 9\\n1 2 2 -1\\n1 0\\n-2 2\\n0 5\", \"2 1\\n0 -1 0 0\\n-1 2 3 0\\n0 2\\n0 4\\n0 7\", \"4 1\\n0 4 2 4\\n0 2 1 2\\n0 -1 2 0\\n-1 0 1 0\\n3 0 2 4\\n0 -1\\n1 1\\n2 2\\n1 4\\n2 1\", \"5 3\\n1 6 2 4\\n0 0 3 2\\n0 0 4 1\\n0 -1 0 7\\n0 1 4 4\\n0 2\\n1 0\\n1 2\\n2 4\\n2 1\", \"1 0\\n-1 1 0 0\\n-2 4 5 1\\n1 6\\n-2 2\\n0 4\", \"2 1\\n0 -1 0 1\\n-1 2 3 0\\n0 2\\n0 4\\n0 7\", \"2 1\\n-1 0 1 6\\n0 2 1 0\\n0 2\\n-1 1\\n0 6\", \"4 1\\n0 4 2 8\\n0 2 1 2\\n0 -1 2 0\\n-1 0 1 0\\n3 0 2 4\\n0 -1\\n1 1\\n2 2\\n1 4\\n2 1\"], \"outputs\": [\"-1\", \"3.0\", \"9.0\", \"6.0000000000\\n\", \"3.0000000000\\n\", \"10.0498756211\\n\", \"6.2360679775\\n\", \"9.2360679775\\n\", \"8.2360679775\\n\", \"4.2360679775\\n\", \"4.4721359550\\n\", \"5.0644951022\\n\", \"5.9907047849\\n\", \"6.1231056256\\n\", \"0.0000000000\\n\", \"-1\\n\", \"7.2360679775\\n\", \"7.0710678119\\n\", \"9.3071357894\\n\", \"9.1622776602\\n\", \"9.0553851381\\n\", \"6.7678289356\\n\", \"7.3350874911\\n\", \"9.5161778668\\n\", \"8.3188305078\\n\", \"18.0277563773\\n\", \"10.1231056256\\n\", \"3.6502815399\\n\", \"5.8416192530\\n\", \"7.4049183473\\n\", \"9.0000000000\\n\", \"8.0000000000\\n\", \"10.4822792287\\n\", \"4.1231056256\\n\", \"7.0827625303\\n\", \"2.2360679775\\n\", \"5.3983456377\\n\", \"5.0000000000\\n\", \"9.1231056256\\n\", \"8.1231056256\\n\", \"12.0415945788\\n\", \"7.9274466383\\n\", \"10.2983257258\\n\", \"32.0156211872\\n\", \"11.0990195136\\n\", \"2.8284271247\\n\", \"5.6055512755\\n\", \"6.1622776602\\n\", \"9.3591736031\\n\", \"14.0000000000\\n\", \"15.0332963784\\n\", \"7.0990195136\\n\", \"11.1817820439\\n\", \"8.4142135624\\n\", \"7.1231056256\\n\", \"4.0000000000\\n\", \"14.8284271247\\n\", \"7.3851648071\\n\", \"10.8906848730\\n\", \"9.0827625303\\n\", \"3.2360679775\\n\", \"4.2426406871\\n\", \"3.6055512755\\n\", \"3.1622776602\\n\", \"14.0710678119\\n\", \"7.6212327846\\n\", \"9.2450401905\\n\", \"6.0827625303\\n\", \"4.1622776602\\n\", \"-0.0000000000\\n\", \"16.0710678119\\n\", \"8.0670198723\\n\", \"2.0000000000\\n\", \"5.1231056256\\n\", \"16.3071357894\\n\", \"5.8309518948\\n\", \"11.0746383760\\n\", \"2.4142135624\\n\", \"6.3851648071\\n\", \"11.0453610172\\n\", \"17.3071357894\\n\", \"11.8517625267\\n\", \"48.0104155366\\n\", \"19.1941734375\\n\", \"12.7183472062\\n\", \"9.4868329805\\n\", \"7.2853832858\\n\", \"13.2462112512\\n\", \"10.4476609460\\n\", \"7.4142135624\\n\", \"3.4142135624\\n\", \"7.6344136152\\n\", \"1.0000000000\\n\", \"19.9712975882\\n\", \"6.4142135624\\n\", \"11.4084889114\\n\", \"5.4721359550\\n\", \"5.2360679775\\n\", \"20.7286569011\\n\", \"1.4142135624\\n\", \"6.4721359550\\n\", \"8.5606232978\\n\", \"9.7082039325\\n\"]}", "source": "primeintellect"}
|
In the International City of Pipe Construction, it is planned to repair the water pipe at a certain point in the water pipe network. The network consists of water pipe segments, stop valves and source point. A water pipe is represented by a segment on a 2D-plane and intersected pair of water pipe segments are connected at the intersection point. A stop valve, which prevents from water flowing into the repairing point while repairing, is represented by a point on some water pipe segment. In the network, just one source point exists and water is supplied to the network from this point.
Of course, while repairing, we have to stop water supply in some areas, but, in order to reduce the risk of riots, the length of water pipes stopping water supply must be minimized. What you have to do is to write a program to minimize the length of water pipes needed to stop water supply when the coordinates of end points of water pipe segments, stop valves, source point and repairing point are given.
Input
A data set has the following format:
> N M
> xs1 ys1 xd1 yd1
> ...
> xsN ysN xdN ydN
> xv1 yv1
> ...
> xvM yvM
> xb yb
> xc yc
>
The first line of the input contains two integers, N (1 ≤ N ≤ 300) and M (0 ≤ M ≤ 1,000) that indicate the number of water pipe segments and stop valves. The following N lines describe the end points of water pipe segments. The i-th line contains four integers, xsi, ysi, xdi and ydi that indicate the pair of coordinates of end points of i-th water pipe segment. The following M lines describe the points of stop valves. The i-th line contains two integers, xvi and yvi that indicate the coordinate of end points of i-th stop valve. The following line contains two integers, xb and yb that indicate the coordinate of the source point. The last line contains two integers, xc and yc that indicate the coordinate of the repairing point.
You may assume that any absolute values of coordinate integers are less than 1,000 (inclusive.) You may also assume each of the stop valves, the source point and the repairing point is always on one of water pipe segments and that that each pair among the stop valves, the source point and the repairing point are different. And, there is not more than one intersection between each pair of water pipe segments. Finally, the water pipe network is connected, that is, all the water pipes are received water supply initially.
Output
Print the minimal length of water pipes needed to stop water supply in a line. The absolute or relative error should be less than or 10-6. When you cannot stop water supply to the repairing point even though you close all stop valves, print "`-1`" in a line.
Examples
Input
1 2
0 0 10 0
1 0
9 0
0 0
5 0
Output
9.0
Input
5 3
0 4 2 4
0 2 2 2
0 0 2 0
0 0 0 4
2 0 2 4
0 2
1 0
2 2
1 4
2 1
Output
3.0
Input
2 1
0 0 0 4
0 2 2 2
1 2
0 1
0 3
Output
-1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\nwhite 10\\nblack 10\\n2\\nblack\\nwhite\", \"2\\nwhite 20\\nblack 10\\n2\\nblack\\norange\", \"2\\nwhite 20\\nblack 10\\n2\\nblack\\nwhite\", \"4\\nred 3444\\nred 3018\\nred 3098\\nred 3319\\n4\\nred\\nred\\nred\\nred\", \"3\\nwhite 10\\nred 20\\nwhite 30\\n3\\nwhite\\nred\\nwhite\", \"2\\nwhite 10\\nblack 10\\n4\\nblack\\nwhite\", \"3\\nwgite 10\\nerd 40\\nwhite 30\\n2\\nwhite\\nerd\\nwhite\", \"2\\nwhite 20\\nblack 10\\n2\\nkcalb\\norange\", \"2\\nwhite 20\\nblack 10\\n2\\nblack\\nhwite\", \"4\\nred 3444\\nred 3018\\nred 3098\\nred 3319\\n4\\nred\\nred\\nrec\\nred\", \"3\\nwhite 10\\nred 40\\nwhite 30\\n3\\nwhite\\nred\\nwhite\", \"2\\nwhite 10\\nblack 10\\n4\\nblack\\netihw\", \"2\\nxhite 20\\nblack 10\\n2\\nkcalb\\norange\", \"2\\nwhite 20\\nblack 18\\n2\\nblack\\nhwite\", \"4\\nred 3444\\nder 3018\\nred 3098\\nred 3319\\n4\\nred\\nred\\nrec\\nred\", \"3\\nwgite 10\\nred 40\\nwhite 30\\n3\\nwhite\\nred\\nwhite\", \"2\\nwhite 10\\nblack 10\\n4\\nkcalb\\netihw\", \"2\\nxhite 20\\nblack 19\\n2\\nkcalb\\norange\", \"2\\nwhite 20\\nblack 26\\n2\\nblack\\nhwite\", \"4\\nred 2133\\nder 3018\\nred 3098\\nred 3319\\n4\\nred\\nred\\nrec\\nred\", \"3\\nwgite 10\\nred 40\\nwhite 30\\n3\\nwhite\\nerd\\nwhite\", \"2\\nwhite 10\\nblacj 10\\n4\\nkcalb\\netihw\", \"2\\nxhite 20\\nbladk 19\\n2\\nkcalb\\norange\", \"2\\nwhite 20\\nblack 26\\n4\\nblack\\nhwite\", \"4\\nred 2133\\nder 3018\\nred 3098\\nred 3319\\n4\\nred\\nred\\ncer\\nred\", \"3\\nwgite 10\\nerd 40\\nwhite 30\\n3\\nwhite\\nerd\\nwhite\", \"2\\nwhite 10\\nblacj 10\\n4\\nblack\\netihw\", \"2\\nxhite 20\\nbmadk 19\\n2\\nkcalb\\norange\", \"2\\nwhite 20\\nblack 26\\n4\\nkcalb\\nhwite\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nred 3319\\n4\\nred\\nred\\ncer\\nred\", \"2\\nwiite 10\\nblacj 10\\n4\\nblack\\netihw\", \"2\\nxhite 20\\nbmadk 19\\n2\\nkcalb\\negnaro\", \"2\\nwihte 20\\nblack 26\\n4\\nkcalb\\nhwite\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nred 3319\\n4\\nred\\nrdd\\ncer\\nred\", \"3\\nwgite 10\\nerd 40\\nwhite 22\\n2\\nwhite\\nerd\\nwhite\", \"2\\nwiite 10\\nblacj 10\\n5\\nblack\\netihw\", \"2\\nxhite 20\\nbmadk 19\\n4\\nkcalb\\negnaro\", \"2\\nwihte 20\\nblack 26\\n4\\nkcalb\\nhwitf\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nred 3319\\n4\\nsed\\nrdd\\ncer\\nred\", \"3\\nwgite 10\\neqd 40\\nwhite 22\\n2\\nwhite\\nerd\\nwhite\", \"2\\nwiite 10\\nblacj 19\\n5\\nblack\\netihw\", \"2\\nxhite 20\\nbmadk 19\\n4\\nbcalk\\negnaro\", \"2\\nwihte 20\\nkcalb 26\\n4\\nkcalb\\nhwitf\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nred 3319\\n4\\nsde\\nrdd\\ncer\\nred\", \"3\\nwgite 10\\neqd 40\\nxhite 22\\n2\\nwhite\\nerd\\nwhite\", \"2\\nwiite 4\\nblacj 19\\n5\\nblack\\netihw\", \"2\\nxhite 34\\nbmadk 19\\n4\\nbcalk\\negnaro\", \"2\\nwihte 20\\nkcalb 26\\n4\\nblack\\nhwitf\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nrec 3319\\n4\\nsde\\nrdd\\ncer\\nred\", \"3\\nwgite 10\\neqd 40\\nxhite 22\\n0\\nwhite\\nerd\\nwhite\", \"2\\nwihte 4\\nblacj 19\\n5\\nblack\\netihw\", \"2\\nxhite 34\\nbmadk 19\\n4\\nbcalk\\norange\", \"2\\nwihte 20\\nkcalb 26\\n4\\nblack\\nftiwh\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nrec 3319\\n4\\nsde\\nddr\\ncer\\nred\", \"3\\nwgite 10\\neqd 40\\nxhite 22\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 4\\nblacj 19\\n5\\nblack\\netihw\", \"2\\nxhite 34\\nbmadk 17\\n4\\nbcalk\\norange\", \"2\\nwihte 32\\nkcalb 26\\n4\\nblack\\nftiwh\", \"4\\nrec 2133\\nder 3018\\nred 3098\\nrec 3319\\n4\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 10\\neqd 57\\nxhite 22\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 8\\nblacj 19\\n5\\nblack\\netihw\", \"2\\netihx 34\\nbmadk 17\\n4\\nbcalk\\norange\", \"2\\nwihte 32\\nkcalb 26\\n7\\nblack\\nftiwh\", \"4\\nrec 2133\\nder 3018\\nred 3098\\ncer 3319\\n4\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 10\\ndqe 57\\nxhite 22\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 8\\nblacj 19\\n8\\nblack\\netihw\", \"2\\netihx 34\\nbmadk 17\\n4\\nbcamk\\norange\", \"2\\nwihte 35\\nkcalb 26\\n7\\nblack\\nftiwh\", \"4\\nrec 2133\\nder 4487\\nred 3098\\ncer 3319\\n4\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 10\\ndqe 57\\nxhite 40\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 8\\nblacj 19\\n8\\nbcalk\\netihw\", \"2\\netihx 34\\nkdamb 17\\n4\\nbcamk\\norange\", \"2\\nwihte 35\\nkcamb 26\\n7\\nblack\\nftiwh\", \"4\\nrec 2133\\nder 6618\\nred 3098\\ncer 3319\\n4\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 10\\ndqe 8\\nxhite 40\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 8\\nblacj 21\\n8\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n4\\nbcamk\\norange\", \"2\\nwihte 35\\nkcamb 26\\n7\\nclack\\nftiwh\", \"4\\nrec 2133\\nder 6618\\nred 3098\\nrec 3319\\n4\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 18\\ndqe 8\\nxhite 40\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 8\\nblacj 21\\n2\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n8\\nbcamk\\norange\", \"2\\nwihte 35\\nkcamb 26\\n11\\nclack\\nftiwh\", \"4\\ncer 2133\\nder 6618\\nred 3098\\nrec 3319\\n4\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 18\\neqd 8\\nxhite 40\\n0\\nwhite\\nere\\nwhite\", \"2\\nwieth 8\\nblacj 40\\n2\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n8\\nkmacb\\norange\", \"2\\nwihte 66\\nkcamb 26\\n11\\nclack\\nftiwh\", \"4\\ncer 2133\\nder 6618\\nred 3098\\nrec 3319\\n5\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 18\\neqd 8\\nxhite 40\\n0\\nwhite\\nese\\nwhite\", \"2\\nwieth 8\\njcalb 40\\n2\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n0\\nkmacb\\norange\", \"2\\nwihte 66\\nkcamb 26\\n11\\nkcalc\\nftiwh\", \"4\\ncre 2133\\nder 6618\\nred 3098\\nrec 3319\\n5\\nsde\\nddr\\ncer\\nrde\", \"3\\nwgite 18\\neqd 8\\nxhite 40\\n0\\nwiite\\nese\\nwhite\", \"2\\nwieth 6\\njcalb 40\\n2\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n0\\nkmaca\\norange\", \"2\\nwiite 66\\nkcamb 26\\n11\\nclack\\nftiwh\", \"4\\ncre 2133\\nder 6618\\nred 3098\\nrce 3319\\n5\\nsde\\nddr\\ncer\\nrde\", \"2\\nwieth 6\\njcalb 40\\n3\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n1\\nkmaca\\norange\", \"2\\nwiite 49\\nkcamb 26\\n11\\nclack\\nftiwh\", \"4\\ncre 2133\\nder 6618\\nqed 3098\\nrce 3319\\n5\\nsde\\nddr\\ncer\\nrde\", \"2\\nwieth 6\\njcalb 40\\n0\\nbcalk\\netihw\", \"2\\nesihx 34\\nkdamb 17\\n1\\ncmaka\\norange\"], \"outputs\": [\"No\", \"No\", \"Yes\", \"Yes\", \"Yes\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\"]}", "source": "primeintellect"}
|
In the Jambo Amusement Garden (JAG), you sell colorful drinks consisting of multiple color layers. This colorful drink can be made by pouring multiple colored liquids of different density from the bottom in order.
You have already prepared several colored liquids with various colors and densities. You will receive a drink request with specified color layers. The colorful drink that you will serve must satisfy the following conditions.
* You cannot use a mixed colored liquid as a layer. Thus, for instance, you cannot create a new liquid with a new color by mixing two or more different colored liquids, nor create a liquid with a density between two or more liquids with the same color by mixing them.
* Only a colored liquid with strictly less density can be an upper layer of a denser colored liquid in a drink. That is, you can put a layer of a colored liquid with density $x$ directly above the layer of a colored liquid with density $y$ if $x < y$ holds.
Your task is to create a program to determine whether a given request can be fulfilled with the prepared colored liquids under the above conditions or not.
Input
The input consists of a single test case in the format below.
$N$
$C_1$ $D_1$
$\vdots$
$C_N$ $D_N$
$M$
$O_1$
$\vdots$
$O_M$
The first line consists of an integer $N$ ($1 \leq N \leq 10^5$), which represents the number of the prepared colored liquids. The following $N$ lines consists of $C_i$ and $D_i$ ($1 \leq i \leq N$). $C_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th prepared colored liquid. The length of $C_i$ is between $1$ and $20$ inclusive. $D_i$ is an integer and represents the density of the $i$-th prepared colored liquid. The value of $D_i$ is between $1$ and $10^5$ inclusive. The ($N+2$)-nd line consists of an integer $M$ ($1 \leq M \leq 10^5$), which represents the number of color layers of a drink request. The following $M$ lines consists of $O_i$ ($1 \leq i \leq M$). $O_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th layer from the top of the drink request. The length of $O_i$ is between $1$ and $20$ inclusive.
Output
If the requested colorful drink can be served by using some of the prepared colored liquids, print 'Yes'. Otherwise, print 'No'.
Examples
Input
2
white 20
black 10
2
black
white
Output
Yes
Input
2
white 10
black 10
2
black
white
Output
No
Input
2
white 20
black 10
2
black
orange
Output
No
Input
3
white 10
red 20
white 30
3
white
red
white
Output
Yes
Input
4
red 3444
red 3018
red 3098
red 3319
4
red
red
red
red
Output
Yes
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 1 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 0\\n2 0\\n2 0\\n0 0 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n2 0\\n0 0 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n2 0\\n0 1 4\\n1 0\\n0 0 8\\n1 1\", \"4 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 9\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 1 2\\n1 1\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 3\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n2 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 9\\n1 1\", \"3 10\\n0 0 3\\n0 0 16\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 1 2\\n1 1\\n2 1\\n1 0\\n0 0 4\\n1 0\\n0 0 3\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n2 0\\n2 1\\n1 0\\n0 0 4\\n1 0\\n0 1 9\\n1 1\", \"3 10\\n0 0 3\\n0 0 16\\n0 0 0\\n1 0\\n2 1\\n1 1\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n2 0\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 1 9\\n1 1\", \"2 4\\n0 0 3\\n0 1 14\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 1 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n1 1\", \"2 6\\n0 0 3\\n0 0 9\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 0\\n2 0\\n2 0\\n0 0 4\\n1 1\\n0 0 8\\n1 1\", \"4 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 1\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n0 1\", \"2 10\\n0 0 6\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 1 14\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 1\\n1 1\", \"2 10\\n0 1 3\\n0 0 17\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n2 1\\n0 1 8\\n0 1\", \"2 6\\n0 0 6\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"1 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 0\\n1 0\", \"2 10\\n0 0 3\\n0 0 7\\n0 0 2\\n1 1\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"4 6\\n0 0 5\\n0 1 14\\n0 0 2\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 2 7\\n1 0\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 1 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n2 0\\n0 0 2\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 1\\n1 0\\n0 1 4\\n1 1\\n0 1 9\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 4\\n1 1\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 4\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n2 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 9\\n1 1\", \"2 10\\n0 0 3\\n0 1 14\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 4\\n1 1\", \"2 10\\n0 1 3\\n0 0 3\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 0\\n2 0\\n1 0\\n0 0 1\\n1 0\\n0 0 8\\n1 0\", \"2 10\\n0 0 5\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 5\\n1 0\\n0 1 8\\n1 1\", \"2 4\\n0 0 3\\n0 0 14\\n0 0 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 2 7\\n1 1\", \"2 10\\n0 0 1\\n0 0 7\\n0 0 2\\n1 0\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"2 10\\n0 1 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n2 0\\n0 0 2\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 1\\n2 1\\n1 0\\n0 1 4\\n1 1\\n0 1 9\\n1 1\", \"2 10\\n0 0 3\\n0 0 7\\n0 1 1\\n1 1\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"4 4\\n0 0 0\\n0 1 14\\n0 0 1\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 2\\n0 2 7\\n1 1\", \"2 10\\n0 0 3\\n0 1 14\\n0 1 0\\n1 1\\n2 1\\n2 0\\n0 0 4\\n2 1\\n0 1 4\\n1 1\", \"2 10\\n0 0 1\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n1 0\\n0 0 -1\\n2 1\\n0 0 12\\n0 0\", \"2 10\\n0 0 3\\n0 1 9\\n0 0 2\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 1 2\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 0 5\\n1 0\\n0 0 3\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"4 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 1 8\\n1 1\", \"3 10\\n0 0 3\\n0 0 16\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n2 1\", \"3 10\\n0 0 3\\n0 0 16\\n0 0 0\\n1 0\\n2 1\\n1 1\\n0 0 4\\n1 1\\n0 1 10\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 0\\n1 0\\n1 0\\n0 0 4\\n1 0\\n0 0 8\\n1 0\", \"2 10\\n0 0 3\\n0 0 7\\n0 0 4\\n1 1\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"2 10\\n0 0 5\\n0 0 9\\n0 0 1\\n1 0\\n2 1\\n2 0\\n0 0 5\\n1 0\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 7\\n0 0 2\\n1 1\\n2 1\\n1 0\\n0 0 10\\n1 0\\n0 0 8\\n0 1\", \"2 10\\n0 1 1\\n0 0 7\\n0 0 2\\n1 1\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"2 10\\n0 1 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 1 4\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n2 0\\n0 0 2\\n1 0\\n0 0 8\\n1 0\", \"4 10\\n0 0 3\\n0 0 9\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 1 2\\n1 1\", \"2 10\\n0 0 3\\n0 1 14\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 0 4\\n1 1\", \"2 18\\n0 0 3\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 1\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 6\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n2 0\\n0 1 1\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 1 3\\n0 0 7\\n0 0 1\\n1 1\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"2 10\\n0 0 1\\n0 0 0\\n0 0 2\\n1 0\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"4 10\\n0 0 3\\n0 0 1\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 0 8\\n1 0\", \"2 10\\n0 1 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n2 0\\n0 0 2\\n1 1\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 1\\n2 1\\n1 1\\n0 1 4\\n1 1\\n0 1 9\\n1 1\", \"6 10\\n0 0 1\\n0 0 1\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 8\\n1 1\", \"2 10\\n0 0 3\\n0 0 7\\n0 1 1\\n1 1\\n2 0\\n1 0\\n0 0 8\\n1 0\\n1 0 8\\n0 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n1 0\\n0 0 0\\n2 1\\n0 0 12\\n1 0\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 1\\n1 1\\n0 0 -1\\n2 1\\n0 0 12\\n0 0\", \"4 6\\n0 1 2\\n0 0 26\\n0 0 2\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 2 7\\n1 0\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 1\\n0 1 11\\n1 1\", \"4 10\\n0 0 3\\n0 0 9\\n0 0 1\\n1 1\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 1 8\\n1 1\", \"3 10\\n0 0 3\\n0 0 16\\n0 0 0\\n1 0\\n2 1\\n1 1\\n0 0 4\\n1 0\\n0 1 10\\n1 1\", \"2 10\\n0 0 3\\n0 0 17\\n0 0 2\\n1 0\\n1 0\\n1 0\\n0 0 4\\n1 0\\n0 0 8\\n1 0\", \"2 10\\n0 1 3\\n0 0 9\\n0 0 2\\n1 1\\n2 0\\n1 0\\n0 1 3\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 0 3\\n0 1 14\\n0 1 1\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 4\\n1 1\", \"2 18\\n0 0 5\\n0 0 9\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 1\\n1 0\\n0 0 8\\n1 1\", \"2 10\\n0 1 3\\n0 0 7\\n0 0 1\\n1 0\\n2 0\\n1 0\\n0 0 8\\n1 0\\n0 0 8\\n0 1\", \"6 10\\n0 0 1\\n0 0 1\\n0 0 0\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 1 5\\n1 1\", \"4 4\\n0 0 0\\n0 1 14\\n0 0 0\\n1 0\\n2 1\\n2 0\\n0 0 4\\n1 0\\n0 2 7\\n1 1\", \"2 10\\n0 0 3\\n0 1 9\\n0 1 0\\n1 0\\n2 0\\n1 0\\n0 0 4\\n1 0\\n0 1 11\\n1 1\", \"2 10\\n0 0 3\\n0 1 14\\n0 1 1\\n2 0\\n2 1\\n2 0\\n0 0 4\\n1 1\\n0 1 4\\n1 1\", \"5 6\\n0 0 6\\n0 1 24\\n0 0 2\\n1 0\\n2 1\\n1 0\\n0 0 4\\n1 1\\n0 2 7\\n1 0\", \"6 10\\n0 0 1\\n0 0 1\\n0 0 0\\n1 0\\n2 1\\n1 1\\n0 0 4\\n1 1\\n0 1 5\\n1 1\", \"2 10\\n0 0 4\\n0 0 9\\n0 1 2\\n2 0\\n2 0\\n1 0\\n0 0 4\\n1 1\\n0 1 9\\n1 1\", \"4 7\\n0 0 5\\n0 1 14\\n0 0 1\\n1 0\\n2 1\\n2 0\\n1 0 4\\n1 1\\n0 2 7\\n1 0\", \"4 10\\n0 0 3\\n0 0 9\\n0 2 0\\n1 0\\n2 1\\n1 0\\n0 0 8\\n1 0\\n0 1 1\\n1 1\", \"2 10\\n0 0 4\\n0 0 9\\n0 1 2\\n2 0\\n1 0\\n1 0\\n0 0 4\\n1 1\\n0 1 9\\n1 1\", \"5 6\\n0 0 6\\n0 1 24\\n0 0 2\\n1 0\\n2 0\\n1 0\\n-1 0 4\\n1 1\\n0 2 7\\n1 0\"], \"outputs\": [\"9\\n3\\n4\\n8\", \"9\\n3\\n4\\n\", \"9\\n9\\n9\\n8\\n\", \"3\\n4\\n\", \"9\\n9\\n8\\n\", \"9\\n3\\n3\\n4\\n\", \"9\\n4\\n\", \"3\\n3\\n8\\n\", \"4\\n\", \"2\\n4\\n\", \"9\\n3\\n4\\n8\\n\", \"9\\n9\\n9\\n\", \"3\\n3\\n0\\n8\\n\", \"2\\n3\\n4\\n2\\n\", \"3\\n9\\n\", \"16\\n16\\n8\\n\", \"3\\n0\\n8\\n\", \"2\\n9\\n9\\n\", \"3\\n4\\n9\\n\", \"16\\n8\\n\", \"3\\n8\\n9\\n\", \"3\\n\", \"9\\n1\\n4\\n8\\n\", \"3\\n8\\n\", \"9\\n9\\n\", \"9\\n\", \"3\\n4\\n8\\n\", \"3\\n3\\n0\\n\", \"6\\n0\\n8\\n\", \"3\\n0\\n1\\n\", \"17\\n1\\n4\\n8\\n\", \"3\\n3\\n\", \"6\\n\", \"9\\n3\\n4\\n4\\n\", \"7\\n8\\n\", \"5\\n\", \"3\\n3\\n4\\n\", \"9\\n8\\n\", \"2\\n\", \"9\\n9\\n4\\n9\\n\", \"4\\n4\\n\", \"1\\n4\\n9\\n\", \"3\\n0\\n4\\n\", \"3\\n1\\n4\\n8\\n\", \"9\\n3\\n3\\n8\\n\", \"9\\n5\\n5\\n8\\n\", \"14\\n\", \"7\\n7\\n8\\n\", \"3\\n2\\n3\\n\", \"9\\n4\\n9\\n\", \"1\\n3\\n8\\n\", \"1\\n\", \"14\\n4\\n\", \"1\\n1\\n\", \"3\\n2\\n4\\n9\\n\", \"9\\n3\\n3\\n2\\n\", \"3\\n5\\n\", \"3\\n9\\n9\\n\", \"9\\n3\\n8\\n8\\n\", \"16\\n16\\n\", \"16\\n10\\n\", \"9\\n9\\n9\\n9\\n9\\n\", \"4\\n8\\n\", \"9\\n5\\n8\\n\", \"7\\n10\\n\", \"1\\n7\\n8\\n\", \"3\\n2\\n2\\n4\\n\", \"2\\n8\\n\", \"9\\n9\\n9\\n2\\n\", \"3\\n0\\n0\\n\", \"9\\n3\\n3\\n\", \"6\\n1\\n8\\n\", \"3\\n1\\n8\\n\", \"2\\n2\\n8\\n\", \"2\\n4\\n8\\n\", \"3\\n3\\n3\\n\", \"4\\n9\\n\", \"1\\n1\\n8\\n\", \"1\\n3\\n8\\n8\\n\", \"3\\n3\\n12\\n\", \"3\\n0\\n\", \"26\\n\", \"3\\n9\\n11\\n\", \"3\\n8\\n8\\n\", \"16\\n16\\n10\\n\", \"17\\n17\\n17\\n17\\n17\\n\", \"3\\n2\\n2\\n3\\n\", \"3\\n1\\n4\\n\", \"9\\n5\\n5\\n\", \"7\\n1\\n8\\n\", \"1\\n1\\n5\\n\", \"0\\n\", \"3\\n4\\n11\\n\", \"1\\n4\\n\", \"6\\n6\\n\", \"1\\n5\\n\", \"2\\n9\\n\", \"5\\n1\\n\", \"9\\n9\\n9\\n1\\n\", \"4\\n4\\n2\\n9\\n\", \"6\\n2\\n\"]}", "source": "primeintellect"}
|
Priority queue is a container of elements which the element with the highest priority should be extracted first.
For $n$ priority queues $Q_i$ ($i = 0, 1, ..., n-1$) of integers, perform a sequence of the following operations.
* insert($t$, $x$): Insert $x$ to $Q_t$.
* getMax($t$): Report the maximum value in $Q_t$. If $Q_t$ is empty, do nothing.
* deleteMax($t$): Delete the maximum element from $Q_t$. If $Q_t$ is empty, do nothing.
In the initial state, all queues are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 200,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent insert, getMax and deleteMax operations respectively.
Output
For each getMax operation, print an integer in a line.
Example
Input
2 10
0 0 3
0 0 9
0 0 1
1 0
2 0
1 0
0 0 4
1 0
0 1 8
1 1
Output
9
3
4
8
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 3\\n1 2\\n2 3\\n1 3\\n1 2\\n2 3\\n1 3\\n\", \"5 3\\n-1 3\\n2 4\\n1 1\\n3 5\\n2 2\\n1 4\\n2 3\\n3 5\\n\", \"3 2\\n1 2\\n2 3\\n1 3\\n1 2\\n2 3\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n-2 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n0 1\\n1 -1\\n-1 -2\\n-2 -1\\n1 1\\n2 -2\\n2 2\\n\", \"40 39\\n0 -2\\n-2 3\\n3 3\\n3 -2\\n-1 1\\n2 0\\n-3 2\\n-2 1\\n0 -3\\n-1 -3\\n1 -1\\n-3 -1\\n2 1\\n0 2\\n1 -3\\n-2 -1\\n1 2\\n-1 -2\\n-1 0\\n3 2\\n1 3\\n-3 1\\n-2 -3\\n-3 -2\\n3 0\\n-1 3\\n3 1\\n-2 2\\n0 3\\n3 -1\\n2 -3\\n1 1\\n-1 -1\\n0 1\\n-3 0\\n1 0\\n-3 3\\n-3 -3\\n2 2\\n-1 2\\n1 29\\n29 2\\n29 3\\n29 4\\n5 29\\n29 6\\n7 29\\n8 29\\n29 9\\n29 10\\n11 29\\n12 29\\n29 13\\n14 29\\n29 15\\n16 29\\n17 29\\n18 29\\n19 29\\n29 20\\n29 21\\n22 29\\n23 29\\n29 24\\n25 29\\n26 29\\n27 29\\n29 28\\n29 30\\n31 29\\n32 29\\n33 29\\n29 34\\n35 29\\n36 29\\n37 29\\n38 29\\n39 29\\n29 40\\n\", \"2 0\\n0 0\\n1 1\\n\", \"40 3\\n-1 -3\\n0 3\\n-2 -1\\n1 2\\n-3 3\\n-3 1\\n1 1\\n3 -1\\n3 -2\\n2 3\\n3 -3\\n2 2\\n-3 2\\n-2 -3\\n2 1\\n-2 -2\\n-1 -1\\n2 -1\\n-1 3\\n0 1\\n-1 0\\n1 -2\\n0 -2\\n-3 0\\n-3 -2\\n2 -2\\n1 0\\n3 0\\n2 -3\\n0 -1\\n-1 -2\\n0 0\\n3 2\\n3 3\\n0 2\\n-1 2\\n-1 1\\n1 3\\n-3 -3\\n0 -3\\n34 33\\n34 10\\n33 10\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n3 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 -1\\n2 0\\n-3 3\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -2\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 0\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n19 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"2 1\\n0 0\\n10 10\\n1 2\\n\", \"4 0\\n-1000000000 -1000000000\\n1000000000 -1000000000\\n-1000000000 1000000000\\n1000000000 1000000000\\n\", \"20 19\\n0 1\\n3 2\\n0 0\\n2 2\\n1 -3\\n0 -2\\n-1 -1\\n-2 0\\n2 0\\n-1 0\\n-3 0\\n3 -3\\n2 -1\\n-3 -2\\n-2 2\\n0 3\\n1 3\\n-1 -3\\n1 -1\\n2 -2\\n1 2\\n3 2\\n4 2\\n5 2\\n6 2\\n2 7\\n8 2\\n9 2\\n2 10\\n11 2\\n12 2\\n2 13\\n14 2\\n2 15\\n2 16\\n2 17\\n2 18\\n2 19\\n2 20\\n\", \"2 0\\n-1 -1\\n1 1\\n\", \"4 4\\n-1000000000 -1000000000\\n1000000000 -1000000000\\n-1000000000 1000000000\\n1000000000 1000000000\\n1 2\\n1 3\\n2 4\\n3 4\\n\", \"20 1\\n-2 -2\\n-2 -1\\n-1 0\\n2 2\\n0 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n1 -2\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 2\\n-1 2\\n4 13\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n-2 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n-1 1\\n1 -1\\n-1 -2\\n-2 -1\\n1 1\\n2 -2\\n2 2\\n\", \"40 39\\n0 -2\\n-2 3\\n3 3\\n3 -2\\n-1 1\\n2 0\\n-3 2\\n-2 1\\n0 -3\\n-1 -3\\n1 -1\\n-3 -1\\n2 2\\n0 2\\n1 -3\\n-2 -1\\n1 2\\n-1 -2\\n-1 0\\n3 2\\n1 3\\n-3 1\\n-2 -3\\n-3 -2\\n3 0\\n-1 3\\n3 1\\n-2 2\\n0 3\\n3 -1\\n2 -3\\n1 1\\n-1 -1\\n0 1\\n-3 0\\n1 0\\n-3 3\\n-3 -3\\n2 2\\n-1 2\\n1 29\\n29 2\\n29 3\\n29 4\\n5 29\\n29 6\\n7 29\\n8 29\\n29 9\\n29 10\\n11 29\\n12 29\\n29 13\\n14 29\\n29 15\\n16 29\\n17 29\\n18 29\\n19 29\\n29 20\\n29 21\\n22 29\\n23 29\\n29 24\\n25 29\\n26 29\\n27 29\\n29 28\\n29 30\\n31 29\\n32 29\\n33 29\\n29 34\\n35 29\\n36 29\\n37 29\\n38 29\\n39 29\\n29 40\\n\", \"40 3\\n-1 -3\\n0 3\\n-2 -1\\n1 2\\n-3 3\\n-3 1\\n1 1\\n3 -1\\n3 -2\\n2 3\\n3 -3\\n2 2\\n-3 2\\n-2 -3\\n2 1\\n-2 -2\\n-1 -1\\n2 -1\\n-1 3\\n0 1\\n-1 0\\n1 -2\\n0 -2\\n-3 0\\n-3 -2\\n2 -2\\n1 0\\n3 1\\n2 -3\\n0 -1\\n-1 -2\\n0 0\\n3 2\\n3 3\\n0 2\\n-1 2\\n-1 1\\n1 3\\n-3 -3\\n0 -3\\n34 33\\n34 10\\n33 10\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n3 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 -1\\n2 0\\n-3 3\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -2\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 0\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"20 19\\n0 1\\n3 2\\n0 0\\n2 2\\n1 -3\\n0 -2\\n-1 -1\\n-2 0\\n2 0\\n-1 0\\n-3 0\\n3 -3\\n2 -1\\n-3 -2\\n-2 2\\n0 3\\n1 3\\n-2 -3\\n1 -1\\n2 -2\\n1 2\\n3 2\\n4 2\\n5 2\\n6 2\\n2 7\\n8 2\\n9 2\\n2 10\\n11 2\\n12 2\\n2 13\\n14 2\\n2 15\\n2 16\\n2 17\\n2 18\\n2 19\\n2 20\\n\", \"20 1\\n-2 -2\\n-2 -1\\n-1 0\\n2 2\\n0 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n1 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 2\\n-1 2\\n4 13\\n\", \"5 3\\n-1 3\\n4 4\\n1 1\\n3 5\\n2 2\\n1 4\\n2 3\\n3 5\\n\", \"3 2\\n1 2\\n2 3\\n1 3\\n1 2\\n2 1\\n\", \"40 39\\n0 -2\\n-2 3\\n3 3\\n3 -2\\n-1 1\\n2 0\\n-3 2\\n-2 1\\n0 -3\\n-1 -3\\n1 -1\\n-3 -1\\n2 2\\n0 2\\n1 -3\\n-2 -1\\n1 2\\n-1 -2\\n-1 0\\n3 2\\n1 3\\n-3 1\\n-2 -3\\n-3 -1\\n3 0\\n-1 3\\n3 1\\n-2 2\\n0 3\\n3 -1\\n2 -3\\n1 1\\n-1 -1\\n0 1\\n-3 0\\n1 0\\n-3 3\\n-3 -3\\n2 2\\n-1 2\\n1 29\\n29 2\\n29 3\\n29 4\\n5 29\\n29 6\\n7 29\\n8 29\\n29 9\\n29 10\\n11 29\\n12 29\\n29 13\\n14 29\\n29 15\\n16 29\\n17 29\\n18 29\\n19 29\\n29 20\\n29 21\\n22 29\\n23 29\\n29 24\\n25 29\\n26 29\\n27 29\\n29 28\\n29 30\\n31 29\\n32 29\\n33 29\\n29 34\\n35 29\\n36 29\\n37 29\\n38 29\\n39 29\\n29 40\\n\", \"40 3\\n-1 -3\\n0 3\\n-2 -1\\n1 2\\n-3 3\\n0 1\\n1 1\\n3 -1\\n3 -2\\n2 3\\n3 -3\\n2 2\\n-3 2\\n-2 -3\\n2 1\\n-2 -2\\n-1 -1\\n2 -1\\n-1 3\\n0 1\\n-1 0\\n1 -2\\n0 -2\\n-3 0\\n-3 -2\\n2 -2\\n1 0\\n3 1\\n2 -3\\n0 -1\\n-1 -2\\n0 0\\n3 2\\n3 3\\n0 2\\n-1 2\\n-1 1\\n1 3\\n-3 -3\\n0 -3\\n34 33\\n34 10\\n33 10\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n-2 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n-1 1\\n1 -1\\n-1 -2\\n-2 0\\n1 1\\n4 -2\\n2 2\\n\", \"40 39\\n0 -2\\n-2 3\\n3 3\\n3 -2\\n-1 1\\n2 0\\n-3 2\\n-2 1\\n0 -3\\n-1 -3\\n1 -1\\n-3 -1\\n2 2\\n0 2\\n1 -3\\n-2 -1\\n1 2\\n-1 -2\\n-1 0\\n3 2\\n1 3\\n-3 1\\n-2 -3\\n-3 -1\\n3 0\\n-1 3\\n3 1\\n-2 2\\n0 3\\n3 -1\\n2 -3\\n1 1\\n-1 -1\\n0 1\\n-3 0\\n1 0\\n-3 3\\n-3 -3\\n2 2\\n-1 2\\n1 29\\n29 2\\n29 3\\n29 4\\n5 29\\n29 6\\n7 29\\n8 29\\n29 9\\n29 10\\n11 29\\n12 29\\n29 13\\n14 29\\n29 15\\n16 29\\n17 29\\n18 29\\n19 29\\n29 20\\n29 21\\n22 29\\n23 29\\n29 24\\n25 29\\n26 29\\n27 29\\n29 28\\n10 30\\n31 29\\n32 29\\n33 29\\n29 34\\n35 29\\n36 29\\n37 29\\n38 29\\n39 29\\n29 40\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n5 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 -1\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -2\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 0\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 2\\n0 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 2\\n-1 2\\n4 13\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n5 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 -1\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -3\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 0\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 2\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 2\\n-1 2\\n4 13\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n0 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n-1 1\\n1 -1\\n-1 -2\\n-2 0\\n1 1\\n7 -2\\n2 2\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n5 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 -1\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -3\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 1\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 2\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 2\\n-1 2\\n4 2\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n0 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n-1 1\\n1 -1\\n-1 -2\\n-4 0\\n1 1\\n7 -2\\n2 2\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n5 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 0\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -3\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 1\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n5 4\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 0\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -3\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 1\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 2\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n0 0\\n-1 -2\\n1 1\\n-2 1\\n-1 2\\n4 2\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n5 4\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 0\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -3\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 1\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n5 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 2\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n9 4\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 0\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -3\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 1\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n5 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 0\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 0\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-3 1\\n0 1\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 0\\n-2 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-3 1\\n0 1\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 0\\n-2 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 0\\n-2 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -3\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n-2 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -3\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -3\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-3 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -3\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n-1 0\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n-1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -1\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -2\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 -2\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 1\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 -1\\n2 -2\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 1\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 1\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 1\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n0 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -2\\n1 1\\n-4 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n0 0\\n-1 -4\\n1 1\\n-4 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n2 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-4 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-4 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-7 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 -1\\n-1 -4\\n1 1\\n-7 1\\n-1 2\\n7 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 -1\\n-1 -4\\n1 1\\n-7 1\\n-1 2\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-7 1\\n-1 2\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-7 0\\n-1 2\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -2\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-7 0\\n-1 2\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-7 0\\n-1 2\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-7 0\\n-1 2\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-7 0\\n-1 3\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-1 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-7 0\\n-1 3\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 -1\\n1 -1\\n2 1\\n-1 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-7 0\\n-1 3\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 -1\\n1 -1\\n2 1\\n0 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-7 0\\n-1 3\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n-1 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 -1\\n1 -1\\n2 1\\n0 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-7 0\\n-1 3\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n-1 -2\\n2 -1\\n1 -1\\n1 2\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 -1\\n1 -1\\n2 1\\n0 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-9 0\\n-1 3\\n7 3\\n\", \"20 1\\n-2 -2\\n-2 -2\\n-1 -2\\n2 -1\\n1 -1\\n1 1\\n2 -1\\n-2 0\\n0 -2\\n1 0\\n2 -1\\n1 -1\\n2 1\\n0 1\\n0 0\\n-1 0\\n-1 0\\n1 1\\n-9 0\\n-1 3\\n7 3\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n-2 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n-1 1\\n1 -1\\n-1 -2\\n-2 -1\\n1 1\\n4 -2\\n2 2\\n\", \"40 10\\n-1 0\\n0 2\\n2 2\\n-2 2\\n-3 -1\\n-3 -3\\n0 -1\\n3 3\\n0 1\\n2 -2\\n-2 -3\\n-2 -1\\n3 -1\\n2 0\\n-3 5\\n1 3\\n1 -3\\n0 -3\\n0 3\\n-3 -2\\n-2 1\\n-1 -3\\n-1 1\\n1 2\\n-1 2\\n0 -2\\n3 0\\n0 0\\n-2 -2\\n-2 3\\n1 -2\\n1 1\\n-3 2\\n1 0\\n-1 -2\\n3 2\\n2 -1\\n-1 3\\n3 -2\\n-2 0\\n4 7\\n4 37\\n4 15\\n13 4\\n7 37\\n7 15\\n19 7\\n15 37\\n19 37\\n19 15\\n\", \"20 1\\n-2 -2\\n-2 -1\\n-1 0\\n2 2\\n0 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 2\\n-1 2\\n4 13\\n\", \"5 3\\n-1 3\\n4 4\\n1 1\\n3 8\\n2 2\\n1 4\\n2 3\\n3 5\\n\", \"20 0\\n-2 0\\n0 2\\n1 2\\n-2 1\\n2 1\\n0 0\\n-1 2\\n-2 2\\n-2 -2\\n2 -1\\n0 -2\\n2 0\\n0 -1\\n-1 1\\n1 -1\\n-1 -2\\n-2 0\\n1 1\\n7 -2\\n2 2\\n\", \"40 39\\n0 -2\\n-2 3\\n3 3\\n3 -2\\n-1 1\\n2 0\\n-3 2\\n-2 1\\n0 -3\\n-1 -3\\n1 -1\\n-3 -1\\n2 2\\n0 2\\n1 -3\\n-2 -1\\n1 2\\n-1 -2\\n-1 0\\n3 2\\n1 3\\n-3 1\\n-2 -3\\n-3 -1\\n3 0\\n-1 3\\n3 1\\n-2 2\\n0 3\\n3 -1\\n2 -3\\n1 1\\n-1 -1\\n0 1\\n-3 0\\n1 0\\n-3 3\\n-3 -3\\n2 2\\n-1 2\\n1 29\\n29 2\\n29 3\\n29 4\\n5 29\\n29 6\\n7 29\\n8 29\\n29 9\\n29 10\\n11 29\\n12 29\\n29 13\\n14 29\\n29 15\\n16 29\\n17 29\\n18 29\\n19 29\\n29 20\\n29 21\\n22 29\\n23 29\\n29 24\\n25 29\\n26 29\\n27 29\\n29 28\\n10 30\\n31 29\\n32 29\\n33 29\\n29 34\\n25 29\\n36 29\\n37 29\\n38 29\\n39 29\\n29 40\\n\", \"20 1\\n-2 -2\\n-2 -1\\n0 0\\n2 2\\n-1 0\\n1 2\\n0 -1\\n-2 0\\n0 -2\\n1 0\\n2 -4\\n2 -1\\n2 1\\n-2 1\\n0 1\\n2 0\\n-1 -2\\n1 1\\n-2 1\\n-1 2\\n4 2\\n\", \"20 1\\n-2 -2\\n-2 -2\\n0 -1\\n2 -2\\n1 -1\\n1 2\\n1 -1\\n-2 0\\n0 -2\\n1 0\\n2 0\\n1 -1\\n2 1\\n-3 1\\n0 0\\n-1 0\\n-1 -4\\n1 1\\n-7 0\\n-1 2\\n7 3\\n\"], \"outputs\": [\"0 0 0\", \"4 14 4 16 10\\n\", \"3 0 3\", \"-40 -4 10 -38 10 -15 -20 -38 -51 -21 -40 -4 -26 -8 -22 -44 -44 3 -39 21\\n\", \"-94 -75 66 -85 -53 -20 -112 -82 -126 -131 -57 -127 7 -16 -123 -102 9 -104 -65 44 21 -114 -141 -139 -15 -40 17 -77 0 -49 -122 -8 -82 -28 -119 -30 -112 -156 29 -45\", \"1 1\", \"-130 -12 -103 11 -122 -123 -4 -42 -78 40 -116 34 -122 -140 12 -118 -80 -46 -47 -27 -65 -84 -92 -126 -141 -80 -26 -8 -116 -64 -102 -42 41 62 -18 -50 -56 20 -156 -122\\n\", \"-67 -17 30 -76 -131 -160 -60 68 -29 -87 -145 -105 -49 -21 -109 21 -125 -128 -9 -143 -86 -135 -55 9 -48 -97 -14 -46 -122 -80 -90 -8 -118 -31 -107 45 -43 -44 -87 -93\\n\", \"0 0\", \"-4000000000 -4000000000 -4000000000 0\\n\", \"-17 0 -24 10 -56 -44 -41 -47 -10 -34 -62 -56 -24 -68 -45 -11 4 -61 -27 -39\", \"0 0\", \"0 -2000000000 -2000000000 0\", \"-51 -44 -26 18 -15 10 -26 -41 -41 -8 -40 -22 7 -39 -8 -5 -44 3 -39 -21\\n\", \"-40 -4 9 -38 9 -16 -20 -38 -52 -22 -41 -5 -27 -22 -23 -45 -45 2 -40 20\\n\", \"-94 -74 67 -85 -52 -20 -111 -81 -126 -131 -57 -126 30 -15 -123 -101 10 -104 -64 44 22 -113 -141 -138 -15 -39 17 -76 0 -49 -122 -7 -81 -27 -118 -30 -111 -155 30 -44\\n\", \"-129 -11 -102 12 -121 -122 -3 -42 -78 41 -116 35 -121 -139 13 -117 -79 -46 -46 -26 -64 -84 -91 -125 -140 -80 -25 23 -116 -63 -101 -41 42 63 -17 -49 -55 21 -155 -122\\n\", \"-67 -17 30 -72 -131 -160 -60 68 -29 -87 -145 -105 -46 -21 -109 21 -125 -128 -8 -143 -86 -135 -55 9 -48 -97 -14 -46 -122 -80 -90 -8 -118 -31 -107 45 -43 -44 -87 -93\\n\", \"-17 0 -24 10 -57 -45 -41 -47 -11 -34 -62 -57 -25 -68 -45 -11 4 -68 -28 -40\\n\", \"-53 -46 -28 16 -17 8 -28 -43 -43 -10 -78 -24 5 -41 -10 -7 -46 1 -41 -23\\n\", \"4 16 4 16 12\\n\", \"-1 0 7\\n\", \"-94 -73 67 -85 -51 -20 -110 -80 -126 -131 -57 -125 30 -14 -123 -101 10 -104 -64 44 23 -112 -141 -125 -15 -38 17 -75 0 -49 -122 -7 -81 -27 -117 -30 -110 -155 30 -43\\n\", \"-126 -10 -99 15 -121 -23 0 -39 -75 44 -113 38 -121 -136 16 -114 -76 -43 -46 -23 -61 -81 -88 -124 -137 -77 -22 26 -113 -60 -98 -38 45 66 -15 -48 -53 23 -152 -119\\n\", \"-39 -3 9 -37 9 -16 -19 -37 -52 -22 -41 -5 -27 -21 -23 -45 -39 2 -40 20\\n\", \"-94 -73 67 -85 -51 -20 -110 -80 -126 -129 -57 -125 30 -14 -123 -101 10 -104 -64 44 23 -112 -141 -125 -15 -38 17 -75 -1 -48 -122 -7 -81 -27 -117 -30 -110 -155 30 -43\\n\", \"-67 -17 30 -72 -131 -160 -59 95 -29 -85 -144 -105 -44 -19 -109 21 -123 -126 -8 -143 -86 -133 -55 9 -48 -95 -12 -46 -122 -80 -88 -8 -118 -30 -106 46 -41 -44 -85 -93\\n\", \"-52 -46 -16 17 -16 8 -27 -43 -42 -9 -77 -23 6 -41 -10 -6 -45 2 -41 -23\\n\", \"-68 -18 29 -73 -132 -161 -60 94 -30 -85 -145 -106 -44 -20 -110 20 -123 -126 -9 -144 -87 -134 -56 8 -49 -126 -12 -47 -123 -81 -88 -9 -119 -31 -107 45 -41 -45 -85 -94\\n\", \"-53 -46 -17 16 -28 8 -28 -43 -43 -10 -78 -24 5 -41 -10 -7 -46 1 -41 -23\\n\", \"-39 -3 9 -37 10 -16 -19 -37 -39 -20 -39 -3 -26 -21 -21 -44 -39 2 -38 20\\n\", \"-67 -17 30 -72 -131 -160 -60 94 -29 -85 -145 -105 -44 -20 -109 21 -123 -126 -8 -143 -86 -134 -55 9 -48 -126 -12 -46 -122 -80 -88 -8 -118 -8 -107 45 -41 -44 -85 -93\\n\", \"-53 -46 -17 19 -28 8 -28 -43 -43 -10 -78 -24 8 -41 -10 -7 -46 1 -41 -23\\n\", \"-41 -5 7 -38 8 -18 -20 -37 -41 -22 -41 -5 -28 -23 -23 -46 -73 0 -40 18\\n\", \"-66 -16 31 -72 -130 -159 -59 95 -28 -85 -144 -104 -9 -19 -108 22 -123 -125 -7 -142 -85 -133 -54 10 -47 -125 -11 -45 -121 -79 -87 -7 -117 -7 -106 46 -40 -43 -85 -92\\n\", \"-65 -15 32 -71 -129 -158 -58 123 -27 -85 -143 -103 -9 -19 -107 23 -123 -125 -6 -141 -84 -133 -53 11 -46 -125 -11 -44 -120 -78 -87 -6 -116 -6 -105 47 -40 -42 -85 -91\\n\", \"-53 -46 -17 19 -28 8 -29 -43 -45 -11 -80 -26 7 -41 -10 -17 -47 1 -41 -23\\n\", \"-65 -15 32 -71 -125 -158 -58 123 -27 -85 -143 -103 -9 -19 -103 23 -123 -125 -6 -141 -84 -133 -53 11 -46 -125 -11 -44 -120 -78 -87 -6 -116 -6 -105 47 -40 -42 -85 -91\\n\", \"-54 -47 -18 18 -29 7 -30 -44 -46 -12 -81 -27 6 -42 -11 -18 -48 0 -60 -24\\n\", \"-65 -15 32 -71 -125 -158 -58 147 -27 -82 -143 -103 -7 -18 -103 23 -120 -123 -6 -141 -84 -132 -53 11 -46 -123 -9 -44 -120 -78 -85 -6 -116 -6 -105 47 -38 -42 -81 -91\\n\", \"-56 -47 -20 -8 -31 5 -31 -46 -46 -13 -81 -27 5 -44 -13 -20 -49 -2 -62 -26\\n\", \"-57 -48 -21 -9 -32 4 -32 -47 -47 -14 -82 -28 4 -62 -14 -21 -50 -3 -62 -27\\n\", \"-58 -49 -22 -10 -47 3 -33 -47 -48 -15 -83 -29 3 -62 -15 -22 -51 -4 -62 -27\\n\", \"-58 -50 -22 -10 -48 2 -33 -48 -48 -15 -83 -29 3 -63 -22 -22 -51 -4 -63 -28\\n\", \"-57 -49 -21 -9 -47 3 -32 -47 -47 -14 -64 -28 4 -62 -21 -21 -50 -3 -62 -27\\n\", \"-58 -49 -22 -25 -48 2 -33 -48 -48 -15 -64 -28 3 -63 -22 -22 -51 -4 -63 -28\\n\", \"-57 -48 -21 -24 -33 3 -32 -48 -47 -14 -63 -27 4 -63 -21 -21 -50 -3 -63 -28\\n\", \"-58 -49 -22 -25 -34 2 -33 -49 -48 -15 -64 -28 3 -64 -22 -22 -51 -4 -82 -29\\n\", \"-55 -46 -19 -23 -31 5 -30 -46 -45 -12 -9 -26 6 -61 -19 -19 -48 -1 -79 -26\\n\", \"-55 -46 -19 -22 -31 5 -26 -46 -44 -12 -8 -25 6 -61 -19 -19 -48 -1 -79 -26\\n\", \"-55 -47 -19 -22 -37 4 -26 -47 -44 -12 -8 -25 6 -62 -19 -19 -48 -1 -80 -27\\n\", \"-55 -47 -19 -21 -29 4 -25 -47 -43 -11 -7 -24 7 -62 -19 -19 -47 -1 -80 -27\\n\", \"-56 -47 -20 -39 -30 3 -26 -48 -44 -12 -8 -25 6 -63 -20 -20 -48 -2 -81 -28\\n\", \"-55 -46 -19 -39 -30 4 -26 -47 -44 -1 -8 -25 6 -62 -19 -19 -48 -1 -80 -27\\n\", \"-56 -47 -30 -39 -30 3 -26 -48 -44 -2 -8 -25 6 -63 -20 -20 -48 -2 -81 -28\\n\", \"-56 -52 -30 -39 -30 2 -26 -49 -44 -2 -8 -25 6 -64 -20 -20 -48 -2 -82 -29\\n\", \"-56 -53 -30 -43 -30 2 -23 -49 -44 -2 -8 -25 6 -64 -20 -20 -48 -2 -82 -29\\n\", \"-57 -54 -30 -43 -30 1 -23 -50 -44 -12 -8 -25 6 -65 -21 -21 -48 -3 -83 -30\\n\", \"-57 -54 -30 -42 -25 1 -22 -50 -43 -12 -7 -24 6 -65 -21 -21 -48 -3 -83 -30\\n\", \"-59 -56 -32 -42 -26 -1 -23 -52 -44 -14 -8 -24 4 -67 -23 -23 -78 -5 -85 -32\\n\", \"-60 -57 -33 -43 -27 -1 -24 -52 -45 -15 -9 -25 3 -67 -24 -37 -79 -6 -85 -32\\n\", \"-60 -57 -33 -44 -27 -1 -24 -52 -45 -15 -9 -27 3 -67 -24 -37 -80 -6 -85 -32\\n\", \"-63 -60 -36 -47 -30 -4 -27 -55 -48 -18 -12 -30 0 -70 -27 -40 -83 -9 -142 -35\\n\", \"-63 -60 -36 -47 -30 -5 -27 -56 -48 -18 -12 -30 0 -71 -27 -45 -83 -9 -143 -36\\n\", \"-63 -63 -35 -47 -30 -5 -29 -56 -48 -18 -12 -30 0 -71 -27 -45 -83 -9 -143 -36\\n\", \"-63 -63 -35 -47 -30 -4 -29 -55 -48 -18 -12 -30 0 -70 -27 -40 -83 -9 -142 -35\\n\", \"-64 -64 -47 -47 -30 -5 -29 -56 -48 -19 -12 -30 -1 -71 -28 -41 -83 -10 -143 -36\\n\", \"-64 -64 -47 -46 -30 -5 -27 -56 -48 -19 -12 -30 -1 -71 -28 -41 -82 -10 -143 -36\\n\", \"-63 -63 -46 -27 -29 -4 -26 -55 -47 -18 -11 -29 0 -70 -27 -40 -81 -9 -142 -35\\n\", \"-60 -60 -45 -27 -28 0 -26 -51 -46 -16 -10 -28 2 -66 -24 -36 -36 -6 -138 -31\\n\", \"-60 -60 -45 -27 -28 0 -26 -51 -46 -16 -10 -28 2 -65 -24 -36 -36 -6 -137 -29\\n\", \"-58 -58 -43 -25 -26 2 -24 -49 -44 -14 -8 -26 4 -31 -22 -34 -34 -4 -137 -29\\n\", \"-59 -59 -44 -25 -27 1 -24 -50 -45 -15 -25 -27 3 -32 -23 -35 -35 -5 -138 -30\\n\", \"-58 -58 -43 -24 -26 2 -23 -50 -44 -14 -24 -26 4 -16 -22 -34 -34 -4 -138 -30\\n\", \"-58 -58 -48 -25 -27 2 -23 -50 -45 -14 -25 -27 4 -16 -22 -34 -34 -4 -138 -30\\n\", \"-60 -60 -50 -27 -29 0 -25 -52 -47 -16 -27 -29 2 -18 -24 -36 -36 -6 -176 -32\\n\", \"-60 -60 -50 -27 -29 -6 -25 -53 -47 -16 -27 -29 2 -19 -24 -37 -37 -6 -177 -33\\n\", \"-40 -4 9 -38 9 -16 -20 -38 -52 -22 -41 -5 -27 -22 -23 -45 -45 2 -40 20\\n\", \"-67 -17 30 -72 -131 -160 -60 68 -29 -87 -145 -105 -46 -21 -109 21 -125 -128 -8 -143 -86 -135 -55 9 -48 -97 -14 -46 -122 -80 -90 -8 -118 -31 -107 45 -43 -44 -87 -93\\n\", \"-53 -46 -28 16 -17 8 -28 -43 -43 -10 -78 -24 5 -41 -10 -7 -46 1 -41 -23\\n\", \"4 16 4 16 12\\n\", \"-39 -3 9 -37 9 -16 -19 -37 -52 -22 -41 -5 -27 -21 -23 -45 -39 2 -40 20\\n\", \"-94 -73 67 -85 -51 -20 -110 -80 -126 -129 -57 -125 30 -14 -123 -101 10 -104 -64 44 23 -112 -141 -125 -15 -38 17 -75 -1 -48 -122 -7 -81 -27 -117 -30 -110 -155 30 -43\\n\", \"-53 -46 -17 19 -28 8 -28 -43 -43 -10 -78 -24 8 -41 -10 -7 -46 1 -41 -23\\n\", \"-63 -63 -35 -47 -30 -4 -29 -55 -48 -18 -12 -30 0 -70 -27 -40 -83 -9 -142 -35\\n\"]}", "source": "primeintellect"}
|
Zibi is a competitive programming coach. There are n competitors who want to be prepared well. The training contests are quite unusual – there are two people in a team, two problems, and each competitor will code exactly one of them. Of course, people in one team will code different problems.
Rules of scoring also aren't typical. The first problem is always an implementation problem: you have to implement some well-known algorithm very fast and the time of your typing is rated. The second one is an awful geometry task and you just have to get it accepted in reasonable time. Here the length and difficulty of your code are important. After that, Zibi will give some penalty points (possibly negative) for each solution and the final score of the team is the sum of them (the less the score is, the better).
We know that the i-th competitor will always have score x_i when he codes the first task and y_i when he codes the second task. We can assume, that all competitors know each other's skills and during the contest distribute the problems in the way that minimizes their final score. Remember that each person codes exactly one problem in a contest.
Zibi wants all competitors to write a contest with each other. However, there are m pairs of people who really don't like to cooperate and they definitely won't write a contest together. Still, the coach is going to conduct trainings for all possible pairs of people, such that the people in pair don't hate each other. The coach is interested for each participant, what will be his or her sum of scores of all teams he trained in?
Input
The first line contains two integers n and m (2 ≤ n ≤ 300 000, 0 ≤ m ≤ 300 000) — the number of participants and the number of pairs of people who will not write a contest together.
Each of the next n lines contains two integers x_i and y_i (-10^9 ≤ x_i, y_i ≤ 10^9) — the scores which will the i-th competitor get on the first problem and on the second problem. It is guaranteed that there are no two people having both x_i and y_i same.
Each of the next m lines contain two integers u_i and v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i) — indices of people who don't want to write a contest in one team. Each unordered pair of indices will appear at most once.
Output
Output n integers — the sum of scores for all participants in the same order as they appear in the input.
Examples
Input
3 2
1 2
2 3
1 3
1 2
2 3
Output
3 0 3
Input
3 3
1 2
2 3
1 3
1 2
2 3
1 3
Output
0 0 0
Input
5 3
-1 3
2 4
1 1
3 5
2 2
1 4
2 3
3 5
Output
4 14 4 16 10
Note
In the first example, there will be only one team consisting of persons 1 and 3. The optimal strategy for them is to assign the first task to the 3-rd person and the second task to the 1-st person, this will lead to score equal to 1 + 2 = 3.
In the second example, nobody likes anyone, so there won't be any trainings. It seems that Zibi won't be titled coach in that case...
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 4\\n? 1\\nL 5\\n? 1\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 101\\n? 123\\nL 10\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"7\\nL 1\\nR 2\\nR 3\\nL 4\\nL 5\\n? 1\\n? 2\\n\", \"6\\nL 1\\nR 2\\nR 3\\n? 2\\nL 4\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 2\\nL 4\\n? 1\\n\", \"10\\nL 100\\nR 101000\\nR 123\\nL 101\\n? 123\\nL 10\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 4\\n? 1\\nL 10\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 2\\nL 3\\n? 3\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 4\\n? 1\\nL 5\\n? 2\\n\", \"6\\nL 1\\nR 2\\nR 8\\n? 1\\nL 3\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 1\\nL 4\\n? 1\\nL 5\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 3\\nL 7\\n? 1\\nL 5\\n? 2\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 6\\n? 1\\nL 5\\n? 3\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 3\\nL 6\\n? 2\\nL 5\\n? 5\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 2\\nL 3\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 7\\n? 1\\nL 10\\n? 1\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 101\\n? 123\\nL 17\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"6\\nL 1\\nR 2\\nR 8\\n? 2\\nL 3\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 2\\nL 3\\n? 2\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 111\\n? 123\\nL 10\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 7\\n? 1\\nL 15\\n? 1\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 111\\n? 123\\nL 3\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 001\\n? 123\\nL 10\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 2\\nL 8\\n? 1\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 10\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 111\\n? 123\\nL 17\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"10\\nL 100\\nR 100001\\nR 123\\nL 111\\n? 123\\nL 3\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 7\\n? 1\\nL 5\\n? 2\\n\", \"6\\nL 1\\nR 2\\nR 10\\n? 2\\nL 3\\n? 1\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 10\\nR 115\\n? 100\\nR 111\\n? 115\\n\", \"10\\nL 100\\nR 100000\\nR 123\\nL 111\\n? 123\\nL 8\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"6\\nL 1\\nR 2\\nR 15\\n? 2\\nL 3\\n? 1\\n\", \"10\\nL 100\\nR 110000\\nR 123\\nL 101\\n? 123\\nL 10\\nR 115\\n? 100\\nR 111\\n? 115\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 6\\n? 1\\nL 10\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 1\\nL 8\\n? 1\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 13\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 17\\nR 115\\n? 100\\nR 111\\n? 115\\n\", \"10\\nL 100\\nR 111100\\nR 123\\nL 101\\n? 123\\nL 13\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"6\\nL 1\\nR 2\\nR 9\\n? 2\\nL 3\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 7\\n? 1\\nL 6\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 6\\n? 1\\nL 5\\n? 2\\n\", \"6\\nL 1\\nR 2\\nR 30\\n? 2\\nL 3\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 3\\nL 7\\n? 1\\nL 9\\n? 2\\n\", \"6\\nL 1\\nR 2\\nR 30\\n? 2\\nL 4\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 7\\n? 1\\nL 15\\n? 2\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 19\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"6\\nL 1\\nR 2\\nR 8\\n? 1\\nL 3\\n? 2\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 14\\nR 115\\n? 100\\nR 111\\n? 115\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 3\\nL 7\\n? 1\\nL 6\\n? 2\\n\", \"6\\nL 1\\nR 2\\nR 6\\n? 2\\nL 3\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 6\\n? 1\\nL 5\\n? 5\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 4\\n? 2\\nL 5\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 2\\nL 6\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 5\\n? 1\\nL 3\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 7\\n? 2\\nL 10\\n? 1\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 5\\nR 115\\n? 100\\nR 110\\n? 115\\n\", \"6\\nL 1\\nR 2\\nR 7\\n? 1\\nL 8\\n? 1\\n\", \"6\\nL 1\\nR 2\\nR 30\\n? 2\\nL 6\\n? 1\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 12\\n? 1\\nL 15\\n? 2\\n\", \"10\\nL 100\\nR 111000\\nR 123\\nL 101\\n? 123\\nL 19\\nR 115\\n? 100\\nR 010\\n? 115\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 3\\nL 7\\n? 1\\nL 7\\n? 2\\n\", \"8\\nL 1\\nR 2\\nR 3\\n? 2\\nL 6\\n? 2\\nL 5\\n? 5\\n\", \"6\\nL 1\\nR 2\\nR 4\\n? 2\\nL 3\\n? 1\\n\", \"10\\nL 100\\nR 111100\\nR 123\\nL 101\\n? 123\\nL 19\\nR 115\\n? 100\\nR 010\\n? 115\\n\"], \"outputs\": [\"1\\n1\\n2\\n\", \"0\\n2\\n1\\n\", \"2\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n2\\n\", \"1\\n0\\n\", \"1\\n1\\n1\\n\", \"0\\n1\\n\", \"0\\n1\\n2\\n\", \"0\\n1\\n1\\n\", \"1\\n1\\n0\\n\", \"0\\n1\\n0\\n\", \"1\\n1\\n\", \"1\\n1\\n2\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n2\\n\", \"0\\n2\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n1\\n\", \"1\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n2\\n\", \"0\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n2\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n2\\n\", \"1\\n1\\n1\\n\", \"1\\n1\\n\", \"0\\n1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n1\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n0\\n\", \"1\\n1\\n2\\n\", \"1\\n1\\n\", \"0\\n1\\n\", \"1\\n1\\n2\\n\", \"0\\n2\\n1\\n\", \"0\\n1\\n\", \"1\\n1\\n\", \"1\\n1\\n1\\n\", \"0\\n2\\n1\\n\", \"0\\n1\\n1\\n\", \"1\\n1\\n0\\n\", \"1\\n1\\n\", \"0\\n2\\n1\\n\"]}", "source": "primeintellect"}
|
You have got a shelf and want to put some books on it.
You are given q queries of three types:
1. L id — put a book having index id on the shelf to the left from the leftmost existing book;
2. R id — put a book having index id on the shelf to the right from the rightmost existing book;
3. ? id — calculate the minimum number of books you need to pop from the left or from the right in such a way that the book with index id will be leftmost or rightmost.
You can assume that the first book you will put can have any position (it does not matter) and queries of type 3 are always valid (it is guaranteed that the book in each such query is already placed). You can also assume that you don't put the same book on the shelf twice, so ids don't repeat in queries of first two types.
Your problem is to answer all the queries of type 3 in order they appear in the input.
Note that after answering the query of type 3 all the books remain on the shelf and the relative order of books does not change.
If you are Python programmer, consider using PyPy instead of Python when you submit your code.
Input
The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.
Then q lines follow. The i-th line contains the i-th query in format as in the problem statement. It is guaranteed that queries are always valid (for query type 3, it is guaranteed that the book in each such query is already placed, and for other types, it is guaranteed that the book was not placed before).
It is guaranteed that there is at least one query of type 3 in the input.
In each query the constraint 1 ≤ id ≤ 2 ⋅ 10^5 is met.
Output
Print answers to queries of the type 3 in order they appear in the input.
Examples
Input
8
L 1
R 2
R 3
? 2
L 4
? 1
L 5
? 1
Output
1
1
2
Input
10
L 100
R 100000
R 123
L 101
? 123
L 10
R 115
? 100
R 110
? 115
Output
0
2
1
Note
Let's take a look at the first example and let's consider queries:
1. The shelf will look like [1];
2. The shelf will look like [1, 2];
3. The shelf will look like [1, 2, 3];
4. The shelf looks like [1, 2, 3] so the answer is 1;
5. The shelf will look like [4, 1, 2, 3];
6. The shelf looks like [4, 1, 2, 3] so the answer is 1;
7. The shelf will look like [5, 4, 1, 2, 3];
8. The shelf looks like [5, 4, 1, 2, 3] so the answer is 2.
Let's take a look at the second example and let's consider queries:
1. The shelf will look like [100];
2. The shelf will look like [100, 100000];
3. The shelf will look like [100, 100000, 123];
4. The shelf will look like [101, 100, 100000, 123];
5. The shelf looks like [101, 100, 100000, 123] so the answer is 0;
6. The shelf will look like [10, 101, 100, 100000, 123];
7. The shelf will look like [10, 101, 100, 100000, 123, 115];
8. The shelf looks like [10, 101, 100, 100000, 123, 115] so the answer is 2;
9. The shelf will look like [10, 101, 100, 100000, 123, 115, 110];
10. The shelf looks like [10, 101, 100, 100000, 123, 115, 110] so the answer is 1.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n1 2 1 2\\n2 6 3 4\\n2 4 1 3\\n1 2 1 3\\n1 4 5 8\\n\", \"1\\n233 233333 123 456\\n\", \"1\\n1 2 1 2\\n\", \"5\\n1 2 1 2\\n2 6 3 4\\n2 4 1 3\\n1 2 1 3\\n1 4 5 8\\n\", \"1\\n233 233333 79 456\\n\", \"1\\n1 2 0 2\\n\", \"5\\n1 2 1 2\\n2 6 3 4\\n2 4 1 3\\n1 2 1 3\\n2 4 5 8\\n\", \"5\\n1 2 1 2\\n2 6 3 4\\n2 4 1 3\\n1 2 1 3\\n1 4 5 14\\n\", \"1\\n107 233333 79 456\\n\", \"1\\n2 2 0 2\\n\", \"5\\n1 2 1 2\\n2 6 3 4\\n2 4 1 3\\n1 2 1 3\\n2 4 1 8\\n\", \"5\\n1 2 1 2\\n1 6 3 4\\n2 4 1 3\\n1 2 1 3\\n1 4 5 14\\n\", \"1\\n198 233333 79 456\\n\", \"5\\n1 2 1 2\\n1 6 5 4\\n2 4 1 3\\n1 2 1 3\\n1 4 5 14\\n\", \"1\\n60 84301 79 456\\n\", \"1\\n58 84301 79 456\\n\", \"1\\n106 84301 79 456\\n\", \"1\\n106 84301 133 456\\n\", \"1\\n66 84301 133 456\\n\", \"1\\n66 84301 188 456\\n\", \"1\\n108 84301 188 456\\n\", \"1\\n164 84301 188 456\\n\", \"1\\n89 63666 188 502\\n\", \"1\\n4 63666 188 484\\n\", \"1\\n6 63666 188 484\\n\", \"1\\n2 5704 188 484\\n\", \"1\\n0 5704 188 484\\n\", \"1\\n-1 5704 188 484\\n\", \"1\\n-2 6352 188 5\\n\", \"1\\n-2 6352 140 5\\n\", \"1\\n0 11758 140 5\\n\", \"1\\n1 22969 140 3\\n\", \"1\\n1 22969 224 3\\n\", \"1\\n1 22969 212 3\\n\", \"1\\n1 22969 32 3\\n\", \"1\\n2 22969 32 3\\n\", \"1\\n3 22969 32 3\\n\", \"1\\n1 545 25 5\\n\", \"1\\n2 545 25 5\\n\", \"1\\n0 545 25 5\\n\", \"1\\n-1 266 25 1\\n\", \"1\\n0 97 49 0\\n\", \"1\\n0 97 29 -1\\n\", \"1\\n0 136 15 -2\\n\", \"1\\n0 93 30 -1\\n\", \"1\\n0 79 38 -1\\n\", \"1\\n0 79 71 -2\\n\", \"1\\n0 79 45 -2\\n\", \"1\\n-1 79 45 -2\\n\", \"1\\n2 2 0 0\\n\", \"1\\n198 84301 79 456\\n\", \"1\\n2 3 0 0\\n\", \"1\\n164 63666 188 456\\n\", \"1\\n164 63666 188 502\\n\", \"1\\n89 63666 188 562\\n\", \"1\\n89 63666 188 484\\n\", \"1\\n6 49127 188 484\\n\", \"1\\n6 57364 188 484\\n\", \"1\\n6 5704 188 484\\n\", \"1\\n-1 5704 188 116\\n\", \"1\\n-1 3983 188 116\\n\", \"1\\n-1 3983 188 5\\n\", \"1\\n-1 6352 188 5\\n\", \"1\\n-2 11758 140 5\\n\", \"1\\n0 11758 140 3\\n\", \"1\\n0 22969 140 3\\n\", \"1\\n1 22969 32 5\\n\", \"1\\n1 545 32 5\\n\", \"1\\n0 243 25 5\\n\", \"1\\n0 472 25 5\\n\", \"1\\n0 266 25 5\\n\", \"1\\n0 266 25 3\\n\", \"1\\n0 266 25 1\\n\", \"1\\n-1 511 25 1\\n\", \"1\\n-1 137 25 1\\n\", \"1\\n-1 137 25 0\\n\", \"1\\n-1 97 25 0\\n\", \"1\\n0 97 25 0\\n\", \"1\\n0 97 49 -1\\n\", \"1\\n0 136 29 -1\\n\", \"1\\n0 136 29 -2\\n\", \"1\\n0 127 15 -2\\n\", \"1\\n0 240 15 -2\\n\", \"1\\n0 116 15 -2\\n\", \"1\\n0 93 15 -2\\n\", \"1\\n0 93 15 -1\\n\", \"1\\n0 79 30 -1\\n\", \"1\\n0 79 38 -2\\n\", \"1\\n0 8 45 -2\\n\", \"1\\n0 8 45 -4\\n\", \"1\\n0 5 45 -4\\n\", \"1\\n0 6 45 -4\\n\"], \"outputs\": [\"1 2\\n2 3\\n2 1\\n1 3\\n1 5\\n\", \"233 123\\n\", \"1 2\\n\", \"1 2\\n2 3\\n2 1\\n1 3\\n1 5\\n\", \"233 79\\n\", \"1 0\\n\", \"1 2\\n2 3\\n2 1\\n1 3\\n2 5\\n\", \"1 2\\n2 3\\n2 1\\n1 3\\n1 5\\n\", \"107 79\\n\", \"2 0\\n\", \"1 2\\n2 3\\n2 1\\n1 3\\n2 1\\n\", \"1 2\\n1 3\\n2 1\\n1 3\\n1 5\\n\", \"198 79\\n\", \"1 2\\n1 5\\n2 1\\n1 3\\n1 5\\n\", \"60 79\\n\", \"58 79\\n\", \"106 79\\n\", \"106 133\\n\", \"66 133\\n\", \"66 188\\n\", \"108 188\\n\", \"164 188\\n\", \"89 188\\n\", \"4 188\\n\", \"6 188\\n\", \"2 188\\n\", \"0 188\\n\", \"-1 188\\n\", \"-2 188\\n\", \"-2 140\\n\", \"0 140\\n\", \"1 140\\n\", \"1 224\\n\", \"1 212\\n\", \"1 32\\n\", \"2 32\\n\", \"3 32\\n\", \"1 25\\n\", \"2 25\\n\", \"0 25\\n\", \"-1 25\\n\", \"0 49\\n\", \"0 29\\n\", \"0 15\\n\", \"0 30\\n\", \"0 38\\n\", \"0 71\\n\", \"0 45\\n\", \"-1 45\\n\", \"2 0\\n\", \"198 79\\n\", \"2 0\\n\", \"164 188\\n\", \"164 188\\n\", \"89 188\\n\", \"89 188\\n\", \"6 188\\n\", \"6 188\\n\", \"6 188\\n\", \"-1 188\\n\", \"-1 188\\n\", \"-1 188\\n\", \"-1 188\\n\", \"-2 140\\n\", \"0 140\\n\", \"0 140\\n\", \"1 32\\n\", \"1 32\\n\", \"0 25\\n\", \"0 25\\n\", \"0 25\\n\", \"0 25\\n\", \"0 25\\n\", \"-1 25\\n\", \"-1 25\\n\", \"-1 25\\n\", \"-1 25\\n\", \"0 25\\n\", \"0 49\\n\", \"0 29\\n\", \"0 29\\n\", \"0 15\\n\", \"0 15\\n\", \"0 15\\n\", \"0 15\\n\", \"0 15\\n\", \"0 30\\n\", \"0 38\\n\", \"0 45\\n\", \"0 45\\n\", \"0 45\\n\", \"0 45\\n\"]}", "source": "primeintellect"}
|
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 ≤ a ≤ r_1, l_2 ≤ b ≤ r_2 and a ≠ b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 ≤ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} ≤ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) — the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i — such numbers that l_{1_i} ≤ a_i ≤ r_{1_i}, l_{2_i} ≤ b_i ≤ r_{2_i} and a_i ≠ b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"vvvovvv\\n\", \"vvovooovovvovoovoovvvvovovvvov\\n\", \"ovvo\\n\", \"vovoovovvoovvvvvvovo\\n\", \"vvovvovvovvovv\\n\", \"vvoovv\\n\", \"vovvv\\n\", \"vvovv\\n\", \"ovvvvovovvvvovoovovovovvvvvvvoovoovvovvoooooovo\\n\", \"voovovvvoo\\n\", \"o\\n\", \"vo\\n\", \"v\\n\", \"ovvn\\n\", \"ovovvvvvvoovvovoovov\\n\", \"vovvovvooo\\n\", \"vovvvovovvvvoovoovovvovooovovv\\n\", \"ooovvvvvvoovvvvoovov\\n\", \"vovvvvvovovvoovoovovvovooovovv\\n\", \"ooovvvvovoovvvvovvov\\n\", \"ooovvvovvoovvvvovvov\\n\", \"vowvv\\n\", \"n\\n\", \"u\\n\", \"onvv\\n\", \"voovvvvooo\\n\", \"p\\n\", \"t\\n\", \"q\\n\", \"s\\n\", \"r\\n\", \"w\\n\", \"x\\n\", \"y\\n\", \"m\\n\", \"z\\n\", \"l\\n\", \"{\\n\", \"k\\n\", \"|\\n\", \"j\\n\", \"}\\n\", \"i\\n\", \"~\\n\", \"h\\n\", \"\\n\", \"g\\n\", \"f\\n\", \"e\\n\", \"oovvvovoov\\n\", \"d\\n\", \"ov\\n\", \"owvn\\n\", \"ovovvvvvvoovvvvoovoo\\n\", \"vovvoovovo\\n\", \"c\\n\", \"b\\n\", \"a\\n\", \"`\\n\", \"_\\n\", \"^\\n\", \"]\\n\", \"\\\\\\n\", \"[\\n\", \"Z\\n\", \"Y\\n\", \"ow\\n\", \"oxvn\\n\", \"oovoovvvvoovvvvvvovo\\n\", \"X\\n\", \"W\\n\", \"V\\n\", \"U\\n\", \"T\\n\", \"S\\n\", \"R\\n\", \"ox\\n\", \"oxvm\\n\", \"Q\\n\", \"P\\n\", \"O\\n\", \"vovvovvvvoovvovvvooo\\n\", \"N\\n\", \"M\\n\", \"L\\n\", \"K\\n\", \"J\\n\", \"I\\n\", \"H\\n\", \"G\\n\", \"F\\n\", \"E\\n\", \"D\\n\", \"C\\n\", \"B\\n\", \"A\\n\", \"@\\n\", \"?\\n\", \">\\n\", \"=\\n\", \"<\\n\", \";\\n\", \":\\n\", \"9\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"4\\n\", \"vvvov\\n\"], \"outputs\": [\"4\\n\", \"100\\n\", \"0\\n\", \"10\\n\", \"20\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"463\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"10\\n\", \"1\\n\", \"100\\n\", \"30\\n\", \"104\\n\", \"42\\n\", \"40\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"30\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"30\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"40\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Recall that string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly zero or all) characters. For example, for the string a="wowwo", the following strings are subsequences: "wowwo", "wowo", "oo", "wow", "", and others, but the following are not subsequences: "owoo", "owwwo", "ooo".
The wow factor of a string is the number of its subsequences equal to the word "wow". Bob wants to write a string that has a large wow factor. However, the "w" key on his keyboard is broken, so he types two "v"s instead.
Little did he realise that he may have introduced more "w"s than he thought. Consider for instance the string "ww". Bob would type it as "vvvv", but this string actually contains three occurrences of "w":
* "vvvv"
* "vvvv"
* "vvvv"
For example, the wow factor of the word "vvvovvv" equals to four because there are four wows:
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
Note that the subsequence "vvvovvv" does not count towards the wow factor, as the "v"s have to be consecutive.
For a given string s, compute and output its wow factor. Note that it is not guaranteed that it is possible to get s from another string replacing "w" with "vv". For example, s can be equal to "vov".
Input
The input contains a single non-empty string s, consisting only of characters "v" and "o". The length of s is at most 10^6.
Output
Output a single integer, the wow factor of s.
Examples
Input
vvvovvv
Output
4
Input
vvovooovovvovoovoovvvvovovvvov
Output
100
Note
The first example is explained in the legend.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"5 3\\n1 2 3 4 5\\n\", \"5 3\\n1 2 3 3 3\\n\", \"5 3\\n1 2 2 4 5\\n\", \"50 1\\n156420 126738 188531 85575 23728 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 31741 152481 57935 26624 106893 55028 81626 99143 182257 129556 100261 11429 156642 27997 105720 173400 140250 164944 26466 132034 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"5 3\\n2 2 2 2 2\\n\", \"50 50\\n86175 169571 61423 53837 33228 49923 87369 11875 167105 101762 128203 19011 191596 19500 11213 950 192557 164451 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 196697 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 4\\n29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30\\n\", \"50 2\\n72548 51391 1788 171949 148789 151619 19225 8774 52484 74830 20086 51129 151145 87650 108005 112019 126739 124087 158096 59027 34500 87415 115058 194160 171792 136832 1114 112592 171746 199013 101484 182930 185656 154861 191455 165701 140450 3475 160191 122350 66759 93252 60972 124615 119327 108068 149786 8698 63546 187913\\n\", \"10 6\\n7 7 7 7 7 7 7 7 7 7\\n\", \"50 50\\n199987 199984 199987 199977 199996 199923 199984 199995 199991 200000 199998 199990 199983 199981 199973 199989 199981 199993 199959 199994 199973 199962 199998 199970 199999 199981 199996 199996 199985 199980 199959 199990 199982 199987 199992 199997 199985 199976 199947 199998 199962 199987 199984 199982 199999 199997 199985 199992 199979 199974\\n\", \"5 2\\n3 3 3 3 3\\n\", \"4 2\\n3 3 3 3\\n\", \"5 3\\n4 4 4 4 4\\n\", \"4 2\\n9 9 9 9\\n\", \"50 25\\n162847 80339 131433 130128 135933 64805 74277 145697 92574 169638 26992 155045 32254 97675 177503 143802 44012 171388 185307 33652 194764 80214 169507 71832 180118 117737 198279 89826 9941 120250 158894 31871 616 190147 159249 158867 131076 77551 95165 54709 51376 145758 74581 26670 48775 29351 4750 55294 129850 19793\\n\", \"50 7\\n1 2 27 54 6 15 24 1 9 28 3 26 8 12 7 6 8 54 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 39 9 8 10 2 5 6 4 7 67 21 12 6 55\\n\", \"50 50\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 10 21 44 5 13 6 30 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 3 14 15 8 7 11 5 28 9 1\\n\", \"50 7\\n199961 199990 199995 199997 199963 199995 199985 199994 199974 199974 199997 199991 199993 199982 199991 199982 199963 200000 199994 199997 199963 199991 199947 199996 199994 199995 199995 199990 199972 199973 199980 199955 199984 199998 199998 199992 199986 199986 199997 199995 199987 199958 199982 199998 199996 199995 199979 199943 199992 199993\\n\", \"5 2\\n9 9 9 9 9\\n\", \"50 25\\n199970 199997 199998 199988 199999 199981 200000 199990 199974 199985 199932 200000 199966 199999 199999 199951 199983 199975 199974 199996 199974 199992 199979 199995 199955 199989 199960 199975 199983 199990 199950 199952 199999 199999 199962 199939 199979 199977 199962 199996 199910 199997 199976 200000 199999 199997 199998 199973 199996 199917\\n\", \"50 2\\n3 6 10 1 14 5 26 11 6 1 23 43 7 23 20 11 15 11 2 1 8 37 2 19 31 18 2 4 15 84 9 29 38 46 9 21 2 2 13 114 28 9 6 20 14 46 4 20 39 99\\n\", \"50 7\\n155076 162909 18349 8937 38161 128479 127526 128714 164477 163037 130796 160247 17004 73321 175301 175796 79144 75670 46299 197255 10139 2112 195709 124860 6485 137601 63708 117985 94924 65661 113294 85898 7511 137431 115791 66126 146803 121145 96379 126408 195646 70033 131093 86487 94591 3086 59652 188702 27036 78631\\n\", \"7 4\\n3 3 3 3 3 3 3\\n\", \"50 2\\n199995 199977 199982 199979 199998 199991 199999 199976 199974 199971 199966 199999 199978 199987 199989 199995 199968 199987 199988 199987 199987 199998 199988 199958 199985 199999 199997 199939 199992 199999 199985 199994 199987 199965 199947 199991 199993 199997 199998 199994 199971 199999 199999 199990 199993 199983 199983 199999 199970 199952\\n\", \"4 2\\n2 2 2 2\\n\", \"7 3\\n1 1 1 1 1 1 1\\n\", \"1 1\\n1337\\n\", \"50 25\\n19 1 17 6 4 21 9 16 5 21 2 12 17 11 54 18 36 20 34 17 32 1 4 14 26 11 6 2 7 5 2 3 12 16 20 5 16 1 18 55 16 20 2 3 2 12 65 20 7 11\\n\", \"5 2\\n4 4 4 4 4\\n\", \"50 1\\n156420 126738 188531 85575 23728 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 31741 152481 104541 26624 106893 55028 81626 99143 182257 129556 100261 11429 156642 27997 105720 173400 140250 164944 26466 132034 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 50\\n86175 169571 61423 53837 33228 49923 87369 11875 167105 101762 128203 19011 191596 19500 11213 1113 192557 164451 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 196697 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 2\\n72548 51391 2659 171949 148789 151619 19225 8774 52484 74830 20086 51129 151145 87650 108005 112019 126739 124087 158096 59027 34500 87415 115058 194160 171792 136832 1114 112592 171746 199013 101484 182930 185656 154861 191455 165701 140450 3475 160191 122350 66759 93252 60972 124615 119327 108068 149786 8698 63546 187913\\n\", \"50 50\\n199987 199984 199987 24237 199996 199923 199984 199995 199991 200000 199998 199990 199983 199981 199973 199989 199981 199993 199959 199994 199973 199962 199998 199970 199999 199981 199996 199996 199985 199980 199959 199990 199982 199987 199992 199997 199985 199976 199947 199998 199962 199987 199984 199982 199999 199997 199985 199992 199979 199974\\n\", \"50 25\\n162847 80339 131433 130128 135933 64805 74277 145697 92574 169638 26992 155045 32254 97675 177503 143802 44012 171388 185307 33652 194764 80214 169507 71832 180118 117737 198279 89826 9941 120250 158894 31871 616 190147 159249 158867 131076 77551 95165 54709 51376 53064 74581 26670 48775 29351 4750 55294 129850 19793\\n\", \"50 7\\n1 2 27 54 6 15 24 1 9 28 3 26 8 12 7 6 8 54 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 66 9 8 10 2 5 6 4 7 67 21 12 6 55\\n\", \"50 50\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 10 21 44 5 13 6 25 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 3 14 15 8 7 11 5 28 9 1\\n\", \"50 7\\n155076 162909 18349 8937 38161 128479 127526 128714 164477 163037 130796 160247 17004 73321 175301 175796 79144 75670 46299 197255 10139 2112 195709 124860 6485 137601 63708 117985 94924 65661 113294 117270 7511 137431 115791 66126 146803 121145 96379 126408 195646 70033 131093 86487 94591 3086 59652 188702 27036 78631\\n\", \"5 3\\n1 2 3 1 5\\n\", \"50 41\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 10 21 44 5 13 6 25 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 3 14 15 8 7 11 5 28 9 1\\n\", \"5 3\\n1 2 3 6 5\\n\", \"50 50\\n92843 169571 106591 53837 33228 49923 87369 11875 167105 101762 128203 19011 191596 19500 11213 1113 192557 164451 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 196697 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 41\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 18 21 44 5 13 6 25 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 3 14 15 8 7 11 5 28 9 1\\n\", \"50 41\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 18 21 44 5 13 6 25 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 5 14 15 8 7 11 5 28 9 1\\n\", \"50 50\\n92843 169571 106591 53837 33228 49923 87369 11875 167105 101762 128203 8588 191596 19500 11213 1113 192557 115862 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 196697 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 36\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 18 21 44 5 13 6 25 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 5 14 15 8 7 11 5 28 9 1\\n\", \"50 7\\n113598 162909 18349 8937 38161 128479 127526 128714 164477 163037 130796 160247 17004 73321 175301 175796 79144 75670 46299 197255 10139 2112 65899 124860 6485 137601 63708 117985 94924 65661 113294 117270 7511 137431 115791 8658 146803 121145 96379 126408 195646 70033 131093 86487 94591 5740 59652 188702 27036 78631\\n\", \"50 50\\n92843 169571 106591 53837 33228 49923 87369 11875 167105 101762 128203 8588 68649 19500 11213 1113 192557 115862 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 131292 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 36\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 18 21 44 5 13 6 30 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 5 14 15 8 7 16 5 28 9 1\\n\", \"50 36\\n8 63 44 78 3 65 7 27 23 45 7 5 18 94 25 17 26 18 21 44 5 13 6 30 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 5 14 15 8 7 16 5 28 9 1\\n\", \"5 3\\n2 2 3 2 2\\n\", \"50 4\\n29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"10 6\\n7 7 7 7 7 7 7 7 7 12\\n\", \"5 2\\n3 3 3 3 5\\n\", \"5 3\\n4 5 4 4 4\\n\", \"4 2\\n9 9 9 2\\n\", \"5 2\\n9 9 9 9 16\\n\", \"50 2\\n3 6 10 1 14 5 26 11 6 1 23 43 7 23 20 11 15 11 2 1 8 37 2 19 31 18 2 4 15 84 9 29 38 46 5 21 2 2 13 114 28 9 6 20 14 46 4 20 39 99\\n\", \"7 4\\n3 3 3 3 3 3 6\\n\", \"4 2\\n2 3 2 2\\n\", \"7 3\\n1 1 1 1 1 2 1\\n\", \"5 2\\n4 4 4 4 5\\n\", \"5 3\\n1 2 3 6 3\\n\", \"50 1\\n156420 126738 188531 85575 23728 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 31741 152481 104541 26624 106893 55028 81626 99143 182257 129556 100261 11429 156642 27997 105720 173400 140250 164944 26466 122149 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 50\\n92843 169571 61423 53837 33228 49923 87369 11875 167105 101762 128203 19011 191596 19500 11213 1113 192557 164451 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 196697 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 4\\n29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 160 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"10 6\\n7 7 12 7 7 7 7 7 7 12\\n\", \"5 3\\n3 3 3 3 5\\n\", \"50 7\\n1 2 27 54 6 15 24 1 9 28 2 26 8 12 7 6 8 54 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 66 9 8 10 2 5 6 4 7 67 21 12 6 55\\n\", \"50 2\\n3 6 10 1 14 5 26 11 6 1 23 43 7 23 20 11 15 11 2 1 8 37 2 11 31 18 2 4 15 84 9 29 38 46 5 21 2 2 13 114 28 9 6 20 14 46 4 20 39 99\\n\", \"50 7\\n155076 162909 18349 8937 38161 128479 127526 128714 164477 163037 130796 160247 17004 73321 175301 175796 79144 75670 46299 197255 10139 2112 195709 124860 6485 137601 63708 117985 94924 65661 113294 117270 7511 137431 115791 66126 146803 121145 96379 126408 195646 70033 131093 86487 94591 5740 59652 188702 27036 78631\\n\", \"7 4\\n3 5 3 3 3 3 6\\n\", \"5 2\\n2 4 4 4 5\\n\", \"50 1\\n156420 126738 188531 85575 23728 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 21653 152481 104541 26624 106893 55028 81626 99143 182257 129556 100261 11429 156642 27997 105720 173400 140250 164944 26466 122149 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 4\\n29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 160 40 37 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"5 3\\n3 6 3 3 5\\n\", \"50 7\\n1 2 27 54 6 15 24 1 9 28 2 26 8 12 7 6 13 54 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 66 9 8 10 2 5 6 4 7 67 21 12 6 55\\n\", \"50 2\\n3 6 10 1 14 5 26 11 6 1 23 43 7 23 20 11 15 11 2 1 8 37 2 11 31 18 2 4 15 84 9 29 38 46 4 21 2 2 13 114 28 9 6 20 14 46 4 20 39 99\\n\", \"50 7\\n113598 162909 18349 8937 38161 128479 127526 128714 164477 163037 130796 160247 17004 73321 175301 175796 79144 75670 46299 197255 10139 2112 195709 124860 6485 137601 63708 117985 94924 65661 113294 117270 7511 137431 115791 66126 146803 121145 96379 126408 195646 70033 131093 86487 94591 5740 59652 188702 27036 78631\\n\", \"7 4\\n3 5 3 3 3 3 4\\n\", \"5 2\\n2 4 4 4 10\\n\", \"50 1\\n156420 126738 188531 85575 23728 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 21653 152481 104541 26624 106893 55028 81626 99143 182257 129556 100261 11429 156642 27997 151498 173400 140250 164944 26466 122149 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 50\\n92843 169571 106591 53837 33228 49923 87369 11875 167105 101762 128203 19011 191596 19500 11213 1113 192557 115862 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 196697 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 4\\n29 16 86 40 24 1 6 15 7 30 21 16 86 40 24 1 6 15 7 30 29 16 160 40 37 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"5 3\\n3 6 3 5 5\\n\", \"50 7\\n1 2 27 54 6 15 24 1 9 28 2 26 8 12 7 6 13 44 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 66 9 8 10 2 5 6 4 7 67 21 12 6 55\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 11 15 11 2 1 8 37 2 11 31 18 2 4 15 84 9 29 38 46 4 21 2 2 13 114 28 9 6 20 14 46 4 20 39 99\\n\", \"50 7\\n113598 162909 18349 8937 38161 128479 127526 128714 164477 163037 130796 160247 17004 73321 175301 175796 79144 75670 46299 197255 10139 2112 65899 124860 6485 137601 63708 117985 94924 65661 113294 117270 7511 137431 115791 66126 146803 121145 96379 126408 195646 70033 131093 86487 94591 5740 59652 188702 27036 78631\\n\", \"7 4\\n3 5 3 3 3 3 3\\n\", \"5 2\\n2 4 4 4 12\\n\", \"50 1\\n156420 126738 188531 85575 12671 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 21653 152481 104541 26624 106893 55028 81626 99143 182257 129556 100261 11429 156642 27997 151498 173400 140250 164944 26466 122149 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 4\\n29 16 86 40 24 1 6 5 7 30 21 16 86 40 24 1 6 15 7 30 29 16 160 40 37 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"50 7\\n1 2 27 54 6 15 24 1 9 28 2 26 8 12 7 6 13 44 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 66 9 8 10 2 1 6 4 7 67 21 12 6 55\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 11 15 11 2 1 8 37 2 11 31 18 2 4 15 84 9 29 38 46 4 21 2 2 13 114 28 11 6 20 14 46 4 20 39 99\\n\", \"7 4\\n3 5 3 3 2 3 3\\n\", \"50 1\\n156420 126738 188531 85575 12671 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 189417 52337 135886 162083 146559 131125 21653 152481 104541 26624 106893 55028 81626 94399 182257 129556 100261 11429 156642 27997 151498 173400 140250 164944 26466 122149 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 50\\n92843 169571 106591 53837 33228 49923 87369 11875 167105 101762 128203 8588 191596 19500 11213 1113 192557 115862 58008 34390 39704 128606 191084 14227 57911 129189 124795 42481 69510 59862 146348 57352 158069 68387 131292 46595 84330 168274 88721 191842 155836 39164 195031 53880 188281 11150 132256 87853 179233 135499\\n\", \"50 4\\n29 16 86 40 24 1 6 5 7 30 21 16 86 40 24 1 6 15 7 30 29 16 160 40 1 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"50 7\\n1 2 27 72 6 15 24 1 9 28 2 26 8 12 7 6 13 44 23 8 7 13 18 10 1 33 24 10 34 13 12 9 16 11 36 50 66 9 8 10 2 1 6 4 7 67 21 12 6 55\\n\", \"50 36\\n8 63 44 78 3 65 7 27 13 45 7 5 18 94 25 17 26 18 21 44 5 13 6 30 10 11 44 14 71 17 10 5 4 9 8 21 4 9 25 18 5 14 15 8 7 11 5 28 9 1\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 8 15 11 2 1 8 37 2 11 31 18 2 4 15 84 9 29 38 46 4 21 2 2 13 114 28 11 6 20 14 46 4 20 39 99\\n\", \"7 4\\n3 5 3 3 2 2 3\\n\", \"50 1\\n156420 126738 188531 85575 12671 72842 190346 24786 118328 137944 126942 115577 175247 85409 146194 31398 13890 52337 135886 162083 146559 131125 21653 152481 104541 26624 106893 55028 81626 94399 182257 129556 100261 11429 156642 27997 151498 173400 140250 164944 26466 122149 86679 190160 161138 179688 2975 149862 38336 67959\\n\", \"50 4\\n29 16 86 40 24 1 6 5 7 30 21 16 39 40 24 1 6 15 7 30 29 16 160 40 1 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 8 15 11 2 1 8 37 2 11 31 18 2 4 15 84 9 29 38 46 4 21 2 2 13 101 28 11 6 20 14 46 4 20 39 99\\n\", \"7 4\\n3 4 3 3 2 2 3\\n\", \"50 4\\n29 16 86 40 24 1 6 5 7 30 21 16 39 40 24 1 6 15 7 30 29 16 160 77 1 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 8 15 11 2 1 8 37 2 11 31 18 2 4 24 84 9 29 38 46 4 21 2 2 13 101 28 11 6 20 14 46 4 20 39 99\\n\", \"7 4\\n3 4 3 3 2 1 3\\n\", \"50 4\\n29 16 86 40 24 1 6 5 7 30 21 16 39 40 24 1 6 15 7 23 29 16 160 77 1 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 8 22 11 2 1 8 37 2 11 31 18 2 4 24 84 9 29 38 46 4 21 2 2 13 101 28 11 6 20 14 46 4 20 39 99\\n\", \"7 4\\n3 4 5 3 2 1 3\\n\", \"50 4\\n29 16 86 40 24 1 6 5 7 30 21 16 39 40 24 1 6 15 7 23 29 16 30 77 1 1 6 15 7 30 29 16 86 40 24 1 6 15 7 30 29 16 86 40 24 1 9 15 7 30\\n\", \"50 2\\n3 7 10 1 14 5 26 11 6 1 23 43 7 23 20 8 22 11 2 1 8 37 2 11 31 18 2 4 24 84 9 29 38 46 4 21 2 2 13 101 48 11 6 20 14 46 4 20 39 99\\n\"], \"outputs\": [\"2\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"780\\n\", \"0\\n\", \"12\\n\", \"0\\n\", \"450\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"364\\n\", \"3\\n\", \"167\\n\", \"7\\n\", \"0\\n\", \"125\\n\", \"0\\n\", \"79\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"43\\n\", \"0\\n\", \"0\\n\", \"781\\n\", \"12\\n\", \"847\\n\", \"364\\n\", \"3\\n\", \"167\\n\", \"79\\n\", \"1\\n\", \"118\\n\", \"2\\n\", \"782\\n\", \"119\\n\", \"120\\n\", \"780\\n\", \"100\\n\", \"76\\n\", \"779\\n\", \"101\\n\", \"102\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"781\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"79\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"79\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"781\\n\", \"0\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"79\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"780\\n\", \"0\\n\", \"3\\n\", \"100\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
The only difference between easy and hard versions is the number of elements in the array.
You are given an array a consisting of n integers. In one move you can choose any a_i and divide it by 2 rounding down (in other words, in one move you can set a_i := ⌊(a_i)/(2)⌋).
You can perform such an operation any (possibly, zero) number of times with any a_i.
Your task is to calculate the minimum possible number of operations required to obtain at least k equal numbers in the array.
Don't forget that it is possible to have a_i = 0 after some operations, thus the answer always exists.
Input
The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 50) — the number of elements in the array and the number of equal numbers required.
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^5), where a_i is the i-th element of a.
Output
Print one integer — the minimum possible number of operations required to obtain at least k equal numbers in the array.
Examples
Input
5 3
1 2 2 4 5
Output
1
Input
5 3
1 2 3 4 5
Output
2
Input
5 3
1 2 3 3 3
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"5 2\\n3 1\\n\", \"3 3\\n2 2 2\\n\", \"4 10\\n4 1 4 2 2 1 4 3 3 1\\n\", \"7 1\\n3\\n\", \"9 10\\n9 8 7 4 5 8 1 6 8 2\\n\", \"8 1\\n8\\n\", \"8 10\\n7 7 7 7 7 7 7 7 7 2\\n\", \"10 10\\n1 9 7 6 2 4 7 8 1 3\\n\", \"1000 100\\n343 745 296 856 507 192 780 459 9 193 753 28 334 871 589 105 612 751 708 129 32 628 974 641 323 596 604 759 906 272 606 898 726 304 279 448 589 565 735 53 935 966 424 363 153 900 722 597 501 125 512 282 744 460 529 488 67 895 407 863 59 984 211 458 578 461 999 10 411 521 738 842 689 160 168 924 313 926 576 106 11 585 772 694 221 403 20 842 64 113 787 161 457 998 921 813 225 633 231 78\\n\", \"1 1\\n1\\n\", \"100000 6\\n13081 90189 97857 54927 7866 52421\\n\", \"6 10\\n5 3 4 3 2 3 1 6 1 1\\n\", \"100000 2\\n46680 84411\\n\", \"2 1\\n2\\n\", \"10 10\\n9 9 9 9 9 9 9 9 9 6\\n\", \"1 10\\n1 1 1 1 1 1 1 1 1 1\\n\", \"2 10\\n1 2 1 1 2 2 2 2 2 2\\n\", \"7 10\\n1 1 7 7 3 4 6 3 2 3\\n\", \"9 10\\n8 8 8 8 8 8 8 8 8 5\\n\", \"100000 10\\n13202 14678 45343 53910 34297 96330 24175 45117 25650 55090\\n\", \"100000 3\\n62808 76360 42404\\n\", \"10 1\\n1\\n\", \"7 10\\n2 2 2 2 2 2 2 2 2 1\\n\", \"3 10\\n3 2 2 2 3 1 3 3 3 1\\n\", \"8000 100\\n7990 4432 5901 5019 423 1200 7760 5752 7422 4337 4802 2570 7354 4912 2185 2344 6538 2783 1473 5311 3987 4739 7159 1677 3438 502 2800 1318 5223 4518 4448 6451 3455 5012 1588 814 4971 5847 3849 6248 6420 3607 2610 6852 1045 3730 757 6905 5248 3738 2382 7251 1305 7380 2476 7346 5721 5946 7599 5321 620 3802 5744 3744 2548 6230 5241 7059 6020 7842 7816 466 3109 2953 1361 7583 4884 6377 3257 3410 4482 7538 7452 1880 1043 6250 263 6192 5664 4972 6334 4333 1013 5476 2872 7095 2259 4949 5342 2185\\n\", \"100000 1\\n63256\\n\", \"4 10\\n1 1 1 1 1 1 1 1 1 3\\n\", \"4000 100\\n1184 314 3114 3998 471 67 2327 2585 2047 3272 157 894 2981 934 2160 1568 3846 2893 2554 2761 2966 607 1110 792 3098 341 214 926 525 250 1311 1120 2143 1198 1992 3160 2321 1060 1183 1908 3002 2340 1379 3605 2181 2858 2507 1938 849 2789 2781 1075 3152 1721 3096 3734 1992 3517 747 3276 3701 2078 795 3709 2949 3450 3105 2464 3770 2374 170 68 3980 3529 917 75 3940 1374 1944 3689 1186 2294 1276 1801 3161 2356 1180 2952 1710 3535 3274 3992 540 1427 1578 1535 882 2656 3349 3477\\n\", \"8 10\\n2 8 3 8 5 6 5 5 4 4\\n\", \"4 1\\n1\\n\", \"5 10\\n2 2 2 2 2 2 2 2 2 2\\n\", \"5000 100\\n3150 4568 3083 2877 4459 2222 2213 2729 4087 4362 1694 705 3898 553 1910 3586 3599 641 3331 271 349 3464 3319 717 2959 4461 3189 3152 4604 3541 3743 125 3039 2119 3067 3102 1535 2352 4401 3393 1161 1233 3463 1417 721 2772 3973 2051 1901 2074 3113 3267 1090 2311 1717 589 1796 28 260 3908 1979 5 3160 2494 1368 2241 2239 309 3853 93 3385 3944 1114 2881 4204 2728 3256 929 593 2827 1010 3829 2948 2773 103 4297 2999 4186 4018 2846 743 901 2034 1343 1022 181 4306 3925 2624 978\\n\", \"5 10\\n3 2 4 3 3 4 2 5 3 2\\n\", \"9000 100\\n468 4494 1974 6298 8307 5060 942 191 7166 3427 3339 8189 7463 4530 8935 770 4482 6531 6250 116 8666 5004 3176 8194 2491 1815 7670 8249 6493 5105 177 5456 6056 742 7663 3052 8378 7844 2963 3733 1874 3603 6693 8959 8289 6644 224 314 7196 2535 4203 6147 6539 3971 1097 201 6037 8354 1216 3360 4602 6026 5110 1233 6375 3829 1375 1904 806 5857 2624 4341 7835 3409 5648 428 7392 8931 6905 4741 2202 4881 20 6852 7393 1000 6082 130 1780 2283 7099 3242 8507 3584 5019 5037 3683 3026 1912 6687\\n\", \"3 1\\n2\\n\", \"10000 100\\n4544 8312 5862 939 8211 3380 6031 1809 403 6481 9611 1867 3995 2475 8463 6414 8437 1439 7839 417 116 9582 9111 4367 876 1230 5526 4297 4180 5768 9854 1538 8763 4843 5654 5489 9872 584 6600 9378 6633 1476 3123 6181 7533 1721 6122 4206 5642 868 6802 3699 6240 3033 9960 9921 6371 699 6633 6376 7453 6228 617 9754 9977 5875 8269 4880 73 3129 6048 1797 8514 5595 1122 889 2011 7363 8276 8031 3602 207 6829 9279 3398 3136 3032 1013 9246 6893 4900 2208 2288 9614 5923 9876 2283 2657 4523 5304\\n\", \"5 1\\n1\\n\", \"6 1\\n5\\n\", \"7000 100\\n809 6179 2933 5332 6435 4045 4578 3312 678 3247 6664 351 2732 6190 1923 4326 2489 3034 3991 2097 603 3882 1951 456 4577 382 3929 1092 1249 6227 6312 6342 2047 3283 3217 3873 4053 1450 2630 2955 69 3418 526 2336 1505 1112 4099 87 4900 452 1754 2059 3559 6789 4151 3195 5917 435 3982 3282 3534 5067 1379 1959 5424 439 4107 1511 5233 4123 1601 1590 975 4497 74 930 2568 526 5505 2784 5362 3 6484 2908 4396 5796 4444 4254 3251 2660 4569 5720 1622 4560 4724 1961 643 6679 1068 3684\\n\", \"6 10\\n4 4 4 4 4 4 4 4 4 1\\n\", \"3000 100\\n1002 1253 41 1014 483 911 2849 1042 1600 374 2723 867 1872 1212 2898 846 2606 144 968 1252 1287 750 2902 1571 2749 2324 1344 1508 1255 1855 2174 307 31 468 725 923 914 2255 68 2319 2548 2343 592 1794 641 240 2848 824 797 2503 1665 2178 1917 1834 771 2391 2188 2110 1834 2237 423 2047 2430 1732 825 851 971 107 984 2551 658 2489 1550 1777 2334 2422 1433 2332 1784 63 659 1759 2116 1637 514 606 1658 718 1297 2927 2509 1275 2150 2319 2727 401 1266 1683 2075 1784\\n\", \"100000 5\\n29657 41344 93111 68553 91316\\n\", \"100000 7\\n29209 71737 78411 51700 57119 31198 40258\\n\", \"100000 4\\n46233 25204 79854 39075\\n\", \"100000 9\\n96057 12530 96414 43360 31434 80239 8416 37879 56578\\n\", \"9 1\\n7\\n\", \"3 10\\n3 3 3 3 3 3 3 3 3 3\\n\", \"2000 100\\n1525 1999 265 1839 495 1756 666 602 560 1284 186 56 955 785 339 123 1365 1204 486 639 903 189 886 1054 1184 1908 474 282 176 1268 1742 198 430 1738 354 1389 995 666 1850 538 93 154 508 174 397 1622 85 1710 1849 1706 1332 1986 683 1051 1150 535 1872 1599 216 1198 441 719 576 1947 1997 60 133 262 198 1240 954 718 1119 616 1047 577 1629 777 1032 436 835 120 1740 1665 1164 152 839 1780 181 1616 256 366 1951 1211 1876 1459 1842 1606 1505 283\\n\", \"6000 100\\n4331 117 2860 2156 447 5082 3395 4169 2639 5453 2127 3732 2815 5275 4172 2308 3544 1286 1405 1588 1028 1025 743 5234 3524 2069 5059 3378 874 128 4880 234 3151 849 2142 2339 1646 1453 4516 4878 4615 5421 5738 1229 5965 3198 3632 5973 5144 5167 2934 4163 324 2902 338 148 4113 732 4173 3947 4257 1036 3526 5983 3004 840 5565 2858 5151 5108 5897 5819 2840 2041 5491 277 4764 3779 4345 2158 834 5172 2812 5041 2454 4047 4114 316 1431 5053 4804 5811 4424 1451 3873 1019 1218 5706 4794 4479\\n\", \"100000 8\\n79929 87878 83156 81178 82181 77270 36433 21187\\n\", \"100000 1\\n50000\\n\", \"7 1\\n2\\n\", \"100000 6\\n13081 90189 97857 54927 7352 52421\\n\", \"6 10\\n5 3 5 3 2 3 1 6 1 1\\n\", \"2 10\\n2 2 1 1 2 2 2 2 2 2\\n\", \"7 10\\n1 2 7 7 3 4 6 3 2 3\\n\", \"100000 10\\n13202 14678 45343 53910 34337 96330 24175 45117 25650 55090\\n\", \"100000 3\\n62808 76360 39392\\n\", \"16 1\\n1\\n\", \"8000 100\\n7990 4432 5901 5019 423 1200 7760 5752 7422 4337 4802 2570 7354 4912 2185 2344 6538 2783 1473 5311 3987 2490 7159 1677 3438 502 2800 1318 5223 4518 4448 6451 3455 5012 1588 814 4971 5847 3849 6248 6420 3607 2610 6852 1045 3730 757 6905 5248 3738 2382 7251 1305 7380 2476 7346 5721 5946 7599 5321 620 3802 5744 3744 2548 6230 5241 7059 6020 7842 7816 466 3109 2953 1361 7583 4884 6377 3257 3410 4482 7538 7452 1880 1043 6250 263 6192 5664 4972 6334 4333 1013 5476 2872 7095 2259 4949 5342 2185\\n\", \"4 10\\n1 1 1 1 1 1 1 2 1 3\\n\", \"4000 100\\n1184 314 3114 3998 471 67 2327 2585 2047 3272 157 894 2981 934 2160 1568 3846 2893 2554 2761 2966 607 1110 792 3098 341 214 926 525 250 1311 1120 2143 1198 1992 3160 2321 1060 1183 1908 2394 2340 1379 3605 2181 2858 2507 1938 849 2789 2781 1075 3152 1721 3096 3734 1992 3517 747 3276 3701 2078 795 3709 2949 3450 3105 2464 3770 2374 170 68 3980 3529 917 75 3940 1374 1944 3689 1186 2294 1276 1801 3161 2356 1180 2952 1710 3535 3274 3992 540 1427 1578 1535 882 2656 3349 3477\\n\", \"8 10\\n2 8 3 8 5 6 5 1 4 4\\n\", \"5 10\\n2 2 2 3 2 2 2 2 2 2\\n\", \"5000 100\\n3150 4568 3083 2877 4459 2222 2213 2729 4087 4362 1694 705 3898 553 1910 3586 3599 641 3331 271 349 3464 3319 717 2959 4461 3189 3152 4604 3541 3743 125 3039 2119 3067 3102 1535 2352 4401 3393 1161 1233 3463 1417 721 2772 3973 2051 1901 2074 3113 3267 1090 2311 1717 589 1796 28 260 3908 1979 5 3160 2494 1368 2241 2239 309 3853 93 3385 3944 1114 2881 4204 2728 3256 929 593 2827 0010 3829 2948 2773 103 4297 2999 4186 4018 2846 743 901 2034 1343 1022 181 4306 3925 2624 978\\n\", \"9000 100\\n468 4494 1974 6298 8307 5060 942 191 7166 3427 3339 8189 7463 4530 8935 770 4482 6531 6250 116 8666 5004 3176 8194 2491 1815 7670 8249 6493 5105 177 5456 6056 742 7663 3052 8378 7844 2963 3733 1874 3603 6693 8959 8289 6644 224 314 7196 2535 4203 6147 6539 3971 1097 201 6037 8354 1216 3360 4602 6026 5110 1233 6375 3829 1375 1904 806 5857 2624 4341 7835 3409 5648 428 7260 8931 6905 4741 2202 4881 20 6852 7393 1000 6082 130 1780 2283 7099 3242 8507 3584 5019 5037 3683 3026 1912 6687\\n\", \"7000 100\\n809 6179 2933 5332 6435 4045 4578 3312 678 3247 6664 351 2732 6190 1923 4326 2489 3034 3991 2097 603 3882 1951 456 4577 382 3929 1092 1249 6227 6312 6342 2047 3283 3217 3873 4053 1450 2630 2955 69 3418 526 2336 1505 1112 4099 87 4900 452 1754 2059 3559 6789 4151 3195 5917 435 3982 3282 3534 5067 1379 1959 5424 439 4107 1511 5233 4123 2387 1590 975 4497 74 930 2568 526 5505 2784 5362 3 6484 2908 4396 5796 4444 4254 3251 2660 4569 5720 1622 4560 4724 1961 643 6679 1068 3684\\n\", \"3000 100\\n1002 1253 41 1014 483 911 2849 1042 1600 374 2723 867 1872 1212 2898 846 2606 144 968 1252 1287 750 2902 1571 2749 1804 1344 1508 1255 1855 2174 307 31 468 725 923 914 2255 68 2319 2548 2343 592 1794 641 240 2848 824 797 2503 1665 2178 1917 1834 771 2391 2188 2110 1834 2237 423 2047 2430 1732 825 851 971 107 984 2551 658 2489 1550 1777 2334 2422 1433 2332 1784 63 659 1759 2116 1637 514 606 1658 718 1297 2927 2509 1275 2150 2319 2727 401 1266 1683 2075 1784\\n\", \"100000 5\\n29657 4679 93111 68553 91316\\n\", \"100000 7\\n29209 71737 78411 51700 57119 24190 40258\\n\", \"100000 9\\n96057 12530 96414 43360 31434 15720 8416 37879 56578\\n\", \"3 10\\n3 3 3 3 3 3 1 3 3 3\\n\", \"2000 100\\n1525 1999 265 1839 495 1756 666 602 560 1284 186 56 955 785 339 123 1365 1204 486 639 903 189 886 1054 1184 1908 474 282 176 1268 1742 198 430 1738 354 1389 995 666 1850 538 93 154 508 174 397 1622 85 1710 1849 1706 1332 1986 683 1051 1150 535 1872 1599 216 1198 441 719 576 1947 1997 60 133 294 198 1240 954 718 1119 616 1047 577 1629 777 1032 436 835 120 1740 1665 1164 152 839 1780 181 1616 256 366 1951 1211 1876 1459 1842 1606 1505 283\\n\", \"100000 8\\n15206 87878 83156 81178 82181 77270 36433 21187\\n\", \"100000 1\\n13011\\n\", \"3000 100\\n1002 1253 41 1014 483 911 2849 1042 1600 374 2723 867 1872 1212 2898 846 2606 144 968 1252 1287 750 2902 1571 2749 1804 1344 1508 1255 1855 2174 307 31 468 725 923 914 2255 68 2319 2548 2343 592 1794 641 240 2848 824 797 2503 1665 2178 1917 1834 771 2391 2188 2110 1834 2237 423 2047 2430 1732 825 851 971 107 984 2551 658 2489 1550 1777 2334 2422 1433 2332 1784 63 659 1759 2116 1637 514 606 1658 718 1297 2927 2509 1275 2150 2319 2727 49 1266 1683 2075 1784\\n\", \"8765 100\\n3150 4568 3083 2877 4459 2222 2213 2729 4087 4362 1694 705 3898 553 1910 3586 3599 641 3331 271 349 3464 3319 717 2959 4461 3189 3152 4604 3541 3743 125 3039 2119 3067 3102 1535 2352 4401 3393 1161 1233 3463 1417 721 2772 3973 2051 1901 2074 3113 3267 1090 2311 1717 589 1796 28 260 843 1979 5 3160 2494 1368 2241 2239 309 3853 93 3385 3944 1114 2881 4204 2728 3256 929 593 2827 0010 3829 2948 2773 103 4297 2999 4186 4018 2846 743 901 2034 1343 486 181 4306 3925 2624 978\\n\", \"2 1\\n1\\n\", \"100000 6\\n13081 90189 97857 54927 8404 52421\\n\", \"2 10\\n2 2 1 1 1 2 2 2 2 2\\n\", \"7 10\\n1 2 7 7 3 7 6 3 2 3\\n\", \"100000 10\\n13202 14678 45343 53910 60969 96330 24175 45117 25650 55090\\n\", \"8000 100\\n7990 4432 5901 5019 423 1200 7760 5752 7422 4337 4802 2570 7354 4912 2185 2344 6538 2783 1473 5311 3987 2490 7159 1677 3438 502 3550 1318 5223 4518 4448 6451 3455 5012 1588 814 4971 5847 3849 6248 6420 3607 2610 6852 1045 3730 757 6905 5248 3738 2382 7251 1305 7380 2476 7346 5721 5946 7599 5321 620 3802 5744 3744 2548 6230 5241 7059 6020 7842 7816 466 3109 2953 1361 7583 4884 6377 3257 3410 4482 7538 7452 1880 1043 6250 263 6192 5664 4972 6334 4333 1013 5476 2872 7095 2259 4949 5342 2185\\n\", \"4 10\\n1 1 1 1 1 1 2 2 1 3\\n\", \"4000 100\\n1184 314 3114 3998 471 67 2327 2585 2047 3272 157 894 2981 934 2160 1568 3846 2893 2554 2761 2966 607 1110 792 3098 341 214 926 525 250 1311 1120 2143 1198 1992 3160 2321 1060 1183 1908 2394 2340 1379 3605 2181 2858 2507 1938 849 2789 2781 1075 3152 1721 3096 3734 1992 3517 747 3276 73 2078 795 3709 2949 3450 3105 2464 3770 2374 170 68 3980 3529 917 75 3940 1374 1944 3689 1186 2294 1276 1801 3161 2356 1180 2952 1710 3535 3274 3992 540 1427 1578 1535 882 2656 3349 3477\\n\", \"8 10\\n2 8 3 8 5 6 7 1 4 4\\n\", \"5000 100\\n3150 4568 3083 2877 4459 2222 2213 2729 4087 4362 1694 705 3898 553 1910 3586 3599 641 3331 271 349 3464 3319 717 2959 4461 3189 3152 4604 3541 3743 125 3039 2119 3067 3102 1535 2352 4401 3393 1161 1233 3463 1417 721 2772 3973 2051 1901 2074 3113 3267 1090 2311 1717 589 1796 28 260 843 1979 5 3160 2494 1368 2241 2239 309 3853 93 3385 3944 1114 2881 4204 2728 3256 929 593 2827 0010 3829 2948 2773 103 4297 2999 4186 4018 2846 743 901 2034 1343 1022 181 4306 3925 2624 978\\n\", \"100000 5\\n29657 1804 93111 68553 91316\\n\", \"100000 9\\n96057 12530 63958 43360 31434 15720 8416 37879 56578\\n\", \"3 10\\n3 3 2 3 3 3 1 3 3 3\\n\", \"2000 100\\n1525 1999 265 1839 495 1756 666 602 560 1284 186 56 955 785 339 123 1365 1204 600 639 903 189 886 1054 1184 1908 474 282 176 1268 1742 198 430 1738 354 1389 995 666 1850 538 93 154 508 174 397 1622 85 1710 1849 1706 1332 1986 683 1051 1150 535 1872 1599 216 1198 441 719 576 1947 1997 60 133 294 198 1240 954 718 1119 616 1047 577 1629 777 1032 436 835 120 1740 1665 1164 152 839 1780 181 1616 256 366 1951 1211 1876 1459 1842 1606 1505 283\\n\", \"100000 10\\n13202 14678 45343 53910 1988 96330 24175 45117 25650 55090\\n\", \"8000 100\\n7990 4432 5901 5019 423 1582 7760 5752 7422 4337 4802 2570 7354 4912 2185 2344 6538 2783 1473 5311 3987 2490 7159 1677 3438 502 3550 1318 5223 4518 4448 6451 3455 5012 1588 814 4971 5847 3849 6248 6420 3607 2610 6852 1045 3730 757 6905 5248 3738 2382 7251 1305 7380 2476 7346 5721 5946 7599 5321 620 3802 5744 3744 2548 6230 5241 7059 6020 7842 7816 466 3109 2953 1361 7583 4884 6377 3257 3410 4482 7538 7452 1880 1043 6250 263 6192 5664 4972 6334 4333 1013 5476 2872 7095 2259 4949 5342 2185\\n\", \"4000 100\\n1184 314 3114 3998 471 67 2327 2585 2047 3272 157 894 2981 934 2160 1568 3846 2893 2554 2761 2966 607 1110 792 3098 341 214 926 525 250 1311 1120 2143 1198 1992 3160 2321 1060 432 1908 2394 2340 1379 3605 2181 2858 2507 1938 849 2789 2781 1075 3152 1721 3096 3734 1992 3517 747 3276 73 2078 795 3709 2949 3450 3105 2464 3770 2374 170 68 3980 3529 917 75 3940 1374 1944 3689 1186 2294 1276 1801 3161 2356 1180 2952 1710 3535 3274 3992 540 1427 1578 1535 882 2656 3349 3477\\n\", \"5000 100\\n3150 4568 3083 2877 4459 2222 2213 2729 4087 4362 1694 705 3898 553 1910 3586 3599 641 3331 271 349 3464 3319 717 2959 4461 3189 3152 4604 3541 3743 125 3039 2119 3067 3102 1535 2352 4401 3393 1161 1233 3463 1417 721 2772 3973 2051 1901 2074 3113 3267 1090 2311 1717 589 1796 28 260 843 1979 5 3160 2494 1368 2241 2239 309 3853 93 3385 3944 1114 2881 4204 2728 3256 929 593 2827 0010 3829 2948 2773 103 4297 2999 4186 4018 2846 743 901 2034 1343 486 181 4306 3925 2624 978\\n\", \"3000 100\\n1002 1253 41 1014 483 911 2849 1042 1600 374 2723 867 1872 1212 2898 846 2606 144 968 1252 1287 750 2902 1571 2749 1804 1344 1508 1255 1855 2174 307 31 468 725 923 914 2255 68 2319 2548 2343 483 1794 641 240 2848 824 797 2503 1665 2178 1917 1834 771 2391 2188 2110 1834 2237 423 2047 2430 1732 825 851 971 107 984 2551 658 2489 1550 1777 2334 2422 1433 2332 1784 63 659 1759 2116 1637 514 606 1658 718 1297 2927 2509 1275 2150 2319 2727 49 1266 1683 2075 1784\\n\", \"100000 5\\n29657 1804 93111 68553 92008\\n\", \"3 10\\n3 3 2 3 3 3 1 2 3 3\\n\", \"100000 10\\n13202 14678 45343 53910 1988 64783 24175 45117 25650 55090\\n\", \"8000 100\\n7990 4432 5901 5019 423 1582 7760 5752 7422 4337 4802 2570 7354 4912 2185 2344 6538 2783 1473 5311 3987 2490 7159 1677 3438 502 3550 1318 5223 4518 4448 6451 3455 5012 1588 814 4971 5847 3849 6248 6420 3607 2610 6852 1045 3730 757 6905 5248 3738 2382 7251 1305 7380 2476 7346 5721 4004 7599 5321 620 3802 5744 3744 2548 6230 5241 7059 6020 7842 7816 466 3109 2953 1361 7583 4884 6377 3257 3410 4482 7538 7452 1880 1043 6250 263 6192 5664 4972 6334 4333 1013 5476 2872 7095 2259 4949 5342 2185\\n\", \"4000 100\\n1184 314 3114 3998 471 67 2327 2585 2047 3272 157 894 2981 934 2160 1568 3846 2893 2554 2761 2966 607 1110 792 3098 341 214 926 525 250 1311 1120 2143 1198 1992 3160 2321 1025 432 1908 2394 2340 1379 3605 2181 2858 2507 1938 849 2789 2781 1075 3152 1721 3096 3734 1992 3517 747 3276 73 2078 795 3709 2949 3450 3105 2464 3770 2374 170 68 3980 3529 917 75 3940 1374 1944 3689 1186 2294 1276 1801 3161 2356 1180 2952 1710 3535 3274 3992 540 1427 1578 1535 882 2656 3349 3477\\n\"], \"outputs\": [\"21\\n\", \"7\\n\", \"16\\n\", \"27\\n\", \"81\\n\", \"34\\n\", \"59\\n\", \"100\\n\", \"192528\\n\", \"0\\n\", \"1499932\\n\", \"36\\n\", \"699984\\n\", \"4\\n\", \"93\\n\", \"0\\n\", \"4\\n\", \"49\\n\", \"75\\n\", \"2299848\\n\", \"899974\\n\", \"44\\n\", \"45\\n\", \"9\\n\", \"1613498\\n\", \"499992\\n\", \"16\\n\", \"801509\\n\", \"64\\n\", \"14\\n\", \"19\\n\", \"1004505\\n\", \"25\\n\", \"1816501\\n\", \"7\\n\", \"2019503\\n\", \"19\\n\", \"22\\n\", \"1410500\\n\", \"29\\n\", \"598503\\n\", \"1299948\\n\", \"1699914\\n\", \"1099962\\n\", \"2099872\\n\", \"37\\n\", \"9\\n\", \"395503\\n\", \"1207504\\n\", \"1899894\\n\", \"499992\\n\", \"27\\n\", \"1499932\\n\", \"36\\n\", \"4\\n\", \"49\\n\", \"2299848\\n\", \"899974\\n\", \"74\\n\", \"1613498\\n\", \"16\\n\", \"801509\\n\", \"64\\n\", \"25\\n\", \"1004507\\n\", \"1816501\\n\", \"1410501\\n\", \"598503\\n\", \"1299948\\n\", \"1699914\\n\", \"2099872\\n\", \"9\\n\", \"395503\\n\", \"1899894\\n\", \"499992\\n\", \"598504\\n\", \"1768802\\n\", \"4\\n\", \"1499932\\n\", \"4\\n\", \"49\\n\", \"2299848\\n\", \"1613498\\n\", \"16\\n\", \"801509\\n\", \"64\\n\", \"1004507\\n\", \"1299948\\n\", \"2099872\\n\", \"9\\n\", \"395503\\n\", \"2299848\\n\", \"1613498\\n\", \"801509\\n\", \"1004507\\n\", \"598504\\n\", \"1299948\\n\", \"9\\n\", \"2299848\\n\", \"1613498\\n\", \"801509\\n\"]}", "source": "primeintellect"}
|
Alice is playing a game with her good friend, Marisa.
There are n boxes arranged in a line, numbered with integers from 1 to n from left to right. Marisa will hide a doll in one of the boxes. Then Alice will have m chances to guess where the doll is. If Alice will correctly guess the number of box, where doll is now, she will win the game, otherwise, her friend will win the game.
In order to win, Marisa will use some unfair tricks. After each time Alice guesses a box, she can move the doll to the neighboring box or just keep it at its place. Boxes i and i + 1 are neighboring for all 1 ≤ i ≤ n - 1. She can also use this trick once before the game starts.
So, the game happens in this order: the game starts, Marisa makes the trick, Alice makes the first guess, Marisa makes the trick, Alice makes the second guess, Marisa makes the trick, …, Alice makes m-th guess, Marisa makes the trick, the game ends.
Alice has come up with a sequence a_1, a_2, …, a_m. In the i-th guess, she will ask if the doll is in the box a_i. She wants to know the number of scenarios (x, y) (for all 1 ≤ x, y ≤ n), such that Marisa can win the game if she will put the doll at the x-th box at the beginning and at the end of the game, the doll will be at the y-th box. Help her and calculate this number.
Input
The first line contains two integers n and m, separated by space (1 ≤ n, m ≤ 10^5) — the number of boxes and the number of guesses, which Alice will make.
The next line contains m integers a_1, a_2, …, a_m, separated by spaces (1 ≤ a_i ≤ n), the number a_i means the number of the box which Alice will guess in the i-th guess.
Output
Print the number of scenarios in a single line, or the number of pairs of boxes (x, y) (1 ≤ x, y ≤ n), such that if Marisa will put the doll into the box with number x, she can make tricks in such way, that at the end of the game the doll will be in the box with number y and she will win the game.
Examples
Input
3 3
2 2 2
Output
7
Input
5 2
3 1
Output
21
Note
In the first example, the possible scenarios are (1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3).
Let's take (2, 2) as an example. The boxes, in which the doll will be during the game can be 2 → 3 → 3 → 3 → 2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 2 2 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 2 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 2 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 1\\n2\\n2 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 2 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 2 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 2 2 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 2 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 2 2 2 2 2 1 2 1 2 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 2 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 2 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 2 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 2 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 2\\n\", \"4\\n6\\n1 1 1 1 2 2 2 1 2 2 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 2 2\\n3\\n1 1 1 1 2 2\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 2 1 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 1 1 2 1 2 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 1 1 2 1 2 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n2 2 2 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 2 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n2 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 2\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 2 1 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 2 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 2\\n\", \"4\\n6\\n1 2 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 2 1 2 2\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 2 1 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 2 2 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 2\\n2\\n1 2 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 2 2 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 2 2 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 1 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 2 1 1 1 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 2 1 2 1 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 2 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 2 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 2\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 2 2 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 1\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 2 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 2 1 2 2 2 1 2 1 1 2\\n2\\n1 2 2 1\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 1 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 2 2 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n2 2 2 1 2 2 2 1 1 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n2 2 2 1 2 2 2 1 1 2 1 2\\n2\\n2 2 1 1\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n2 2 2 1 2 2 2 1 1 2 1 2\\n2\\n2 2 1 1\\n3\\n1 1 1 1 2 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 2 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 1 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 2 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 1 2\\n2\\n1 1 2 2\\n3\\n1 1 1 1 1 2\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 2 2 1 2 1 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 2 1 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 2 2 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 1 2 2\\n\", \"4\\n6\\n1 1 1 1 2 2 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 2\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 2 2\\n2\\n1 2 1 2\\n3\\n1 1 2 1 2 1\\n2\\n2 2 1 1\\n\", \"4\\n6\\n1 1 2 2 2 1 2 1 2 1 2 2\\n2\\n2 2 1 2\\n3\\n1 2 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 2 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 2 1 2 1\\n2\\n2 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 2 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 2\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 2 2 1 2 2 2 2 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 2 2\\n2\\n2 2 1 2\\n3\\n1 1 2 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 2 2 1 2 1 2 1 2 1 1 1\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 1 2 1 2 1 2 2\\n2\\n2 2 1 2\\n3\\n1 2 1 1 2 1\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 2 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n1 2 2 1\\n\", \"4\\n6\\n1 1 1 2 2 1 2 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 2\\n2\\n1 1 2 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 2 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 2 1 2 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 2 1 2 2 1 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 2\\n\", \"4\\n6\\n1 1 2 1 2 2 1 1 2 2 1 2\\n2\\n2 2 1 2\\n3\\n1 1 2 1 2 1\\n2\\n2 1 1 2\\n\", \"4\\n6\\n1 1 1 2 2 2 2 1 2 1 1 2\\n2\\n1 2 1 2\\n3\\n1 1 1 1 1 1\\n2\\n2 1 1 1\\n\", \"4\\n6\\n1 1 1 1 2 1 2 1 1 1 1 2\\n2\\n2 2 1 2\\n3\\n1 1 1 1 2 1\\n2\\n2 1 1 1\\n\"], \"outputs\": [\"6\\n0\\n6\\n2\\n\", \"6\\n0\\n6\\n2\\n\", \"6\\n2\\n6\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n2\\n6\\n0\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n0\\n4\\n2\\n\", \"6\\n0\\n6\\n0\\n\", \"0\\n0\\n4\\n2\\n\", \"6\\n2\\n2\\n0\\n\", \"6\\n0\\n4\\n0\\n\", \"0\\n2\\n4\\n2\\n\", \"0\\n0\\n4\\n0\\n\", \"4\\n2\\n6\\n2\\n\", \"12\\n2\\n6\\n0\\n\", \"6\\n2\\n2\\n2\\n\", \"2\\n0\\n4\\n0\\n\", \"0\\n2\\n2\\n2\\n\", \"4\\n0\\n4\\n0\\n\", \"4\\n2\\n4\\n0\\n\", \"2\\n0\\n4\\n2\\n\", \"0\\n0\\n6\\n2\\n\", \"0\\n2\\n4\\n0\\n\", \"0\\n2\\n6\\n2\\n\", \"6\\n4\\n2\\n2\\n\", \"2\\n2\\n4\\n2\\n\", \"2\\n0\\n6\\n2\\n\", \"2\\n0\\n6\\n0\\n\", \"10\\n2\\n4\\n2\\n\", \"4\\n2\\n4\\n2\\n\", \"4\\n2\\n6\\n0\\n\", \"4\\n2\\n2\\n2\\n\", \"2\\n2\\n2\\n2\\n\", \"2\\n2\\n4\\n0\\n\", \"4\\n2\\n0\\n0\\n\", \"2\\n2\\n0\\n2\\n\", \"0\\n2\\n2\\n0\\n\", \"6\\n2\\n0\\n2\\n\", \"6\\n2\\n0\\n0\\n\", \"8\\n2\\n6\\n2\\n\", \"6\\n2\\n6\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n0\\n4\\n2\\n\", \"6\\n0\\n6\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"0\\n0\\n4\\n0\\n\", \"6\\n2\\n2\\n2\\n\", \"0\\n2\\n4\\n2\\n\", \"0\\n2\\n4\\n2\\n\", \"6\\n0\\n4\\n2\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n0\\n\", \"0\\n0\\n4\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"0\\n0\\n4\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"6\\n0\\n4\\n2\\n\", \"6\\n0\\n4\\n0\\n\", \"6\\n0\\n6\\n2\\n\", \"6\\n2\\n6\\n2\\n\", \"0\\n2\\n4\\n2\\n\", \"6\\n0\\n4\\n0\\n\", \"0\\n0\\n6\\n2\\n\", \"0\\n2\\n4\\n2\\n\", \"2\\n0\\n4\\n0\\n\", \"0\\n2\\n4\\n0\\n\", \"0\\n2\\n4\\n0\\n\", \"2\\n0\\n4\\n0\\n\", \"4\\n2\\n2\\n2\\n\", \"4\\n2\\n4\\n0\\n\", \"6\\n2\\n4\\n0\\n\", \"6\\n2\\n2\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"4\\n2\\n4\\n2\\n\", \"6\\n0\\n6\\n2\\n\", \"0\\n2\\n2\\n2\\n\", \"4\\n2\\n4\\n0\\n\", \"0\\n2\\n2\\n2\\n\", \"6\\n2\\n4\\n2\\n\", \"0\\n2\\n4\\n0\\n\", \"0\\n2\\n4\\n0\\n\", \"0\\n0\\n6\\n2\\n\", \"10\\n2\\n4\\n2\\n\"]}", "source": "primeintellect"}
|
Karlsson has recently discovered a huge stock of berry jam jars in the basement of the house. More specifically, there were 2n jars of strawberry and blueberry jam.
All the 2n jars are arranged in a row. The stairs to the basement are exactly in the middle of that row. So when Karlsson enters the basement, he sees exactly n jars to his left and n jars to his right.
For example, the basement might look like this:
<image>
Being the starightforward man he is, he immediately starts eating the jam. In one minute he chooses to empty either the first non-empty jar to his left or the first non-empty jar to his right.
Finally, Karlsson decided that at the end the amount of full strawberry and blueberry jam jars should become the same.
For example, this might be the result:
<image> He has eaten 1 jar to his left and then 5 jars to his right. There remained exactly 3 full jars of both strawberry and blueberry jam.
Jars are numbered from 1 to 2n from left to right, so Karlsson initially stands between jars n and n+1.
What is the minimum number of jars Karlsson is required to empty so that an equal number of full strawberry and blueberry jam jars is left?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).
The second line of each test case contains 2n integers a_1, a_2, ..., a_{2n} (1 ≤ a_i ≤ 2) — a_i=1 means that the i-th jar from the left is a strawberry jam jar and a_i=2 means that it is a blueberry jam jar.
It is guaranteed that the sum of n over all test cases does not exceed 10^5.
Output
For each test case print the answer to it — the minimum number of jars Karlsson is required to empty so that an equal number of full strawberry and blueberry jam jars is left.
Example
Input
4
6
1 1 1 2 2 1 2 1 2 1 1 2
2
1 2 1 2
3
1 1 1 1 1 1
2
2 1 1 1
Output
6
0
6
2
Note
The picture from the statement describes the first test case.
In the second test case the number of strawberry and blueberry jam jars is already equal.
In the third test case Karlsson is required to eat all 6 jars so that there remain 0 jars of both jams.
In the fourth test case Karlsson can empty either the second and the third jars or the third and the fourth one. The both scenarios will leave 1 jar of both jams.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n5\\n7\\n11\\n1\\n2000000000000\\n\", \"3\\n576460752303423484\\n576460752303423484\\n576460752303423485\\n\", \"1\\n576460752303423487\\n\", \"1\\n1\\n\", \"3\\n576460752303423484\\n576460752303423484\\n361364603326849558\\n\", \"1\\n728718360623737783\\n\", \"5\\n5\\n7\\n11\\n1\\n2880328956332\\n\", \"3\\n576460752303423484\\n576460752303423484\\n180247288234291864\\n\", \"1\\n602006303855446509\\n\", \"5\\n2\\n7\\n11\\n1\\n2880328956332\\n\", \"3\\n576460752303423484\\n877325853786446869\\n180247288234291864\\n\", \"1\\n507279574089141988\\n\", \"5\\n2\\n7\\n17\\n1\\n2880328956332\\n\", \"3\\n576460752303423484\\n877325853786446869\\n240944980276375877\\n\", \"1\\n454777081508105168\\n\", \"5\\n2\\n7\\n17\\n1\\n5347367141003\\n\", \"3\\n469556123351326115\\n877325853786446869\\n240944980276375877\\n\", \"1\\n319701909189686733\\n\", \"5\\n2\\n4\\n17\\n1\\n5347367141003\\n\", \"3\\n469556123351326115\\n877325853786446869\\n119339599917140019\\n\", \"1\\n568609622880937466\\n\", \"5\\n2\\n4\\n22\\n1\\n5347367141003\\n\", \"3\\n469556123351326115\\n315333671632893054\\n119339599917140019\\n\", \"1\\n115179454258582550\\n\", \"5\\n4\\n4\\n22\\n1\\n5347367141003\\n\", \"3\\n469556123351326115\\n315333671632893054\\n58948863679733028\\n\", \"1\\n221046514607623000\\n\", \"5\\n4\\n4\\n22\\n1\\n3589159915542\\n\", \"3\\n735231676677923229\\n315333671632893054\\n58948863679733028\\n\", \"1\\n234134124553595372\\n\", \"3\\n735231676677923229\\n299128162050456407\\n58948863679733028\\n\", \"1\\n441342083622843232\\n\", \"3\\n735231676677923229\\n299128162050456407\\n59128865440432622\\n\", \"1\\n838676036416923985\\n\", \"3\\n735231676677923229\\n553892277652059228\\n59128865440432622\\n\", \"1\\n93012189849493242\\n\", \"3\\n735231676677923229\\n628066981806539048\\n59128865440432622\\n\", \"1\\n127997067220343627\\n\", \"3\\n735231676677923229\\n628066981806539048\\n69302616042148119\\n\", \"1\\n231654992900294638\\n\", \"1\\n457226532364492124\\n\", \"1\\n423117929860087259\\n\", \"1\\n209405166115248600\\n\", \"1\\n209938661208615239\\n\", \"1\\n152446398287411953\\n\", \"1\\n100180616658392850\\n\", \"1\\n85134512633621932\\n\", \"1\\n63699126931555713\\n\", \"1\\n81426348608158874\\n\", \"1\\n29919675425581460\\n\", \"1\\n2022304732546191\\n\", \"1\\n448703618469411\\n\", \"1\\n147743191708243\\n\", \"1\\n272002009713671\\n\", \"1\\n86608797922357\\n\", \"1\\n18112201673693\\n\", \"1\\n26188370094697\\n\", \"1\\n23189318689130\\n\", \"1\\n5414785231456\\n\", \"1\\n5189873720426\\n\", \"1\\n594622998032\\n\", \"1\\n457367244613\\n\", \"1\\n578528227898\\n\", \"1\\n214508339216\\n\", \"1\\n151665549277\\n\", \"1\\n35423210823\\n\", \"1\\n58474793948\\n\", \"1\\n43948021835\\n\", \"1\\n84009298508\\n\", \"1\\n10946794489\\n\", \"1\\n6431934796\\n\", \"1\\n10471680494\\n\", \"1\\n18608666169\\n\", \"1\\n27521151810\\n\", \"1\\n51442033587\\n\", \"1\\n97786269406\\n\", \"1\\n100679495400\\n\", \"1\\n139101020088\\n\", \"1\\n206890299065\\n\", \"1\\n343981611593\\n\", \"1\\n156903180095\\n\", \"1\\n39042305033\\n\", \"1\\n51107186765\\n\", \"1\\n53010593162\\n\", \"1\\n53135543902\\n\", \"1\\n20327329588\\n\", \"1\\n20856756599\\n\", \"1\\n5835997993\\n\", \"1\\n9234064134\\n\", \"1\\n1349634466\\n\", \"1\\n2168516752\\n\", \"1\\n3952010895\\n\", \"1\\n399462040\\n\", \"1\\n338186953\\n\", \"1\\n158575687\\n\", \"1\\n313577823\\n\", \"1\\n247528392\\n\", \"1\\n452215226\\n\", \"1\\n737471489\\n\", \"1\\n1352738574\\n\", \"1\\n857300758\\n\"], \"outputs\": [\"8\\n11\\n19\\n1\\n3999999999987\\n\", \"1152921504606846911\\n1152921504606846911\\n1152921504606846912\\n\", \"1152921504606846915\\n\", \"1\\n\", \"1152921504606846911\\n1152921504606846911\\n722729206653699089\\n\", \"1457436721247475532\\n\", \"8\\n11\\n19\\n1\\n5760657912639\\n\", \"1152921504606846911\\n1152921504606846911\\n360494576468583701\\n\", \"1204012607710892988\\n\", \"3\\n11\\n19\\n1\\n5760657912639\\n\", \"1152921504606846911\\n1754651707572893708\\n360494576468583701\\n\", \"1014559148178283947\\n\", \"3\\n11\\n32\\n1\\n5760657912639\\n\", \"1152921504606846911\\n1754651707572893708\\n481889960552751727\\n\", \"909554163016210306\\n\", \"3\\n11\\n32\\n1\\n10694734281981\\n\", \"939112246702652199\\n1754651707572893708\\n481889960552751727\\n\", \"639403818379373432\\n\", \"3\\n7\\n32\\n1\\n10694734281981\\n\", \"939112246702652199\\n1754651707572893708\\n238679199834280004\\n\", \"1137219245761874895\\n\", \"3\\n7\\n41\\n1\\n10694734281981\\n\", \"939112246702652199\\n630667343265786077\\n238679199834280004\\n\", \"230358908517165076\\n\", \"7\\n7\\n41\\n1\\n10694734281981\\n\", \"939112246702652199\\n630667343265786077\\n117897727359466025\\n\", \"442093029215245979\\n\", \"7\\n7\\n41\\n1\\n7178319831067\\n\", \"1470463353355846439\\n630667343265786077\\n117897727359466025\\n\", \"468268249107190706\\n\", \"1470463353355846439\\n598256324100912783\\n117897727359466025\\n\", \"882684167245686434\\n\", \"1470463353355846439\\n598256324100912783\\n118257730880865219\\n\", \"1677352072833847943\\n\", \"1470463353355846439\\n1107784555304118426\\n118257730880865219\\n\", \"186024379698986457\\n\", \"1470463353355846439\\n1256133963613078067\\n118257730880865219\\n\", \"255994134440687219\\n\", \"1470463353355846439\\n1256133963613078067\\n138605232084296209\\n\", \"463309985800589247\\n\", \"914453064728984218\\n\", \"846235859720174480\\n\", \"418810332230497166\\n\", \"419877322417230444\\n\", \"304892796574823878\\n\", \"200361233316785668\\n\", \"170269025267243831\\n\", \"127398253863111406\\n\", \"162852697216317724\\n\", \"59839350851162895\\n\", \"4044609465092358\\n\", \"897407236938796\\n\", \"295486383416462\\n\", \"544004019427317\\n\", \"173217595844691\\n\", \"36224403347363\\n\", \"52376740189368\\n\", \"46378637378238\\n\", \"10829570462891\\n\", \"10379747440832\\n\", \"1189245996048\\n\", \"914734489204\\n\", \"1157056455777\\n\", \"429016678418\\n\", \"303331098529\\n\", \"70846421627\\n\", \"116949587874\\n\", \"87896043654\\n\", \"168018596999\\n\", \"21893588958\\n\", \"12863869572\\n\", \"20943360972\\n\", \"37217332321\\n\", \"55042303604\\n\", \"102884067152\\n\", \"195572538795\\n\", \"201358990778\\n\", \"278202040160\\n\", \"413780598108\\n\", \"687963223168\\n\", \"313806360174\\n\", \"78084610052\\n\", \"102214373511\\n\", \"106021186304\\n\", \"106271087787\\n\", \"40654659156\\n\", \"41713513178\\n\", \"11671995969\\n\", \"18468128255\\n\", \"2699268919\\n\", \"4337033495\\n\", \"7904021770\\n\", \"798924063\\n\", \"676373895\\n\", \"317151359\\n\", \"627155631\\n\", \"495056769\\n\", \"904430437\\n\", \"1474942963\\n\", \"2705477136\\n\", \"1714601500\\n\"]}", "source": "primeintellect"}
|
The last contest held on Johnny's favorite competitive programming platform has been received rather positively. However, Johnny's rating has dropped again! He thinks that the presented tasks are lovely, but don't show the truth about competitors' skills.
The boy is now looking at the ratings of consecutive participants written in a binary system. He thinks that the more such ratings differ, the more unfair is that such people are next to each other. He defines the difference between two numbers as the number of bit positions, where one number has zero, and another has one (we suppose that numbers are padded with leading zeros to the same length). For example, the difference of 5 = 101_2 and 14 = 1110_2 equals to 3, since 0101 and 1110 differ in 3 positions. Johnny defines the unfairness of the contest as the sum of such differences counted for neighboring participants.
Johnny has just sent you the rating sequence and wants you to find the unfairness of the competition. You have noticed that you've got a sequence of consecutive integers from 0 to n. That's strange, but the boy stubbornly says that everything is right. So help him and find the desired unfairness for received numbers.
Input
The input consists of multiple test cases. The first line contains one integer t (1 ≤ t ≤ 10 000) — the number of test cases. The following t lines contain a description of test cases.
The first and only line in each test case contains a single integer n (1 ≤ n ≤ 10^{18}).
Output
Output t lines. For each test case, you should output a single line with one integer — the unfairness of the contest if the rating sequence equals to 0, 1, ..., n - 1, n.
Example
Input
5
5
7
11
1
2000000000000
Output
8
11
19
1
3999999999987
Note
For n = 5 we calculate unfairness of the following sequence (numbers from 0 to 5 written in binary with extra leading zeroes, so they all have the same length):
* 000
* 001
* 010
* 011
* 100
* 101
The differences are equal to 1, 2, 1, 3, 1 respectively, so unfairness is equal to 1 + 2 + 1 + 3 + 1 = 8.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"4 2 1\\n1 1 10\\n2 2 20\\n2 3 30\\n5 2 40\\n\", \"4 1 0\\n1 1 10\\n1 999 30\\n1 1000 40\\n1 2 20\\n\", \"1 1 0\\n1 1 10\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 980092\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 779 947360\\n1 800 977424\\n1 792 958202\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"5 2 0\\n500 500 50\\n1 1 10\\n1000 1 40\\n1 1000 30\\n1000 1000 20\\n\", \"2 2 0\\n1000 1000 10\\n999 1000 20\\n\", \"4 2 1\\n1 1 10\\n2 2 20\\n2 3 30\\n4 2 40\\n\", \"2 1 0\\n1 2 20\\n1 1 10\\n\", \"20 5 998\\n1 100 27850\\n1000 1000 39150\\n154 1 844290\\n365 1 301071\\n280 1 484115\\n1 463 157556\\n290 1 23931\\n1 849 533321\\n1 764 583356\\n1 1000 35786\\n1 310 192558\\n1 1 643970\\n1000 586 493625\\n842 1 450372\\n229 1000 914591\\n954 1 560639\\n1000 1 154505\\n545 1000 137486\\n1000 975 549244\\n1 364 763250\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 457 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 875865\\n247 1 591835\\n933 1 16036\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n409 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"1 1 0\\n1 1000 1000000\\n\", \"4 1 0\\n1 1 10\\n1 999 30\\n1 1000 40\\n1 3 20\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 980092\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 779 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"5 2 1\\n500 500 50\\n1 1 10\\n1000 1 40\\n1 1000 30\\n1000 1000 20\\n\", \"2 2 0\\n1000 1000 10\\n999 1000 9\\n\", \"4 3 1\\n1 1 10\\n2 2 20\\n2 3 30\\n4 2 40\\n\", \"2 1 0\\n1 2 20\\n1 1 12\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 457 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 875865\\n247 1 591835\\n933 1 16036\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"4 2 1\\n1 1 10\\n2 2 5\\n2 3 30\\n5 2 40\\n\", \"2 4 0\\n1000 1000 10\\n999 1000 9\\n\", \"4 3 1\\n1 1 10\\n2 2 20\\n2 3 1\\n4 2 40\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 457 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 16036\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"4 2 1\\n1 1 10\\n2 2 5\\n2 3 30\\n5 2 28\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 1150114\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 457 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"4 3 1\\n1 1 4\\n2 2 20\\n2 3 1\\n7 2 40\\n\", \"20 17 0\\n1 964 972064\\n1 215 914335\\n1 926 994468\\n1 603 1150114\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 519143\\n1 646 978054\\n\", \"4 3 1\\n1 1 1\\n2 2 20\\n2 3 1\\n7 2 40\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 579 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 496 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n84 1000 190525\\n1000 591 246736\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 980092\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 779 947360\\n1 800 977424\\n1 792 958202\\n1 833 941466\\n1 21 617378\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"2 2 0\\n1000 1000 10\\n700 1000 20\\n\", \"4 2 1\\n1 1 10\\n2 2 31\\n2 3 30\\n4 2 40\\n\", \"1 1 1\\n1 1000 1000000\\n\", \"4 2 1\\n1 1 10\\n2 2 22\\n2 3 30\\n5 2 40\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 980092\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 779 433455\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"2 2 0\\n1000 1000 10\\n999 1000 6\\n\", \"4 3 1\\n1 1 17\\n2 2 20\\n2 3 30\\n4 2 40\\n\", \"2 1 0\\n1 2 20\\n1 1 3\\n\", \"4 3 1\\n1 1 10\\n2 2 20\\n2 6 1\\n4 2 40\\n\", \"4 2 2\\n1 1 10\\n2 2 5\\n2 3 30\\n5 2 28\\n\", \"4 3 1\\n1 1 5\\n2 2 20\\n2 3 1\\n7 2 40\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 457 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 22943\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 0\\n1 964 972064\\n1 215 914335\\n1 926 994468\\n1 603 1150114\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 1009196\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"20 17 0\\n1 964 972064\\n1 215 914335\\n1 926 994468\\n1 603 1150114\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 1176275\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 519143\\n1 646 978054\\n\", \"4 3 1\\n1 1 1\\n2 2 20\\n2 3 0\\n7 2 40\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 261403\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 1697617\\n1 603 980092\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 779 947360\\n1 800 977424\\n1 792 958202\\n1 833 941466\\n1 21 617378\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"4 2 1\\n1 1 10\\n2 2 31\\n2 3 30\\n4 2 3\\n\", \"4 2 1\\n1 1 10\\n2 2 22\\n2 3 31\\n5 2 40\\n\", \"4 1 0\\n1 2 10\\n1 999 2\\n1 1000 40\\n1 3 20\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 980092\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"2 4 0\\n1000 1000 10\\n999 1000 5\\n\", \"4 3 1\\n1 1 10\\n2 2 20\\n2 3 1\\n7 2 40\\n\", \"20 17 0\\n1 964 972064\\n1 215 914335\\n1 926 994468\\n1 603 1150114\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"2 4 0\\n1000 1000 7\\n999 1000 5\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 175 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 579 600207\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 496 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 496 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n84 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 496 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 931 156116\\n84 1000 190525\\n1000 591 246736\\n\", \"4 1 0\\n1 1 10\\n2 999 30\\n1 1000 40\\n1 2 20\\n\", \"4 1 0\\n1 2 10\\n1 999 30\\n1 1000 40\\n1 3 20\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 980092\\n1 545 946148\\n1 146 952185\\n1 979 918633\\n1 438 967889\\n1 871 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"2 4 0\\n1000 1000 10\\n999 1000 16\\n\", \"20 17 0\\n1 964 972064\\n1 529 914335\\n1 926 994468\\n1 603 1150114\\n1 545 946148\\n1 88 952185\\n1 979 918633\\n1 438 967889\\n1 198 926455\\n1 424 952048\\n1 892 911827\\n1 517 947360\\n1 800 977424\\n1 792 607193\\n1 833 941466\\n1 21 910590\\n1 384 963993\\n1 72 975862\\n1 569 953738\\n1 646 978054\\n\", \"2 4 1\\n1000 1000 7\\n999 1000 5\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 579 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n7 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n121 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 496 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n216 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 649 839096\\n1 865 156116\\n84 1000 148597\\n1000 591 246736\\n\", \"20 17 998\\n1000 1000 295133\\n1 1000 322998\\n31 1 412809\\n1 14 347941\\n1000 496 237237\\n1 708 315587\\n1 159 302269\\n1000 447 1582128\\n247 1 591835\\n933 1 15831\\n140 1 305582\\n1 1 147502\\n1000 1 631288\\n148 1000 145614\\n402 1000 875933\\n594 1000 874200\\n1000 963 839096\\n1 865 156116\\n84 1000 190525\\n1000 591 246736\\n\"], \"outputs\": [\"33800\\n\", \"3000\\n\", \"100\\n\", \"351865268\\n\", \"39000\\n\", \"900\\n\", \"33800\\n\", \"500\\n\", \"664324738\\n\", \"993249832\\n\", \"999993007\\n\", \"3000\\n\", \"222243430\\n\", \"39000\\n\", \"361\\n\", \"33600\\n\", \"544\\n\", \"993249832\\n\", \"21950\\n\", \"0\\n\", \"16084\\n\", \"532534976\\n\", \"17222\\n\", \"279601935\\n\", \"314961636\\n\", \"13300\\n\", \"474626917\\n\", \"12016\\n\", \"373801934\\n\", \"553455569\\n\", \"542844501\\n\", \"900\\n\", \"44206\\n\", \"999993007\\n\", \"35584\\n\", \"402593184\\n\", \"256\\n\", \"38836\\n\", \"409\\n\", \"15943\\n\", \"22062\\n\", \"13744\\n\", \"660797811\\n\", \"29634411\\n\", \"345927429\\n\", \"11604\\n\", \"468246516\\n\", \"721233667\\n\", \"26631\\n\", \"36349\\n\", \"2104\\n\", \"222243430\\n\", \"0\\n\", \"16084\\n\", \"279601935\\n\", \"0\\n\", \"314961636\\n\", \"314961636\\n\", \"373801934\\n\", \"373801934\\n\", \"553455569\\n\", \"3000\\n\", \"3000\\n\", \"222243430\\n\", \"0\\n\", \"279601935\\n\", \"0\\n\", \"373801934\\n\", \"373801934\\n\", \"553455569\\n\"]}", "source": "primeintellect"}
|
Mr. Chanek The Ninja is one day tasked with a mission to handle mad snakes that are attacking a site. Now, Mr. Chanek already arrived at the hills where the destination is right below these hills. The mission area can be divided into a grid of size 1000 × 1000 squares. There are N mad snakes on the site, the i'th mad snake is located on square (X_i, Y_i) and has a danger level B_i.
Mr. Chanek is going to use the Shadow Clone Jutsu and Rasengan that he learned from Lord Seventh to complete this mission. His attack strategy is as follows:
1. Mr. Chanek is going to make M clones.
2. Each clone will choose a mad snake as the attack target. Each clone must pick a different mad snake to attack.
3. All clones jump off the hills and attack their respective chosen target at once with Rasengan of radius R. If the mad snake at square (X, Y) is attacked with a direct Rasengan, it and all mad snakes at squares (X', Y') where max(|X' - X|, |Y' - Y|) ≤ R will die.
4. The real Mr. Chanek will calculate the score of this attack. The score is defined as the square of the sum of the danger levels of all the killed snakes.
Now Mr. Chanek is curious, what is the sum of scores for every possible attack strategy? Because this number can be huge, Mr. Chanek only needs the output modulo 10^9 + 7.
Input
The first line contains three integers N M R (1 ≤ M ≤ N ≤ 2 ⋅ 10^3, 0 ≤ R < 10^3), the number of mad snakes, the number of clones, and the radius of the Rasengan.
The next N lines each contains three integers, X_i, Y_i, dan B_i (1 ≤ X_i, Y_i ≤ 10^3, 1 ≤ B_i ≤ 10^6). It is guaranteed that no two mad snakes occupy the same square.
Output
A line with an integer that denotes the sum of scores for every possible attack strategy.
Example
Input
4 2 1
1 1 10
2 2 20
2 3 30
5 2 40
Output
33800
Note
Here is the illustration of all six possible attack strategies. The circles denote the chosen mad snakes, and the blue squares denote the region of the Rasengan:
<image>
So, the total score of all attacks is: 3.600 + 3.600 + 4.900 + 3.600 + 10.000 + 8.100 = 33.800.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -3\\n-1 -2 -3 -4\\n-2 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -2 -1\\n-3 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -2 -2\\n-3 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -3\\n-1 -2 -3 -6\\n-2 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -2 -2 -3\\n-1 -2 -3 -4\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -2 -2\\n-5 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -2 -2 -3\\n-1 -2 -3 -3\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -2 -2\\n0 -2 -1\\n-3 -2 -1\\n\", \"1\\n3 3\\n-1 -2 -2\\n0 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 -1 -2 -4\\n0 -2 -3 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -3\\n-1 -2 -3 -4\\n-2 -1 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -6 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n-1 -2 -3 -6\\n-2 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -1 -2\\n-5 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -4\\n0 -2 -3 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -6 -4 -5\\n\", \"1\\n3 3\\n-3 -1 -2\\n-8 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-2 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n0 -2 -3 -6\\n-2 -3 0 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -8\\n0 -2 -4 -6\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-4 -2 -1\\n-3 -4 -2\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -6 -4 -5\\n\", \"1\\n3 3\\n-3 -1 -2\\n-8 -2 -2\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -8\\n0 -2 -5 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -8\\n0 -2 -1 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -10\\n0 -2 -5 -6\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-4 -4 -1\\n-3 -4 -2\\n-3 -2 0\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -1\\n-1 -1 -3 -4\\n0 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -10\\n0 -2 -5 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -1\\n0 -2 -1 -6\\n-1 -3 -4 -6\\n\", \"1\\n3 3\\n-6 -4 -1\\n-3 -4 -2\\n-3 -2 0\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -1\\n-1 -2 -3 -4\\n0 -3 -4 -5\\n\", \"1\\n3 3\\n0 -1 -2\\n-8 -4 -3\\n-3 -2 -1\\n\", \"2\\n2 2\\n0 1\\n1 1\\n3 4\\n0 -1 -1 0\\n1 -2 -3 -9\\n0 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -1\\n0 -2 -1 -5\\n-1 -3 -4 -6\\n\", \"1\\n3 3\\n-6 -4 -1\\n-3 -4 -2\\n-3 -2 1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 -2 -2 -3\\n-2 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -1\\n0 -2 -1 -5\\n-1 -3 -4 -1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n-1 0\\n0 1\\n3 4\\n0 0 -2 -1\\n0 -2 -1 -5\\n-1 -3 -4 -1\\n\", \"1\\n3 3\\n-6 -4 -1\\n-3 -6 -2\\n-3 -1 1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 0 -2 -3\\n-1 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n0 0\\n0 1\\n3 4\\n0 0 -2 -1\\n0 -2 -1 -5\\n-1 -3 -4 -1\\n\", \"1\\n3 3\\n-8 -4 -1\\n-3 -6 -2\\n-3 -1 1\\n\", \"2\\n2 2\\n0 0\\n0 1\\n3 4\\n0 0 -2 -1\\n0 -2 -1 -5\\n-1 -3 -4 0\\n\", \"2\\n2 2\\n-1 1\\n-1 1\\n3 4\\n1 0 -2 -2\\n-1 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n-1 1\\n-1 1\\n3 4\\n1 0 -2 -2\\n-2 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n-1 1\\n-1 1\\n3 4\\n1 0 -2 -3\\n-2 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -3\\n0 -2 -3 -6\\n-2 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n0 -2 -3 -6\\n-2 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n0 -2 -3 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -4\\n0 -2 -3 -6\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-4 -2 -1\\n-3 -2 -1\\n-3 -2 -1\\n\", \"1\\n3 3\\n-3 -2 0\\n-3 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -4 -3\\n0 -2 -3 -6\\n-2 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -2 -3\\n0 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n0 -2 -3 -6\\n-2 -3 0 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -1 -4\\n0 -2 -3 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -4\\n0 -2 -4 -6\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-4 -2 -1\\n-3 -2 -2\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -3\\n-1 -2 -3 -4\\n-2 -1 -8 -5\\n\", \"1\\n3 3\\n-3 -2 -1\\n-3 -2 0\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n-1 -2 -3 -6\\n0 -3 -4 -5\\n\", \"1\\n3 3\\n-3 -3 -3\\n0 -2 -1\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -1 -4\\n0 -2 -3 -9\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -4\\n0 -2 -1 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -3\\n-1 -2 -3 -4\\n-2 -1 -8 -5\\n\", \"1\\n3 3\\n-3 -2 -1\\n0 -2 0\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n-1 -1 -3 -6\\n0 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -1 0\\n0 -2 -3 -9\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-4 -2 -1\\n-3 -4 -2\\n-3 -2 0\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -3\\n-1 -2 -2 -4\\n-2 -1 -8 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -6 0 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -4\\n-1 -1 -3 -4\\n0 -3 -4 -5\\n\", \"1\\n3 3\\n0 -1 -2\\n-8 -2 -2\\n-3 -2 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -1 0\\n1 -2 -3 -9\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n0 0 -2 -8\\n0 -2 -1 -6\\n-1 -3 -4 -6\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -3\\n0 -2 -2 -4\\n-2 -1 -8 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 -2 -2 -3\\n-1 -2 -3 -4\\n-2 -6 0 -7\\n\", \"1\\n3 3\\n0 -1 -2\\n-8 -4 -2\\n-3 -2 -1\\n\", \"2\\n2 2\\n0 1\\n1 1\\n3 4\\n0 -1 -1 0\\n1 -2 -3 -9\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 -2 -2 -3\\n-2 -2 -3 -4\\n-2 -6 0 -7\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -10\\n0 0 -5 -6\\n-1 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n0 -1 -2 -1\\n-1 -2 -3 -4\\n0 -3 -6 -5\\n\", \"1\\n3 3\\n0 -1 -2\\n-8 -4 -3\\n-3 0 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -5\\n0 0 -5 -6\\n-1 -3 -4 -5\\n\", \"1\\n3 3\\n-6 -4 -1\\n-3 -4 -2\\n-3 -1 1\\n\", \"2\\n2 2\\n-1 1\\n1 2\\n3 4\\n0 -1 -2 -1\\n-1 -2 -3 -4\\n0 -3 -6 -5\\n\", \"1\\n3 3\\n0 -1 -4\\n-8 -4 -3\\n-3 0 -1\\n\", \"2\\n2 2\\n-1 1\\n1 1\\n3 4\\n-1 -1 -2 -5\\n0 0 -5 -6\\n0 -3 -4 -5\\n\", \"2\\n2 2\\n-1 1\\n1 2\\n3 4\\n0 -1 -2 -1\\n-1 -2 -3 -4\\n0 -1 -6 -5\\n\", \"1\\n3 3\\n0 -1 -4\\n-8 -4 -3\\n-1 0 -1\\n\", \"2\\n2 2\\n-1 1\\n0 1\\n3 4\\n1 0 -2 -2\\n-1 -2 -3 -4\\n-2 -6 0 -11\\n\", \"2\\n2 2\\n-1 1\\n1 2\\n3 4\\n0 -1 -2 0\\n-1 -2 -3 -4\\n0 -1 -6 -5\\n\", \"1\\n3 3\\n-1 -1 -4\\n-8 -4 -3\\n-1 0 -1\\n\", \"2\\n2 2\\n0 0\\n0 1\\n3 4\\n0 0 -2 -1\\n-1 -2 -1 -5\\n-1 -3 -4 0\\n\"], \"outputs\": [\"2\\n30\\n\", \"16\\n\", \"2\\n31\\n\", \"17\\n\", \"2\\n32\\n\", \"2\\n30\\n\", \"19\\n\", \"2\\n29\\n\", \"16\\n\", \"14\\n\", \"3\\n31\\n\", \"2\\n28\\n\", \"2\\n34\\n\", \"2\\n33\\n\", \"18\\n\", \"3\\n30\\n\", \"3\\n34\\n\", \"21\\n\", \"3\\n28\\n\", \"2\\n37\\n\", \"20\\n\", \"3\\n33\\n\", \"22\\n\", \"2\\n38\\n\", \"3\\n32\\n\", \"2\\n40\\n\", \"23\\n\", \"2\\n25\\n\", \"2\\n39\\n\", \"3\\n26\\n\", \"25\\n\", \"2\\n26\\n\", \"24\\n\", \"3\\n29\\n\", \"3\\n25\\n\", \"26\\n\", \"3\\n38\\n\", \"3\\n20\\n\", \"3\\n37\\n\", \"2\\n20\\n\", \"27\\n\", \"3\\n35\\n\", \"1\\n20\\n\", \"29\\n\", \"1\\n19\\n\", \"4\\n34\\n\", \"4\\n35\\n\", \"4\\n36\\n\", \"2\\n31\\n\", \"2\\n32\\n\", \"2\\n31\\n\", \"2\\n32\\n\", \"17\\n\", \"17\\n\", \"2\\n33\\n\", \"17\\n\", \"2\\n28\\n\", \"2\\n30\\n\", \"2\\n33\\n\", \"18\\n\", \"2\\n32\\n\", \"17\\n\", \"2\\n31\\n\", \"18\\n\", \"2\\n33\\n\", \"3\\n28\\n\", \"2\\n33\\n\", \"14\\n\", \"2\\n30\\n\", \"2\\n29\\n\", \"21\\n\", \"2\\n32\\n\", \"3\\n31\\n\", \"2\\n28\\n\", \"21\\n\", \"2\\n30\\n\", \"3\\n33\\n\", \"2\\n31\\n\", \"3\\n33\\n\", \"23\\n\", \"3\\n30\\n\", \"3\\n34\\n\", \"2\\n38\\n\", \"2\\n28\\n\", \"22\\n\", \"2\\n33\\n\", \"25\\n\", \"3\\n28\\n\", \"24\\n\", \"2\\n32\\n\", \"3\\n26\\n\", \"22\\n\", \"3\\n34\\n\", \"3\\n25\\n\", \"23\\n\", \"1\\n20\\n\"]}", "source": "primeintellect"}
|
You are given a rectangular grid with n rows and m columns. The cell located on the i-th row from the top and the j-th column from the left has a value a_{ij} written in it.
You can perform the following operation any number of times (possibly zero):
* Choose any two adjacent cells and multiply the values in them by -1. Two cells are called adjacent if they share a side.
Note that you can use a cell more than once in different operations.
You are interested in X, the sum of all the numbers in the grid.
What is the maximum X you can achieve with these operations?
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.
The first line of each test case contains two integers n,m (2 ≤ n, m ≤ 10).
The following n lines contain m integers each, the j-th element in the i-th line is a_{ij} (-100≤ a_{ij}≤ 100).
Output
For each testcase, print one integer X, the maximum possible sum of all the values in the grid after applying the operation as many times as you want.
Example
Input
2
2 2
-1 1
1 1
3 4
0 -1 -2 -3
-1 -2 -3 -4
-2 -3 -4 -5
Output
2
30
Note
In the first test case, there will always be at least one -1, so the answer is 2.
In the second test case, we can use the operation six times to elements adjacent horizontally and get all numbers to be non-negative. So the answer is: 2× 1 + 3×2 + 3× 3 + 2× 4 + 1× 5 = 30.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"5\\n2 2 3\\n3 3 2\\n5 10 2\\n11 13 1\\n1 4 4\\n\", \"1\\n1024 1024 22212\\n\", \"1\\n8192 8192 67108864\\n\", \"1\\n8192 8192 1000000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 67108863\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1257 1895 12\\n1574 4984 164\\n1564 8917 15\\n150 15 2\\n1500 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"8\\n6144 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 8192 67108865\\n6144 8192 67108864\\n8192 6044 67108864\\n6144 8192 16777217\\n8192 6044 16777217\\n\", \"1\\n8192 8192 67108865\\n\", \"1\\n1024 1593 22212\\n\", \"1\\n8192 8192 1001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 67108863\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1574 4984 164\\n1564 8917 15\\n150 15 2\\n1500 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 8192 67108865\\n6144 8192 67108864\\n8192 6044 67108864\\n6144 8192 16777217\\n8192 6044 16777217\\n\", \"5\\n2 2 3\\n3 3 2\\n5 10 2\\n14 13 1\\n1 4 4\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 67108863\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1888 4984 164\\n1564 8917 15\\n150 15 2\\n1500 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8149 6144 16777216\\n8192 8192 67108864\\n8192 1515 67108865\\n5724 8192 67108864\\n8192 7057 67108864\\n6144 8192 16777217\\n8192 7716 16777217\\n\", \"8\\n4256 8192 16777216\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n5724 8192 67108864\\n8192 7057 67108864\\n6144 137 16777217\\n8192 7716 16777217\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 2\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 40\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n6144 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 8192 67108865\\n6144 8192 67108864\\n8192 6044 67108864\\n6144 8192 16777217\\n8192 10215 16777217\\n\", \"5\\n2 2 3\\n3 3 2\\n5 10 3\\n11 13 1\\n1 4 4\\n\", \"1\\n2971 8192 67108864\\n\", \"1\\n8192 8192 31270788\\n\", \"1\\n1024 170 22212\\n\", \"1\\n2971 8192 384142\\n\", \"1\\n8192 5862 1001000\\n\", \"8\\n4256 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 1515 67108865\\n6144 8192 67108864\\n8192 6044 67108864\\n6144 8192 16777217\\n8192 6044 16777217\\n\", \"1\\n13479 8192 31270788\\n\", \"5\\n2 2 3\\n3 3 2\\n5 10 2\\n14 8 1\\n1 4 4\\n\", \"1\\n1024 240 22212\\n\", \"1\\n3237 8192 384142\\n\", \"1\\n8192 5757 1001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1888 4984 164\\n1564 8917 15\\n150 15 2\\n1500 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 1515 67108865\\n6144 8192 67108864\\n8192 7057 67108864\\n6144 8192 16777217\\n8192 6044 16777217\\n\", \"1\\n2665 8192 31270788\\n\", \"1\\n1024 101 22212\\n\", \"1\\n1082 8192 384142\\n\", \"1\\n8192 5757 0001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1888 4984 154\\n1564 8917 15\\n150 15 2\\n1500 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 1515 67108865\\n6144 8192 67108864\\n8192 7057 67108864\\n6144 8192 16777217\\n8192 7716 16777217\\n\", \"1\\n2665 8192 47338777\\n\", \"1\\n1024 100 22212\\n\", \"1\\n1082 8192 451555\\n\", \"1\\n8192 9372 0001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n1500 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8192 6144 16777216\\n8192 8192 67108864\\n8192 1515 67108865\\n5724 8192 67108864\\n8192 7057 67108864\\n6144 8192 16777217\\n8192 7716 16777217\\n\", \"1\\n2047 8192 47338777\\n\", \"1\\n587 100 22212\\n\", \"1\\n1082 11856 451555\\n\", \"1\\n8192 12968 0001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 40\\n1 10000 1000\\n1 10000 10000\\n\", \"1\\n1528 8192 47338777\\n\", \"1\\n587 100 13408\\n\", \"1\\n1082 11856 799754\\n\", \"1\\n8192 12675 0001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 1\\n13 13 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 40\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8149 6144 16777216\\n8192 8192 67108864\\n8192 1515 67108865\\n5724 8192 67108864\\n8192 7057 67108864\\n6144 137 16777217\\n8192 7716 16777217\\n\", \"1\\n1528 14291 47338777\\n\", \"1\\n453 100 13408\\n\", \"1\\n1235 11856 799754\\n\", \"1\\n8192 6597 0001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n1 1 1\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 40\\n1 10000 1001\\n1 10000 10000\\n\", \"1\\n1528 14291 7097355\\n\", \"1\\n453 110 13408\\n\", \"1\\n1235 11856 674185\\n\", \"1\\n6182 6597 0001000\\n\", \"8\\n4256 8192 16777216\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n5724 8192 67108864\\n8192 7057 67108864\\n6144 137 16777217\\n8260 7716 16777217\\n\", \"1\\n1528 10800 7097355\\n\", \"1\\n453 110 17232\\n\", \"1\\n1033 11856 674185\\n\", \"1\\n6182 6024 0001000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n2 1 2\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 40\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n5724 8192 67108864\\n8192 7057 67108864\\n8726 137 16777217\\n8260 7716 16777217\\n\", \"1\\n2532 10800 7097355\\n\", \"1\\n639 110 17232\\n\", \"1\\n167 11856 674185\\n\", \"1\\n6182 6024 0101000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 8192 70000000\\n8192 8192 21916808\\n2 1 2\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 6\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n4256 8192 16777216\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n5724 8192 94149279\\n8192 7057 67108864\\n8726 137 16777217\\n8260 7716 16777217\\n\", \"1\\n2532 10800 13220378\\n\", \"1\\n639 110 17021\\n\", \"1\\n137 11856 674185\\n\", \"1\\n11676 6024 0101000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 9125 70000000\\n8192 8192 21916808\\n2 1 2\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 185 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 6\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n5724 8192 94149279\\n8192 7057 67108864\\n8726 137 16777217\\n8260 7716 16777217\\n\", \"1\\n2532 21499 13220378\\n\", \"1\\n639 010 17021\\n\", \"1\\n137 17022 674185\\n\", \"1\\n13096 6024 0101000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 9125 70000000\\n8192 8192 21916808\\n2 1 2\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 113 95\\n1992 1895 12\\n1189 4984 154\\n1564 8917 15\\n150 15 2\\n579 10 6\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n5724 8192 94149279\\n8192 7057 67108864\\n8726 134 16777217\\n8260 7716 16777217\\n\", \"1\\n2532 21499 4610583\\n\", \"1\\n639 011 17021\\n\", \"1\\n10 17022 674185\\n\", \"1\\n13096 11336 0101000\\n\", \"16\\n8192 8192 67108864\\n8192 8192 67108865\\n8192 9125 70000000\\n8192 8192 21916808\\n2 1 2\\n13 17 1\\n1000 1000 100\\n100 15 16\\n157 113 95\\n1992 1895 12\\n1189 4984 206\\n1564 8917 15\\n150 15 2\\n579 10 6\\n1 10000 1001\\n1 10000 10000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 94149279\\n8192 7057 67108864\\n8726 134 16777217\\n8260 7716 16777217\\n\", \"1\\n3792 21499 4610583\\n\", \"1\\n639 001 17021\\n\", \"1\\n1 17022 674185\\n\", \"1\\n13096 2256 0101000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 94149279\\n330 7057 67108864\\n8726 134 16777217\\n8260 7716 16777217\\n\", \"1\\n3792 21499 7379104\\n\", \"1\\n1178 001 17021\\n\", \"1\\n1 17022 716877\\n\", \"1\\n13096 814 0101000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 94149279\\n504 7057 67108864\\n8726 134 16777217\\n8260 7716 16777217\\n\", \"1\\n3792 21499 4342276\\n\", \"1\\n1284 001 17021\\n\", \"1\\n1 17022 146695\\n\", \"1\\n13096 814 1101000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 16777217\\n8260 7716 16777217\\n\", \"1\\n7286 21499 4342276\\n\", \"1\\n1284 011 17021\\n\", \"1\\n1 17022 285890\\n\", \"1\\n10909 814 1101000\\n\", \"8\\n4256 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n7286 21499 3701977\\n\", \"1\\n671 011 17021\\n\", \"1\\n1 17022 429379\\n\", \"1\\n10909 575 1101000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 16777216\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n7286 31827 3701977\\n\", \"1\\n671 011 4442\\n\", \"1\\n1 6435 429379\\n\", \"1\\n10909 355 1101000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n8192 11282 67108864\\n8192 1515 67108865\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n7286 31827 6180739\\n\", \"1\\n671 011 7638\\n\", \"1\\n2 6435 429379\\n\", \"1\\n10717 355 1101000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n8192 11282 67108864\\n13754 1515 67108865\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n7286 63109 6180739\\n\", \"1\\n136 011 7638\\n\", \"1\\n2 11315 429379\\n\", \"1\\n10717 59 1101000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n8192 11282 67108864\\n13754 1515 12973953\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n9725 63109 6180739\\n\", \"1\\n136 011 14309\\n\", \"1\\n2 15464 429379\\n\", \"1\\n4401 59 1101000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n9911 11282 67108864\\n13754 1515 12973953\\n3360 8192 13434627\\n504 7057 67108864\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n6826 63109 6180739\\n\", \"1\\n104 011 14309\\n\", \"1\\n2 15464 766584\\n\", \"1\\n4401 59 1001000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n9911 11282 67108864\\n13754 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n8464 63109 6180739\\n\", \"1\\n54 011 14309\\n\", \"1\\n4401 113 1001000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n9911 11282 67108864\\n18958 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n8726 134 6160311\\n8260 7716 16777217\\n\", \"1\\n8464 63109 1087172\\n\", \"1\\n59 011 14309\\n\", \"1\\n4401 154 1001000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 30806803\\n9911 11282 67108864\\n18958 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n8726 134 4198927\\n8260 7716 16777217\\n\", \"1\\n8464 27212 1087172\\n\", \"1\\n59 011 12542\\n\", \"1\\n5595 154 1001000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n9911 11282 67108864\\n18958 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n8726 134 4198927\\n8260 7716 16777217\\n\", \"1\\n8464 42204 1087172\\n\", \"1\\n98 011 12542\\n\", \"1\\n5595 87 1001000\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n9911 11282 67108864\\n18958 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n8726 60 4198927\\n8260 7716 16777217\\n\", \"1\\n8464 73376 1087172\\n\", \"1\\n98 111 12542\\n\", \"1\\n5595 87 1001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n9911 11282 67108864\\n18958 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n10561 60 4198927\\n8260 7716 16777217\\n\", \"1\\n12029 73376 1087172\\n\", \"1\\n98 101 12542\\n\", \"1\\n1981 87 1001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n9911 11282 67108864\\n3769 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n10561 60 4198927\\n8260 7716 16777217\\n\", \"1\\n12029 61314 1087172\\n\", \"1\\n98 101 9313\\n\", \"1\\n1981 118 1001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n9911 9809 67108864\\n3769 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n10561 60 4198927\\n8260 7716 16777217\\n\", \"1\\n12029 61314 1792457\\n\", \"1\\n156 101 9313\\n\", \"1\\n1981 118 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n9911 9809 67108864\\n3769 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n10561 60 5194098\\n8260 7716 16777217\\n\", \"1\\n17994 61314 1792457\\n\", \"1\\n156 101 7876\\n\", \"1\\n2915 118 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n16965 9809 67108864\\n3769 1515 12973953\\n3360 8192 13434627\\n504 7057 65027126\\n10561 60 5194098\\n8260 7716 16777217\\n\", \"1\\n33917 61314 1792457\\n\", \"1\\n156 001 7876\\n\", \"1\\n5517 118 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 32073943\\n16965 9809 67108864\\n3769 1515 12973953\\n3360 8192 13434627\\n504 7057 38336540\\n10561 60 5194098\\n8260 7716 16777217\\n\", \"1\\n33917 61314 1962389\\n\", \"1\\n156 001 2674\\n\", \"1\\n5517 215 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 50525613\\n16965 9809 67108864\\n3769 1515 12973953\\n3360 8192 13434627\\n504 7057 38336540\\n10561 60 5194098\\n8260 7716 16777217\\n\", \"1\\n156 011 2674\\n\", \"1\\n5517 291 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 50525613\\n16965 9809 67108864\\n3769 1515 12973953\\n3360 8192 4133925\\n504 7057 38336540\\n10561 60 5194098\\n8260 7716 16777217\\n\", \"1\\n120 001 2674\\n\", \"1\\n5517 213 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 50525613\\n16965 9809 67108864\\n3769 1515 12973953\\n3360 8192 4133925\\n504 7057 38336540\\n14891 60 5194098\\n8260 7716 16777217\\n\", \"1\\n120 001 1334\\n\", \"1\\n5517 237 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 50525613\\n26430 9809 67108864\\n3769 1515 12973953\\n3360 8192 4133925\\n504 7057 38336540\\n14891 60 5194098\\n8260 7716 16777217\\n\", \"1\\n1 001 1334\\n\", \"1\\n1606 237 0001100\\n\", \"8\\n7545 8192 11620828\\n8149 6144 50525613\\n26430 9809 67108864\\n3769 1515 12973953\\n3360 8192 4133925\\n504 7057 38336540\\n14891 60 2534780\\n8260 7716 16777217\\n\", \"1\\n2 001 1334\\n\", \"1\\n1606 215 0001100\\n\", \"8\\n7545 8192 11620828\\n804 6144 50525613\\n26430 9809 67108864\\n3769 1515 12973953\\n3360 8192 4133925\\n504 7057 38336540\\n14891 60 2534780\\n8260 7716 16777217\\n\", \"1\\n2 011 1334\\n\", \"1\\n1714 215 0001100\\n\", \"8\\n7545 8192 11620828\\n804 6144 50525613\\n24098 9809 67108864\\n3769 1515 12973953\\n3360 8192 4133925\\n504 7057 38336540\\n14891 60 2534780\\n8260 7716 16777217\\n\", \"1\\n2 111 1334\\n\"], \"outputs\": [\"\\nYES\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"YES\\nNO\\nYES\\nYES\\nYES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"YES\\nNO\\nNO\\nYES\\nNO\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"YES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"YES\\nNO\\nYES\\nYES\\nYES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\nNO\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nNO\\nNO\\nNO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\", \"NO\\n\"]}", "source": "primeintellect"}
|
For the New Year, Polycarp decided to send postcards to all his n friends. He wants to make postcards with his own hands. For this purpose, he has a sheet of paper of size w × h, which can be cut into pieces.
Polycarp can cut any sheet of paper w × h that he has in only two cases:
* If w is even, then he can cut the sheet in half and get two sheets of size w/2 × h;
* If h is even, then he can cut the sheet in half and get two sheets of size w × h/2;
If w and h are even at the same time, then Polycarp can cut the sheet according to any of the rules above.
After cutting a sheet of paper, the total number of sheets of paper is increased by 1.
Help Polycarp to find out if he can cut his sheet of size w × h at into n or more pieces, using only the rules described above.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
Each test case consists of one line containing three integers w, h, n (1 ≤ w, h ≤ 10^4, 1 ≤ n ≤ 10^9) — the width and height of the sheet Polycarp has and the number of friends he needs to send a postcard to.
Output
For each test case, output on a separate line:
* "YES", if it is possible to cut a sheet of size w × h into at least n pieces;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
5
2 2 3
3 3 2
5 10 2
11 13 1
1 4 4
Output
YES
NO
YES
YES
YES
Note
In the first test case, you can first cut the 2 × 2 sheet into two 2 × 1 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 1 × 1. We can choose any three of them and send them to our friends.
In the second test case, a 3 × 3 sheet cannot be cut, so it is impossible to get two sheets.
In the third test case, you can cut a 5 × 10 sheet into two 5 × 5 sheets.
In the fourth test case, there is no need to cut the sheet, since we only need one sheet.
In the fifth test case, you can first cut the 1 × 4 sheet into two 1 × 2 sheets, and then cut each of them into two more sheets. As a result, we get four sheets 1 × 1.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"3\\n1 1\\n1 500\\n500 250\\n\", \"4\\n2 3\\n2 2\\n3 1\\n1 3\\n\", \"37\\n30 16\\n22 37\\n37 43\\n25 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 14\\n25 11\\n16 14\\n28 31\\n49 45\\n48 24\\n28 20\\n21 19\\n43 49\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 10\\n14 22\\n\", \"1\\n828 434\\n\", \"6\\n156 130\\n198 180\\n133 195\\n121 112\\n148 169\\n196 160\\n\", \"2\\n496 492\\n481 407\\n\", \"5\\n41 197\\n36 180\\n39 192\\n44 104\\n10 161\\n\", \"8\\n36 151\\n43 187\\n37 189\\n46 186\\n44 146\\n73 37\\n37 73\\n557 17\\n\", \"1\\n404 905\\n\", \"1\\n939 879\\n\", \"6\\n169 106\\n140 102\\n177 169\\n144 163\\n139 194\\n196 172\\n\", \"7\\n149 38\\n114 15\\n120 32\\n161 39\\n140 34\\n104 20\\n173 28\\n\", \"32\\n33 20\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 24\\n34 48\\n30 17\\n44 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n15 10\\n27 46\\n20 38\\n20 32\\n50 34\\n19 18\\n17 39\\n45 17\\n\", \"1\\n459 704\\n\", \"1\\n651 410\\n\", \"3\\n998 997\\n1 1\\n1 2\\n\", \"1\\n762 765\\n\", \"1\\n991 983\\n\", \"2\\n441 401\\n467 430\\n\", \"6\\n103 39\\n161 13\\n177 45\\n116 34\\n193 28\\n172 35\\n\", \"6\\n38 188\\n18 158\\n27 139\\n38 154\\n44 137\\n49 185\\n\", \"1\\n1000 1000\\n\", \"1\\n1000 999\\n\", \"37\\n30 16\\n22 37\\n37 43\\n25 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 14\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 49\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 10\\n14 22\\n\", \"1\\n194 434\\n\", \"6\\n156 130\\n198 180\\n5 195\\n121 112\\n148 169\\n196 160\\n\", \"2\\n496 492\\n481 65\\n\", \"5\\n41 197\\n36 180\\n39 192\\n44 104\\n10 276\\n\", \"8\\n36 151\\n43 187\\n38 189\\n46 186\\n44 146\\n73 37\\n37 73\\n557 17\\n\", \"1\\n52 905\\n\", \"6\\n169 106\\n140 102\\n177 169\\n144 163\\n139 194\\n153 172\\n\", \"7\\n149 38\\n114 15\\n120 32\\n161 39\\n140 34\\n104 20\\n338 28\\n\", \"32\\n33 20\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 24\\n34 48\\n30 17\\n44 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n15 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 39\\n45 17\\n\", \"1\\n459 519\\n\", \"1\\n463 410\\n\", \"3\\n998 465\\n1 1\\n1 2\\n\", \"1\\n762 5\\n\", \"1\\n991 672\\n\", \"2\\n441 401\\n467 590\\n\", \"6\\n103 39\\n161 13\\n177 57\\n116 34\\n193 28\\n172 35\\n\", \"6\\n38 188\\n34 158\\n27 139\\n38 154\\n44 137\\n49 185\\n\", \"3\\n1 1\\n1 500\\n500 305\\n\", \"4\\n2 5\\n2 2\\n3 1\\n1 3\\n\", \"37\\n30 16\\n22 37\\n37 43\\n25 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 14\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 49\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 22\\n\", \"1\\n319 434\\n\", \"6\\n156 130\\n198 3\\n5 195\\n121 112\\n148 169\\n196 160\\n\", \"2\\n496 492\\n498 65\\n\", \"5\\n41 197\\n36 180\\n39 192\\n44 104\\n10 131\\n\", \"8\\n36 151\\n43 187\\n38 189\\n46 186\\n44 146\\n73 37\\n37 73\\n557 11\\n\", \"6\\n169 106\\n140 102\\n177 169\\n144 163\\n139 194\\n153 47\\n\", \"7\\n149 38\\n114 15\\n120 32\\n161 39\\n140 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 24\\n34 48\\n30 17\\n44 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n15 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 39\\n45 17\\n\", \"1\\n218 519\\n\", \"1\\n314 410\\n\", \"1\\n762 3\\n\", \"1\\n991 412\\n\", \"2\\n441 401\\n93 590\\n\", \"6\\n103 39\\n161 13\\n177 57\\n116 34\\n193 28\\n172 56\\n\", \"6\\n38 188\\n34 158\\n27 139\\n38 84\\n44 137\\n49 185\\n\", \"3\\n1 1\\n1 500\\n500 412\\n\", \"37\\n30 16\\n22 37\\n37 43\\n25 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 49\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 22\\n\", \"1\\n319 487\\n\", \"6\\n156 130\\n198 3\\n5 195\\n121 112\\n148 169\\n354 160\\n\", \"2\\n496 492\\n205 65\\n\", \"5\\n41 197\\n36 180\\n39 192\\n44 104\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 186\\n44 146\\n73 37\\n37 73\\n557 11\\n\", \"6\\n169 106\\n181 102\\n177 169\\n144 163\\n139 194\\n153 47\\n\", \"7\\n119 38\\n114 15\\n120 32\\n161 39\\n140 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n44 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n15 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 39\\n45 17\\n\", \"1\\n218 92\\n\", \"1\\n491 410\\n\", \"1\\n214 3\\n\", \"2\\n441 401\\n93 442\\n\", \"6\\n188 39\\n161 13\\n177 57\\n116 34\\n193 28\\n172 56\\n\", \"6\\n38 188\\n34 158\\n19 139\\n38 84\\n44 137\\n49 185\\n\", \"3\\n1 1\\n1 500\\n802 412\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 49\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 22\\n\", \"1\\n521 487\\n\", \"6\\n156 130\\n198 3\\n5 195\\n121 112\\n148 169\\n354 257\\n\", \"2\\n496 32\\n205 65\\n\", \"5\\n41 197\\n36 180\\n39 109\\n44 104\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 186\\n44 146\\n73 37\\n10 73\\n557 11\\n\", \"6\\n169 106\\n181 102\\n177 169\\n144 208\\n139 194\\n153 47\\n\", \"7\\n119 38\\n114 16\\n120 32\\n161 39\\n140 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n11 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n15 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 39\\n45 17\\n\", \"1\\n133 92\\n\", \"1\\n491 374\\n\", \"1\\n214 4\\n\", \"2\\n441 401\\n93 261\\n\", \"6\\n37 39\\n161 13\\n177 57\\n116 34\\n193 28\\n172 56\\n\", \"6\\n22 188\\n34 158\\n19 139\\n38 84\\n44 137\\n49 185\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 45\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 22\\n\", \"1\\n703 487\\n\", \"6\\n156 130\\n198 3\\n5 195\\n121 112\\n22 169\\n354 257\\n\", \"2\\n932 32\\n205 65\\n\", \"5\\n41 197\\n36 180\\n39 109\\n71 104\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 186\\n44 146\\n73 37\\n1 73\\n557 11\\n\", \"6\\n169 106\\n29 102\\n177 169\\n144 208\\n139 194\\n153 47\\n\", \"7\\n119 38\\n114 16\\n120 52\\n161 39\\n140 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n11 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n7 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 39\\n45 17\\n\", \"1\\n166 92\\n\", \"1\\n509 374\\n\", \"1\\n214 2\\n\", \"2\\n441 401\\n58 261\\n\", \"6\\n37 62\\n161 13\\n177 57\\n116 34\\n193 28\\n172 56\\n\", \"6\\n22 188\\n34 158\\n19 139\\n38 84\\n18 137\\n49 185\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 45\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 33\\n\", \"1\\n171 487\\n\", \"6\\n156 130\\n198 3\\n5 195\\n157 112\\n22 169\\n354 257\\n\", \"2\\n932 6\\n205 65\\n\", \"5\\n60 197\\n36 180\\n39 109\\n71 104\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 186\\n44 146\\n73 37\\n1 73\\n557 4\\n\", \"6\\n169 106\\n29 102\\n177 169\\n144 208\\n139 71\\n153 47\\n\", \"7\\n119 38\\n114 16\\n120 52\\n161 39\\n271 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n26 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n11 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n7 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 37\\n45 17\\n\", \"1\\n166 69\\n\", \"1\\n509 398\\n\", \"2\\n441 691\\n58 261\\n\", \"6\\n37 62\\n161 13\\n177 57\\n116 44\\n193 28\\n172 56\\n\", \"6\\n22 188\\n34 158\\n19 139\\n38 84\\n18 196\\n49 185\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n11 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 45\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 51\\n\", \"1\\n171 572\\n\", \"6\\n156 130\\n198 3\\n5 195\\n157 112\\n22 169\\n235 257\\n\", \"2\\n932 3\\n205 65\\n\", \"5\\n60 197\\n31 180\\n39 109\\n71 104\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 186\\n44 146\\n73 19\\n1 73\\n557 4\\n\", \"6\\n37 106\\n29 102\\n177 169\\n144 208\\n139 71\\n153 47\\n\", \"7\\n119 52\\n114 16\\n120 52\\n161 39\\n271 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n50 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n11 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n7 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 18\\n17 37\\n45 17\\n\", \"1\\n166 137\\n\", \"1\\n560 398\\n\", \"2\\n441 691\\n58 191\\n\", \"6\\n37 62\\n161 13\\n177 57\\n116 44\\n165 28\\n172 56\\n\", \"6\\n22 188\\n34 158\\n19 139\\n38 84\\n18 196\\n89 185\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n3 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 35\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 45\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 51\\n\", \"6\\n156 130\\n198 3\\n5 195\\n157 112\\n22 328\\n235 257\\n\", \"2\\n932 3\\n205 41\\n\", \"5\\n60 197\\n31 180\\n39 109\\n71 50\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 186\\n44 248\\n73 19\\n1 73\\n557 4\\n\", \"6\\n37 106\\n29 102\\n177 169\\n13 208\\n139 71\\n153 47\\n\", \"7\\n119 52\\n114 10\\n120 52\\n161 39\\n271 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n50 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n11 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n7 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 19\\n17 37\\n45 17\\n\", \"1\\n166 52\\n\", \"1\\n560 39\\n\", \"2\\n441 691\\n58 282\\n\", \"6\\n37 62\\n161 13\\n177 57\\n116 74\\n165 28\\n172 56\\n\", \"6\\n22 188\\n34 77\\n19 139\\n38 84\\n18 196\\n89 185\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n3 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 24\\n42 16\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 45\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 51\\n\", \"6\\n156 130\\n198 3\\n5 195\\n157 112\\n22 252\\n235 257\\n\", \"2\\n932 3\\n43 41\\n\", \"5\\n60 197\\n31 180\\n39 109\\n71 51\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 28\\n44 248\\n73 19\\n1 73\\n557 4\\n\", \"6\\n37 106\\n29 102\\n177 169\\n13 185\\n139 71\\n153 47\\n\", \"7\\n119 52\\n114 10\\n120 75\\n161 39\\n271 34\\n205 20\\n338 28\\n\", \"32\\n33 5\\n41 44\\n45 26\\n35 36\\n28 11\\n15 18\\n48 10\\n35 34\\n46 11\\n13 43\\n45 11\\n18 20\\n34 48\\n30 17\\n11 14\\n24 24\\n32 42\\n29 27\\n42 48\\n22 10\\n38 22\\n11 28\\n29 48\\n38 27\\n7 10\\n27 46\\n20 38\\n20 32\\n50 34\\n38 19\\n17 37\\n45 17\\n\", \"1\\n150 52\\n\", \"1\\n560 77\\n\", \"2\\n189 691\\n58 282\\n\", \"6\\n37 62\\n161 13\\n177 57\\n116 74\\n288 28\\n172 56\\n\", \"6\\n22 188\\n34 86\\n19 139\\n38 84\\n18 196\\n89 185\\n\", \"37\\n30 16\\n22 37\\n37 43\\n9 31\\n12 12\\n15 30\\n42 11\\n29 28\\n26 32\\n12 32\\n18 12\\n3 48\\n24 25\\n15 40\\n40 38\\n17 12\\n22 27\\n35 32\\n11 29\\n35 13\\n42 16\\n21 15\\n25 11\\n16 14\\n28 49\\n49 45\\n48 24\\n28 20\\n21 19\\n43 45\\n42 24\\n14 21\\n23 19\\n19 16\\n32 35\\n28 7\\n14 51\\n\", \"6\\n156 130\\n198 3\\n5 195\\n157 112\\n22 431\\n235 257\\n\", \"2\\n932 3\\n18 41\\n\", \"5\\n60 197\\n31 180\\n39 109\\n71 25\\n14 131\\n\", \"6\\n37 106\\n13 102\\n177 169\\n13 185\\n139 71\\n153 47\\n\", \"7\\n119 52\\n74 10\\n120 75\\n161 39\\n271 34\\n205 20\\n338 28\\n\", \"1\\n150 80\\n\", \"1\\n188 77\\n\", \"6\\n37 62\\n161 13\\n177 57\\n116 134\\n288 28\\n172 56\\n\", \"6\\n22 188\\n34 86\\n19 139\\n38 84\\n18 247\\n89 185\\n\", \"6\\n263 130\\n198 3\\n5 195\\n157 112\\n22 431\\n235 257\\n\", \"2\\n932 6\\n18 41\\n\", \"5\\n60 197\\n57 180\\n39 109\\n71 25\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 28\\n69 248\\n73 19\\n1 112\\n557 4\\n\", \"6\\n51 106\\n13 102\\n177 169\\n13 185\\n139 71\\n153 47\\n\", \"7\\n119 52\\n74 10\\n120 75\\n265 39\\n271 34\\n205 20\\n338 28\\n\", \"1\\n150 127\\n\", \"1\\n188 5\\n\", \"6\\n22 188\\n34 86\\n10 139\\n38 84\\n18 247\\n89 185\\n\", \"6\\n263 130\\n198 2\\n5 195\\n157 112\\n22 431\\n235 257\\n\", \"2\\n932 6\\n18 42\\n\", \"5\\n60 197\\n57 180\\n39 169\\n71 25\\n14 131\\n\", \"8\\n36 285\\n43 187\\n38 189\\n46 28\\n69 248\\n125 19\\n1 112\\n557 4\\n\", \"6\\n51 106\\n13 102\\n177 169\\n24 185\\n139 71\\n153 47\\n\", \"7\\n119 52\\n74 10\\n120 75\\n265 39\\n64 34\\n205 20\\n338 28\\n\", \"1\\n60 127\\n\", \"1\\n145 5\\n\", \"6\\n22 188\\n34 10\\n10 139\\n38 84\\n18 247\\n89 185\\n\", \"6\\n263 130\\n198 4\\n5 195\\n157 112\\n22 431\\n235 257\\n\", \"2\\n932 9\\n18 42\\n\", \"5\\n60 197\\n57 180\\n39 169\\n71 25\\n14 153\\n\", \"8\\n36 330\\n43 187\\n38 189\\n46 28\\n69 248\\n125 19\\n1 112\\n557 4\\n\", \"6\\n51 106\\n13 102\\n177 169\\n24 185\\n139 98\\n153 47\\n\", \"7\\n119 52\\n74 15\\n120 75\\n265 39\\n64 34\\n205 20\\n338 28\\n\", \"1\\n60 198\\n\", \"1\\n30 5\\n\", \"6\\n6 188\\n34 10\\n10 139\\n38 84\\n18 247\\n89 185\\n\", \"6\\n263 130\\n186 4\\n5 195\\n157 112\\n22 431\\n235 257\\n\", \"2\\n932 15\\n18 42\\n\", \"5\\n60 197\\n58 180\\n39 169\\n71 25\\n14 153\\n\", \"8\\n2 330\\n43 187\\n38 189\\n46 28\\n69 248\\n125 19\\n1 112\\n557 4\\n\", \"6\\n51 106\\n13 173\\n177 169\\n24 185\\n139 98\\n153 47\\n\", \"7\\n169 52\\n74 15\\n120 75\\n265 39\\n64 34\\n205 20\\n338 28\\n\", \"1\\n93 198\\n\", \"1\\n30 8\\n\", \"6\\n6 129\\n34 10\\n10 139\\n38 84\\n18 247\\n89 185\\n\", \"6\\n263 26\\n186 4\\n5 195\\n157 112\\n22 431\\n235 257\\n\", \"2\\n168 15\\n18 42\\n\", \"5\\n60 197\\n58 180\\n39 33\\n71 25\\n14 153\\n\", \"8\\n2 330\\n43 187\\n38 189\\n46 28\\n69 248\\n23 19\\n1 112\\n557 4\\n\", \"6\\n51 106\\n13 173\\n177 169\\n1 185\\n139 98\\n153 47\\n\", \"7\\n169 52\\n74 15\\n120 110\\n265 39\\n64 34\\n205 20\\n338 28\\n\", \"1\\n93 312\\n\", \"1\\n30 14\\n\", \"6\\n6 129\\n31 10\\n10 139\\n38 84\\n18 247\\n89 185\\n\", \"6\\n263 26\\n186 4\\n5 195\\n157 112\\n44 431\\n235 257\\n\", \"2\\n301 15\\n18 42\\n\", \"5\\n60 197\\n58 180\\n39 5\\n71 25\\n14 153\\n\", \"8\\n2 330\\n43 187\\n38 189\\n46 5\\n69 248\\n23 19\\n1 112\\n557 4\\n\", \"6\\n51 106\\n13 173\\n130 169\\n1 185\\n139 98\\n153 47\\n\", \"7\\n169 52\\n74 15\\n120 111\\n265 39\\n64 34\\n205 20\\n338 28\\n\", \"1\\n58 312\\n\", \"1\\n4 14\\n\"], \"outputs\": [\"\\n1\\n2\\n257950823\\n\", \"\\n4\\n3\\n1\\n2\\n\", \"500692159\\n20910845\\n885314984\\n124845875\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n29319235\\n150022141\\n593419315\\n429944114\\n179833379\\n698577389\\n475197132\\n378602653\\n486740789\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n740895036\\n652573020\\n\", \"888636661\\n\", \"567814382\\n854901202\\n539016936\\n430063302\\n717224051\\n17951434\\n\", \"116485411\\n440948900\\n\", \"108823857\\n454695427\\n134358398\\n446446956\\n122179023\\n\", \"929091785\\n702459752\\n42479847\\n196559214\\n865776926\\n801685809\\n873370071\\n823112467\\n\", \"188669952\\n\", \"956782639\\n\", \"342765823\\n591022461\\n63284704\\n539893464\\n809751744\\n922743455\\n\", \"519522526\\n513936082\\n644154123\\n701014853\\n899036550\\n951094693\\n218466103\\n\", \"475352134\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n867513788\\n689300842\\n2592746\\n267467184\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n696254206\\n47332619\\n154157194\\n161613255\\n102163198\\n333223713\\n493163714\\n57258109\\n\", \"198768780\\n\", \"374205605\\n\", \"258470413\\n1\\n2\\n\", \"784899191\\n\", \"90036032\\n\", \"629952830\\n169004723\\n\", \"425822080\\n290931466\\n447348855\\n601276541\\n399768990\\n498063852\\n\", \"426441393\\n204614662\\n74950768\\n954672123\\n514816121\\n145167864\\n\", \"211715064\\n\", \"444664353\\n\", \"500692159\\n20910845\\n885314984\\n124845875\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n29319235\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n486740789\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n740895036\\n652573020\\n\", \"206423962\\n\", \"567814382\\n854901202\\n783109870\\n430063302\\n717224051\\n17951434\\n\", \"116485411\\n679247729\\n\", \"108823857\\n454695427\\n134358398\\n446446956\\n100267500\\n\", \"929091785\\n702459752\\n732554705\\n196559214\\n865776926\\n801685809\\n873370071\\n823112467\\n\", \"356331112\\n\", \"342765823\\n591022461\\n63284704\\n539893464\\n809751744\\n903320395\\n\", \"519522526\\n513936082\\n644154123\\n701014853\\n899036550\\n951094693\\n615935535\\n\", \"475352134\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n867513788\\n689300842\\n2592746\\n267467184\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n696254206\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n493163714\\n57258109\\n\", \"267985372\\n\", \"77797794\\n\", \"426142650\\n1\\n2\\n\", \"202351486\\n\", \"968237803\\n\", \"629952830\\n906236109\\n\", \"425822080\\n290931466\\n905021329\\n601276541\\n399768990\\n498063852\\n\", \"426441393\\n352931527\\n74950768\\n954672123\\n514816121\\n145167864\\n\", \"1\\n2\\n559716741\\n\", \"6\\n3\\n1\\n2\\n\", \"500692159\\n20910845\\n885314984\\n124845875\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n29319235\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n486740789\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n652573020\\n\", \"513814894\\n\", \"567814382\\n19702\\n783109870\\n430063302\\n717224051\\n17951434\\n\", \"116485411\\n610999955\\n\", \"108823857\\n454695427\\n134358398\\n446446956\\n367554408\\n\", \"929091785\\n702459752\\n732554705\\n196559214\\n865776926\\n801685809\\n873370071\\n448666479\\n\", \"342765823\\n591022461\\n63284704\\n539893464\\n809751744\\n978171499\\n\", \"519522526\\n513936082\\n644154123\\n701014853\\n899036550\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n867513788\\n689300842\\n2592746\\n267467184\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n696254206\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n493163714\\n57258109\\n\", \"404961430\\n\", \"388724707\\n\", \"290704\\n\", \"487338822\\n\", \"629952830\\n191409032\\n\", \"425822080\\n290931466\\n905021329\\n601276541\\n399768990\\n783394011\\n\", \"426441393\\n352931527\\n74950768\\n319347847\\n514816121\\n145167864\\n\", \"1\\n2\\n457944837\\n\", \"500692159\\n20910845\\n885314984\\n124845875\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n486740789\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n652573020\\n\", \"414219210\\n\", \"567814382\\n19702\\n783109870\\n430063302\\n717224051\\n461101164\\n\", \"116485411\\n393475981\\n\", \"108823857\\n454695427\\n134358398\\n446446956\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n196559214\\n865776926\\n801685809\\n873370071\\n448666479\\n\", \"342765823\\n138285636\\n63284704\\n539893464\\n809751744\\n978171499\\n\", \"208308538\\n513936082\\n644154123\\n701014853\\n899036550\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n267467184\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n696254206\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n493163714\\n57258109\\n\", \"870451626\\n\", \"320441783\\n\", \"23006\\n\", \"629952830\\n274280098\\n\", \"115153737\\n290931466\\n905021329\\n601276541\\n399768990\\n783394011\\n\", \"426441393\\n352931527\\n528897296\\n319347847\\n514816121\\n145167864\\n\", \"1\\n2\\n796071264\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n486740789\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n652573020\\n\", \"454523531\\n\", \"567814382\\n19702\\n783109870\\n430063302\\n717224051\\n58437295\\n\", \"831634655\\n393475981\\n\", \"108823857\\n454695427\\n415482350\\n446446956\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n196559214\\n865776926\\n801685809\\n379371142\\n448666479\\n\", \"342765823\\n138285636\\n63284704\\n815754843\\n809751744\\n978171499\\n\", \"208308538\\n442134379\\n644154123\\n701014853\\n899036550\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n233667657\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n696254206\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n493163714\\n57258109\\n\", \"481994791\\n\", \"386056298\\n\", \"3266925\\n\", \"629952830\\n627428294\\n\", \"957947879\\n290931466\\n905021329\\n601276541\\n399768990\\n783394011\\n\", \"91437298\\n352931527\\n528897296\\n319347847\\n514816121\\n145167864\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n187554036\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n652573020\\n\", \"881627564\\n\", \"567814382\\n19702\\n783109870\\n430063302\\n158349967\\n58437295\\n\", \"891787998\\n393475981\\n\", \"108823857\\n454695427\\n415482350\\n908622732\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n196559214\\n865776926\\n801685809\\n2\\n448666479\\n\", \"342765823\\n970385704\\n63284704\\n815754843\\n809751744\\n978171499\\n\", \"208308538\\n442134379\\n600407091\\n701014853\\n899036550\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n233667657\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n602661\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n493163714\\n57258109\\n\", \"133938397\\n\", \"162576103\\n\", \"215\\n\", \"629952830\\n726532903\\n\", \"523096171\\n290931466\\n905021329\\n601276541\\n399768990\\n783394011\\n\", \"91437298\\n352931527\\n528897296\\n319347847\\n171162295\\n145167864\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n187554036\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n697113272\\n\", \"316533992\\n\", \"567814382\\n19702\\n783109870\\n779982034\\n158349967\\n58437295\\n\", \"39445736\\n393475981\\n\", \"109800314\\n454695427\\n415482350\\n908622732\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n196559214\\n865776926\\n801685809\\n2\\n57603270\\n\", \"342765823\\n970385704\\n63284704\\n815754843\\n177916843\\n978171499\\n\", \"208308538\\n442134379\\n600407091\\n701014853\\n133294130\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n472661039\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n233667657\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n602661\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n983703204\\n57258109\\n\", \"326271374\\n\", \"718273958\\n\", \"138050043\\n726532903\\n\", \"523096171\\n290931466\\n905021329\\n196673775\\n399768990\\n783394011\\n\", \"91437298\\n352931527\\n528897296\\n319347847\\n945488413\\n145167864\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n172806682\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n187554036\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n370486319\\n\", \"123497921\\n\", \"567814382\\n19702\\n783109870\\n779982034\\n158349967\\n190813257\\n\", \"434779\\n393475981\\n\", \"109800314\\n702796061\\n415482350\\n908622732\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n196559214\\n865776926\\n245171167\\n2\\n57603270\\n\", \"767365451\\n970385704\\n63284704\\n815754843\\n177916843\\n978171499\\n\", \"726075234\\n442134379\\n600407091\\n701014853\\n133294130\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n435907492\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n233667657\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n602661\\n47332619\\n154157194\\n161613255\\n102163198\\n836624297\\n983703204\\n57258109\\n\", \"340325158\\n\", \"649984913\\n\", \"138050043\\n381259916\\n\", \"523096171\\n290931466\\n905021329\\n196673775\\n184799598\\n783394011\\n\", \"91437298\\n352931527\\n528897296\\n319347847\\n945488413\\n678494946\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n365010933\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n664000967\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n187554036\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n370486319\\n\", \"567814382\\n19702\\n783109870\\n779982034\\n180118959\\n190813257\\n\", \"434779\\n989247386\\n\", \"109800314\\n702796061\\n415482350\\n467354644\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n196559214\\n72965521\\n245171167\\n2\\n57603270\\n\", \"767365451\\n970385704\\n63284704\\n671788629\\n177916843\\n978171499\\n\", \"726075234\\n499832077\\n600407091\\n701014853\\n133294130\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n435907492\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n233667657\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n602661\\n47332619\\n154157194\\n161613255\\n102163198\\n255992982\\n983703204\\n57258109\\n\", \"726277437\\n\", \"64460330\\n\", \"138050043\\n376937748\\n\", \"523096171\\n290931466\\n905021329\\n867972353\\n184799598\\n783394011\\n\", \"91437298\\n149088950\\n528897296\\n319347847\\n945488413\\n678494946\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n365010933\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n496401839\\n746333648\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n187554036\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n370486319\\n\", \"567814382\\n19702\\n783109870\\n779982034\\n386173145\\n190813257\\n\", \"434779\\n16229246\\n\", \"109800314\\n702796061\\n415482350\\n530787852\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n375594148\\n72965521\\n245171167\\n2\\n57603270\\n\", \"767365451\\n970385704\\n63284704\\n924145111\\n177916843\\n978171499\\n\", \"726075234\\n499832077\\n468610414\\n701014853\\n133294130\\n267759694\\n615935535\\n\", \"244410\\n170086427\\n363639095\\n674704496\\n865667198\\n134806806\\n37995993\\n753393037\\n735083411\\n333923785\\n366970062\\n472573539\\n689300842\\n2592746\\n233667657\\n200614161\\n453081314\\n156772147\\n751718033\\n179829755\\n462404021\\n974160834\\n45037792\\n526244741\\n602661\\n47332619\\n154157194\\n161613255\\n102163198\\n255992982\\n983703204\\n57258109\\n\", \"961016533\\n\", \"699006869\\n\", \"116365637\\n376937748\\n\", \"523096171\\n290931466\\n905021329\\n867972353\\n760488799\\n783394011\\n\", \"91437298\\n133692405\\n528897296\\n319347847\\n945488413\\n678494946\\n\", \"500692159\\n20910845\\n885314984\\n370792093\\n797588417\\n276240629\\n994345628\\n193018901\\n822918999\\n929948425\\n954416076\\n365010933\\n974670813\\n700658711\\n904391066\\n286530678\\n854861649\\n62149489\\n873376578\\n697824566\\n746333648\\n362803619\\n150022141\\n593419315\\n225560535\\n179833379\\n698577389\\n475197132\\n378602653\\n187554036\\n737338710\\n660483766\\n24492030\\n320420567\\n694451315\\n38871659\\n370486319\\n\", \"567814382\\n19702\\n783109870\\n779982034\\n763196598\\n190813257\\n\", \"434779\\n849646621\\n\", \"109800314\\n702796061\\n415482350\\n168218934\\n625913747\\n\", \"767365451\\n706150242\\n63284704\\n924145111\\n177916843\\n978171499\\n\", \"726075234\\n755338714\\n468610414\\n701014853\\n133294130\\n267759694\\n615935535\\n\", \"714645359\\n\", \"246043729\\n\", \"523096171\\n290931466\\n905021329\\n362175428\\n760488799\\n783394011\\n\", \"91437298\\n133692405\\n528897296\\n319347847\\n355272621\\n678494946\\n\", \"246879830\\n19702\\n783109870\\n779982034\\n763196598\\n190813257\\n\", \"39445736\\n849646621\\n\", \"109800314\\n414266002\\n415482350\\n168218934\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n375594148\\n594827313\\n245171167\\n2\\n57603270\\n\", \"378006534\\n706150242\\n63284704\\n924145111\\n177916843\\n978171499\\n\", \"726075234\\n755338714\\n468610414\\n548599438\\n133294130\\n267759694\\n615935535\\n\", \"233974669\\n\", \"259706350\\n\", \"91437298\\n133692405\\n682226512\\n319347847\\n355272621\\n678494946\\n\", \"246879830\\n199\\n783109870\\n779982034\\n763196598\\n190813257\\n\", \"39445736\\n113086158\\n\", \"109800314\\n414266002\\n328121170\\n168218934\\n625913747\\n\", \"952109840\\n702459752\\n732554705\\n375594148\\n594827313\\n695226456\\n2\\n57603270\\n\", \"378006534\\n706150242\\n63284704\\n600851742\\n177916843\\n978171499\\n\", \"726075234\\n755338714\\n468610414\\n548599438\\n91993876\\n267759694\\n615935535\\n\", \"965874331\\n\", \"91846046\\n\", \"91437298\\n704416474\\n682226512\\n319347847\\n355272621\\n678494946\\n\", \"246879830\\n2587597\\n783109870\\n779982034\\n763196598\\n190813257\\n\", \"859775268\\n113086158\\n\", \"109800314\\n414266002\\n328121170\\n168218934\\n728259644\\n\", \"580863103\\n702459752\\n732554705\\n375594148\\n594827313\\n695226456\\n2\\n57603270\\n\", \"378006534\\n706150242\\n63284704\\n600851742\\n513052108\\n978171499\\n\", \"726075234\\n573487651\\n468610414\\n548599438\\n91993876\\n267759694\\n615935535\\n\", \"757060918\\n\", \"166781\\n\", \"905737101\\n704416474\\n682226512\\n319347847\\n355272621\\n678494946\\n\", \"246879830\\n2145077\\n783109870\\n779982034\\n763196598\\n190813257\\n\", \"385150366\\n113086158\\n\", \"109800314\\n8351768\\n328121170\\n168218934\\n728259644\\n\", \"331\\n702459752\\n732554705\\n375594148\\n594827313\\n695226456\\n2\\n57603270\\n\", \"378006534\\n325039041\\n63284704\\n600851742\\n513052108\\n978171499\\n\", \"541623490\\n573487651\\n468610414\\n548599438\\n91993876\\n267759694\\n615935535\\n\", \"722079299\\n\", \"108520964\\n\", \"264899378\\n704416474\\n682226512\\n319347847\\n355272621\\n678494946\\n\", \"118493805\\n2145077\\n783109870\\n779982034\\n763196598\\n190813257\\n\", \"144645823\\n113086158\\n\", \"109800314\\n8351768\\n983612062\\n168218934\\n728259644\\n\", \"331\\n702459752\\n732554705\\n375594148\\n594827313\\n24492030\\n2\\n57603270\\n\", \"378006534\\n325039041\\n63284704\\n2\\n513052108\\n978171499\\n\", \"541623490\\n573487651\\n34041635\\n548599438\\n91993876\\n267759694\\n615935535\\n\", \"838694392\\n\", \"447631977\\n\", \"264899378\\n851984618\\n682226512\\n319347847\\n355272621\\n678494946\\n\", \"118493805\\n2145077\\n783109870\\n779982034\\n989177807\\n190813257\\n\", \"200649332\\n113086158\\n\", \"109800314\\n8351768\\n477491\\n168218934\\n728259644\\n\", \"331\\n702459752\\n732554705\\n925337\\n594827313\\n24492030\\n2\\n57603270\\n\", \"378006534\\n325039041\\n683281239\\n2\\n513052108\\n978171499\\n\", \"541623490\\n573487651\\n8758313\\n548599438\\n91993876\\n267759694\\n615935535\\n\", \"427261886\\n\", \"81853\\n\"]}", "source": "primeintellect"}
|
Gaurang has grown up in a mystical universe. He is faced by n consecutive 2D planes. He shoots a particle of decay age k at the planes.
A particle can pass through a plane directly, however, every plane produces an identical copy of the particle going in the opposite direction with a decay age k-1. If a particle has decay age equal to 1, it will NOT produce a copy.
For example, if there are two planes and a particle is shot with decay age 3 (towards the right), the process is as follows: (here, D(x) refers to a single particle with decay age x)
1. the first plane produces a D(2) to the left and lets D(3) continue on to the right;
2. the second plane produces a D(2) to the left and lets D(3) continue on to the right;
3. the first plane lets D(2) continue on to the left and produces a D(1) to the right;
4. the second plane lets D(1) continue on to the right (D(1) cannot produce any copies).
In total, the final multiset S of particles is \\{D(3), D(2), D(2), D(1)\}. (See notes for visual explanation of this test case.)
Gaurang is unable to cope up with the complexity of this situation when the number of planes is too large. Help Gaurang find the size of the multiset S, given n and k.
Since the size of the multiset can be very large, you have to output it modulo 10^9+7.
Note: Particles can go back and forth between the planes without colliding with each other.
Input
The first line of the input contains the number of test cases t (1 ≤ t ≤ 100). Then, t lines follow, each containing two integers n and k (1 ≤ n, k ≤ 1000).
Additionally, the sum of n over all test cases will not exceed 1000, and the sum of k over all test cases will not exceed 1000. All test cases in one test are different.
Output
Output t integers. The i-th of them should be equal to the answer to the i-th test case.
Examples
Input
4
2 3
2 2
3 1
1 3
Output
4
3
1
2
Input
3
1 1
1 500
500 250
Output
1
2
257950823
Note
Let us explain the first example with four test cases.
Test case 1: (n = 2, k = 3) is already explained in the problem statement.
See the below figure of this simulation. Each straight line with a different color represents the path of a different particle. As you can see, there are four distinct particles in the multiset. Note that the vertical spacing between reflected particles is for visual clarity only (as mentioned before, no two distinct particles collide with each other)
<image>
Test case 2: (n = 2, k = 2) is explained as follows:
1. the first plane produces a D(1) to the left and lets D(2) continue on to the right;
2. the second plane produces a D(1) to the left and lets D(2) continue on to the right;
3. the first plane lets D(1) continue on to the left (D(1) cannot produce any copies).
Total size of multiset obtained \\{D(1), D(1), D(2)\} is equal to three.
Test case 3: (n = 3, k = 1), there are three planes, but decay age is only one. So no new copies are produced while the one particle passes through the planes. Hence, the answer is one.
Test case 4: (n = 1, k = 3) there is only one plane. The particle produces a new copy to the left. The multiset \\{D(2), D(3)\} is of size two.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"\\\"RUn.exe O\\\" \\\"\\\" \\\" 2ne, \\\" two! . \\\" \\\"\\n\", \"firstarg second \\\"\\\" \\n\", \"\\\" \\\" \\n\", \"j \\n\", \"B\\n\", \"\\\"7\\\" \\\"W \\\" \\\"\\\" \\\"\\\" \\\"a \\\" \\\"\\\" \\\"\\\" \\\"\\\" y \\n\", \"A\\n\", \"\\\"\\\"\\n\", \"\\\"RUn.exe O\\\" \\\"\\\" \\\" 2ne, \\\" two! . \\\" \\\"\\n\", \"\\\"\\\" \\\"\\\" \\\". \\\" \\\"A\\\" \\\"\\\" \\\"\\\" \\\"\\\" k \\\"\\\" \\n\", \"Lii\\n\", \"\\\"\\\"\\n\", \"firstarg second \\\"\\\" \\n\", \"b \\n\", \"m Z \\\"\\\" \\\" p\\\"\\n\", \"\\\" \\\"\\n\", \"\\\"\\\" ZX \\\"\\\" \\\"\\\" \\\"b\\\" \\\"\\\" \\\" \\\" C \\\"\\\" \\\"\\\" \\\"\\\"\\n\", \"a \\\" \\\" a \\\"\\\" a \\n\", \"\\\" \\\" \\\"wu\\\" \\\"\\\" \\\" \\\" \\\"\\\" \\\"\\\" \\\"\\\" \\n\", \"\\\"\\\" N 3 \\\"\\\" \\\"4\\\" \\\"A\\\" \\\"k\\\" \\\" \\\" \\\"\\\" \\\"\\\" \\n\", \"i \\n\", \"C\\n\", \"@\\n\", \"\\\"RUn.exe N\\\" \\\"\\\" \\\" 2ne, \\\" two! . \\\" \\\"\\n\", \"iLi\\n\", \"firstarg escond \\\"\\\" \\n\", \"c \\n\", \"\\\"RUn.exe O\\\" \\\"\\\" \\\" 2ne- \\\" two! . \\\" \\\"\\n\", \"firstarg dnoces \\\"\\\" \\n\", \"h \\n\", \"D\\n\", \"?\\n\", \"iLh\\n\", \"firstarg dnocse \\\"\\\" \\n\", \"d \\n\", \"firstarg dnobes \\\"\\\" \\n\", \"k \\n\", \"=\\n\", \"hLh\\n\", \"firstarg dnocsf \\\"\\\" \\n\", \"e \\n\", \"fiastrrg dnobes \\\"\\\" \\n\", \"l \\n\", \"hhL\\n\", \"firstarg fscond \\\"\\\" \\n\", \"f \\n\", \"m \\n\", \"hiL\\n\", \"g \\n\", \"n \\n\", \"Lih\\n\", \"a \\n\", \"o \\n\", \"Lhh\\n\", \"` \\n\", \"p \\n\", \"Lhi\\n\", \"_ \\n\", \"q \\n\", \"Lhj\\n\", \"^ \\n\", \"r \\n\", \"ihL\\n\", \"] \\n\", \"s \\n\", \"hhM\\n\", \"t \\n\", \"hMh\\n\", \"u \\n\", \"gMh\\n\", \"v \\n\", \"gNh\\n\", \"w \\n\", \"fNh\\n\", \"x \\n\", \"fhN\\n\", \"y \\n\", \"hfN\\n\", \"z \\n\", \"hfM\\n\", \"{ \\n\", \"Mfh\\n\", \"| \\n\", \"ifM\\n\", \"} \\n\", \"Mfi\\n\", \"~ \\n\", \"Mei\\n\", \" \\n\", \"Mie\\n\", \" \\n\", \"Mje\\n\", \" \\n\", \"eiM\\n\", \" \\n\"], \"outputs\": [\"<RUn.exe O>\\n<>\\n< 2ne, >\\n<two!>\\n<.>\\n< >\\n\", \"<firstarg>\\n<second>\\n<>\\n\", \"< >\\n\", \"<j>\\n\", \"<B>\\n\", \"<7>\\n<W >\\n<>\\n<>\\n<a >\\n<>\\n<>\\n<>\\n<y>\\n\", \"<A>\\n\", \"<>\\n\", \"<RUn.exe O>\\n<>\\n< 2ne, >\\n<two!>\\n<.>\\n< >\\n\", \"<>\\n<>\\n<. >\\n<A>\\n<>\\n<>\\n<>\\n<k>\\n<>\\n\", \"<Lii>\\n\", \"<>\\n\", \"<firstarg>\\n<second>\\n<>\\n\", \"<b>\\n\", \"<m>\\n<Z>\\n<>\\n< p>\\n\", \"< >\\n\", \"<>\\n<ZX>\\n<>\\n<>\\n<b>\\n<>\\n< >\\n<C>\\n<>\\n<>\\n<>\\n\", \"<a>\\n< >\\n<a>\\n<>\\n<a>\\n\", \"< >\\n<wu>\\n<>\\n< >\\n<>\\n<>\\n<>\\n\", \"<>\\n<N>\\n<3>\\n<>\\n<4>\\n<A>\\n<k>\\n< >\\n<>\\n<>\\n\", \"<i>\\n\", \"<C>\\n\", \"<@>\\n\", \"<RUn.exe N>\\n<>\\n< 2ne, >\\n<two!>\\n<.>\\n< >\\n\", \"<iLi>\\n\", \"<firstarg>\\n<escond>\\n<>\\n\", \"<c>\\n\", \"<RUn.exe O>\\n<>\\n< 2ne- >\\n<two!>\\n<.>\\n< >\\n\", \"<firstarg>\\n<dnoces>\\n<>\\n\", \"<h>\\n\", \"<D>\\n\", \"<?>\\n\", \"<iLh>\\n\", \"<firstarg>\\n<dnocse>\\n<>\\n\", \"<d>\\n\", \"<firstarg>\\n<dnobes>\\n<>\\n\", \"<k>\\n\", \"<=>\\n\", \"<hLh>\\n\", \"<firstarg>\\n<dnocsf>\\n<>\\n\", \"<e>\\n\", \"<fiastrrg>\\n<dnobes>\\n<>\\n\", \"<l>\\n\", \"<hhL>\\n\", \"<firstarg>\\n<fscond>\\n<>\\n\", \"<f>\\n\", \"<m>\\n\", \"<hiL>\\n\", \"<g>\\n\", \"<n>\\n\", \"<Lih>\\n\", \"<a>\\n\", \"<o>\\n\", \"<Lhh>\\n\", \"<`>\\n\", \"<p>\\n\", \"<Lhi>\\n\", \"<_>\\n\", \"<q>\\n\", \"<Lhj>\\n\", \"<^>\\n\", \"<r>\\n\", \"<ihL>\\n\", \"<]>\\n\", \"<s>\\n\", \"<hhM>\\n\", \"<t>\\n\", \"<hMh>\\n\", \"<u>\\n\", \"<gMh>\\n\", \"<v>\\n\", \"<gNh>\\n\", \"<w>\\n\", \"<fNh>\\n\", \"<x>\\n\", \"<fhN>\\n\", \"<y>\\n\", \"<hfN>\\n\", \"<z>\\n\", \"<hfM>\\n\", \"<{>\\n\", \"<Mfh>\\n\", \"<|>\\n\", \"<ifM>\\n\", \"<}>\\n\", \"<Mfi>\\n\", \"<~>\\n\", \"<Mei>\\n\", \"<>\\n\", \"<Mie>\\n\", \"<>\\n\", \"<Mje>\\n\", \"<>\\n\", \"<eiM>\\n\", \"<>\\n\"]}", "source": "primeintellect"}
|
The problem describes the properties of a command line. The description somehow resembles the one you usually see in real operating systems. However, there are differences in the behavior. Please make sure you've read the statement attentively and use it as a formal document.
In the Pindows operating system a strings are the lexemes of the command line — the first of them is understood as the name of the program to run and the following lexemes are its arguments. For example, as we execute the command " run.exe one, two . ", we give four lexemes to the Pindows command line: "run.exe", "one,", "two", ".". More formally, if we run a command that can be represented as string s (that has no quotes), then the command line lexemes are maximal by inclusion substrings of string s that contain no spaces.
To send a string with spaces or an empty string as a command line lexeme, we can use double quotes. The block of characters that should be considered as one lexeme goes inside the quotes. Embedded quotes are prohibited — that is, for each occurrence of character """ we should be able to say clearly that the quotes are opening or closing. For example, as we run the command ""run.exe o" "" " ne, " two . " " ", we give six lexemes to the Pindows command line: "run.exe o", "" (an empty string), " ne, ", "two", ".", " " (a single space).
It is guaranteed that each lexeme of the command line is either surrounded by spaces on both sides or touches the corresponding command border. One of its consequences is: the opening brackets are either the first character of the string or there is a space to the left of them.
You have a string that consists of uppercase and lowercase English letters, digits, characters ".,?!"" and spaces. It is guaranteed that this string is a correct OS Pindows command line string. Print all lexemes of this command line string. Consider the character """ to be used only in order to denote a single block of characters into one command line lexeme. In particular, the consequence is that the given string has got an even number of such characters.
Input
The single line contains a non-empty string s. String s consists of at most 105 characters. Each character is either an uppercase or a lowercase English letter, or a digit, or one of the ".,?!"" signs, or a space.
It is guaranteed that the given string is some correct command line string of the OS Pindows. It is guaranteed that the given command line string contains at least one lexeme.
Output
In the first line print the first lexeme, in the second line print the second one and so on. To make the output clearer, print the "<" (less) character to the left of your lexemes and the ">" (more) character to the right. Print the lexemes in the order in which they occur in the command.
Please, follow the given output format strictly. For more clarifications on the output format see the test samples.
Examples
Input
"RUn.exe O" "" " 2ne, " two! . " "
Output
<RUn.exe O>
<>
< 2ne, >
<two!>
<.>
< >
Input
firstarg second ""
Output
<firstarg>
<second>
<>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"10 5\\n2 4 5 7 9\\n\", \"10 5\\n2 4 8 3 6\\n\", \"100 3\\n96 98 99\\n\", \"2 0\\n\", \"1000000000 10\\n1 2 3 5 6 8 9 123 874 1230\\n\", \"10 6\\n2 3 5 6 8 9\\n\", \"4 3\\n2 3 4\\n\", \"1000000000 10\\n2 3 5 6 8 9 123 874 1230 1000000000\\n\", \"10 9\\n2 3 4 5 6 7 8 9 10\\n\", \"10 1\\n10\\n\", \"8 3\\n2 3 4\\n\", \"100 7\\n2 3 5 6 8 9 100\\n\", \"5 2\\n4 5\\n\", \"4 2\\n2 3\\n\", \"100 3\\n97 98 99\\n\", \"10 3\\n1 4 6\\n\", \"50 20\\n22 33 17 23 27 5 26 31 41 20 8 24 6 3 4 29 40 25 13 16\\n\", \"123 12\\n35 95 47 99 79 122 58 94 31 57 18 10\\n\", \"10 10\\n7 6 4 2 5 10 8 3 9 1\\n\", \"10 1\\n1\\n\", \"12312 0\\n\", \"10 2\\n10 1\\n\", \"5 4\\n4 2 5 1\\n\", \"5 3\\n4 2 3\\n\", \"123 13\\n36 73 111 2 92 5 47 55 48 113 7 78 37\\n\", \"5 3\\n4 3 5\\n\", \"500 8\\n365 313 338 410 482 417 325 384\\n\", \"500 50\\n72 474 467 241 442 437 336 234 410 120 438 164 405 177 142 114 27 20 445 235 46 176 88 488 242 391 28 414 145 92 206 334 152 343 367 254 100 243 155 348 148 450 461 483 97 34 471 69 416 362\\n\", \"50 40\\n14 27 19 30 31 20 28 11 37 29 23 33 7 26 22 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 39 12 43 42 40 46\\n\", \"1000000000 10\\n2 4 10 18 40 42 49 58 59 60\\n\", \"500 3\\n18 62 445\\n\", \"2 1\\n1\\n\", \"1 1\\n1\\n\", \"100 3\\n4 5 6\\n\", \"10 5\\n1 3 5 7 9\\n\", \"9817239 1\\n6323187\\n\", \"10 4\\n1 2 4 5\\n\", \"100 3\\n98 99 100\\n\", \"10 6\\n2 3 5 6 10 9\\n\", \"123 12\\n35 95 47 99 79 53 58 94 31 57 18 10\\n\", \"1000000000 10\\n2 3 5 6 8 9 123 1522 1230 1000000000\\n\", \"10 9\\n2 3 4 5 6 7 11 9 10\\n\", \"8 3\\n1 3 4\\n\", \"100 7\\n2 3 5 6 8 15 100\\n\", \"5 2\\n4 1\\n\", \"50 20\\n22 12 17 23 27 5 26 31 41 20 8 24 6 3 4 29 40 25 13 16\\n\", \"10 10\\n7 6 4 2 5 10 8 3 13 1\\n\", \"10 2\\n12 1\\n\", \"6 3\\n4 2 3\\n\", \"123 13\\n36 73 111 2 92 5 47 55 48 113 8 78 37\\n\", \"50 40\\n14 27 19 30 31 8 28 11 37 29 23 33 7 26 22 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 39 12 43 42 40 46\\n\", \"1000000000 10\\n2 4 17 18 40 42 49 58 59 60\\n\", \"941 3\\n18 62 445\\n\", \"100 3\\n2 5 6\\n\", \"10 5\\n1 3 5 7 13\\n\", \"7 4\\n1 2 4 5\\n\", \"100 3\\n98 62 100\\n\", \"10 5\\n2 1 5 7 9\\n\", \"10 6\\n2 3 5 6 10 3\\n\", \"1000000000 10\\n2 3 5 6 8 9 123 1622 1230 1000000000\\n\", \"10 9\\n2 3 4 5 6 9 11 9 10\\n\", \"100 7\\n4 3 5 6 8 15 100\\n\", \"5 2\\n7 1\\n\", \"50 20\\n22 12 17 23 34 5 26 31 41 20 8 24 6 3 4 29 40 25 13 16\\n\", \"123 12\\n35 95 47 99 79 53 58 66 31 57 18 10\\n\", \"10 10\\n7 6 4 2 5 10 2 3 13 1\\n\", \"4 2\\n12 1\\n\", \"50 40\\n14 27 19 30 31 8 28 11 37 29 23 33 7 26 22 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 39 2 43 42 40 46\\n\", \"1000000000 10\\n2 4 17 18 40 42 49 58 59 84\\n\", \"941 3\\n17 62 445\\n\", \"100 3\\n2 7 6\\n\", \"100 3\\n98 12 100\\n\", \"10 5\\n2 1 5 10 9\\n\", \"1000000000 10\\n2 3 5 6 0 9 123 1622 1230 1000000000\\n\", \"100 7\\n7 3 5 6 8 15 100\\n\", \"50 20\\n22 12 17 23 34 5 26 31 41 20 8 24 6 3 4 29 40 25 24 16\\n\", \"123 12\\n35 95 18 99 79 53 58 66 31 57 18 10\\n\", \"10 10\\n7 6 4 2 5 15 2 3 13 1\\n\", \"4 2\\n1 1\\n\", \"50 40\\n14 27 19 30 31 8 28 11 37 29 23 33 7 26 22 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 40 46\\n\", \"1000000000 10\\n2 4 17 18 40 42 76 58 59 84\\n\", \"941 3\\n17 103 445\\n\", \"1000000000 10\\n2 1 5 6 0 9 123 1622 1230 1000000000\\n\", \"100 7\\n7 3 5 6 0 15 100\\n\", \"50 20\\n22 12 17 23 34 5 26 31 41 20 8 24 6 6 4 29 40 25 24 16\\n\", \"123 12\\n35 95 18 99 79 53 58 66 31 74 18 10\\n\", \"10 10\\n7 5 4 2 5 15 2 3 13 1\\n\", \"8 2\\n1 1\\n\", \"50 40\\n14 27 19 30 31 8 28 11 37 29 23 33 7 26 0 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 40 46\\n\", \"1000000000 10\\n4 4 17 18 40 42 76 58 59 84\\n\", \"933 3\\n17 103 445\\n\", \"000 7\\n7 3 5 6 0 15 100\\n\", \"50 20\\n22 12 17 23 34 3 26 31 41 20 8 24 6 6 4 29 40 25 24 16\\n\", \"123 12\\n35 95 18 99 79 53 58 66 31 74 18 7\\n\", \"10 10\\n7 5 4 2 5 15 4 3 13 1\\n\", \"8 2\\n1 2\\n\", \"50 40\\n0 27 19 30 31 8 28 11 37 29 23 33 7 26 0 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 40 46\\n\", \"1000000000 10\\n4 4 17 18 40 42 76 58 65 84\\n\", \"50 20\\n22 12 17 23 34 3 26 31 41 20 8 24 6 5 4 29 40 25 24 16\\n\", \"123 12\\n35 95 18 99 79 53 58 104 31 74 18 7\\n\", \"13 2\\n1 2\\n\", \"50 40\\n0 27 19 30 31 8 28 11 37 29 23 33 7 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 40 46\\n\", \"1000000000 10\\n4 4 17 18 66 42 76 58 65 84\\n\", \"123 12\\n35 95 18 99 79 53 58 104 1 74 18 7\\n\", \"50 40\\n0 36 19 30 31 8 28 11 37 29 23 33 7 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 40 46\\n\", \"123 12\\n35 96 18 99 79 53 58 104 1 74 18 7\\n\", \"50 40\\n0 60 19 30 31 8 28 11 37 29 23 33 7 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 40 46\\n\", \"91 12\\n35 96 18 99 79 53 58 104 1 74 18 7\\n\", \"50 40\\n0 60 19 30 31 8 28 11 37 29 23 33 7 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 73 46\\n\", \"91 12\\n35 96 18 99 79 53 58 104 1 74 18 1\\n\", \"50 40\\n0 60 19 30 31 8 28 11 37 29 23 33 10 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 73 46\\n\", \"50 40\\n0 60 19 10 31 8 28 11 37 29 23 33 10 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 73 46\\n\", \"50 40\\n0 60 19 10 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 5 50 4 45 44 25 44 2 43 42 73 46\\n\", \"50 40\\n0 60 19 10 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 47 36 38 2 48 9 41 8 6 50 4 45 44 25 44 2 43 42 73 46\\n\", \"50 40\\n0 60 19 10 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 38 36 38 2 48 9 41 8 6 50 4 45 44 25 44 2 43 42 73 46\\n\", \"50 40\\n0 60 19 10 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 38 36 38 2 48 9 41 8 6 50 4 45 44 25 44 2 65 42 73 46\\n\", \"50 40\\n0 60 19 10 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 38 36 38 2 48 9 41 8 6 50 4 45 44 25 44 3 65 42 73 46\\n\", \"50 40\\n0 60 19 10 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 38 36 38 2 89 9 41 8 6 50 4 45 44 25 44 3 65 42 73 46\\n\", \"50 40\\n0 60 19 1 31 16 28 11 37 29 23 33 10 26 1 16 1 6 18 3 38 36 38 2 89 9 41 8 6 50 4 45 44 25 44 3 65 42 73 46\\n\"], \"outputs\": [\"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\"]}", "source": "primeintellect"}
|
Little boy Petya loves stairs very much. But he is bored from simple going up and down them — he loves jumping over several stairs at a time. As he stands on some stair, he can either jump to the next one or jump over one or two stairs at a time. But some stairs are too dirty and Petya doesn't want to step on them.
Now Petya is on the first stair of the staircase, consisting of n stairs. He also knows the numbers of the dirty stairs of this staircase. Help Petya find out if he can jump through the entire staircase and reach the last stair number n without touching a dirty stair once.
One has to note that anyway Petya should step on the first and last stairs, so if the first or the last stair is dirty, then Petya cannot choose a path with clean steps only.
Input
The first line contains two integers n and m (1 ≤ n ≤ 109, 0 ≤ m ≤ 3000) — the number of stairs in the staircase and the number of dirty stairs, correspondingly. The second line contains m different space-separated integers d1, d2, ..., dm (1 ≤ di ≤ n) — the numbers of the dirty stairs (in an arbitrary order).
Output
Print "YES" if Petya can reach stair number n, stepping only on the clean stairs. Otherwise print "NO".
Examples
Input
10 5
2 4 8 3 6
Output
NO
Input
10 5
2 4 5 7 9
Output
YES
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1 1 1 -1 -1 2\\n\", \"5 1 2 0 1 2\\n\", \"487599125 469431740 316230350 -77 57 18\\n\", \"321575625 2929581 31407414 -40 -44 920902537044\\n\", \"5928 1508 4358 75 -4 794927060433551549\\n\", \"642762664 588605882 1 -47 82 8\\n\", \"1 1 1 1 1 0\\n\", \"147834 6 2565 15 -35 166779\\n\", \"910958510 60 98575 38 -99 97880\\n\", \"95 70 7 -36 -100 5\\n\", \"923 452 871 -95 -55 273135237285890\\n\", \"75081054 91 47131957 -94 -54 5588994022550344\\n\", \"568980902 147246752 87068387 -17 58 677739653\\n\", \"230182675 73108597 42152975 -72 -8 93667970058209518\\n\", \"976890548 675855343 988 -11 46 796041265897304\\n\", \"38 10 36 19 30 4054886\\n\", \"546978166 115293871 313560296 -33 54 215761558342792301\\n\", \"560010572 4172512 514044248 -78 13 97386\\n\", \"85 37 69 30 47 131\\n\", \"1000000000 1 2 -100 -100 1\\n\", \"67163467 36963416 50381 -49 -12 76558237\\n\", \"138971202 137695723 48931985 -28 -3 68901440898766\\n\", \"372903 106681 40781 54 -40 6188704\\n\", \"25699863 23288611 24796719 -45 46 437606836\\n\", \"61728 24280 17963 -19 81 652432745607745078\\n\", \"907122235 107269653 309181328 26 -64 242045007473044676\\n\", \"2 2 1 -2 -2 5\\n\", \"224 81 30 57 -13 8363\\n\", \"852525230 538352221 97088953 -12 98 9197937568\\n\", \"2 1 1 31 -74 2712360435504330\\n\", \"557911547 9 460221236 -58 -96 74518856\\n\", \"1000000000 1000000000 1000000000 100 -100 1000000000000000000\\n\", \"108774060 15274597 430014 -85 -94 6\\n\", \"900854530 82 7 30 -88 6797628981503799\\n\", \"713835677 404390162 67429 -91 10 178697004637242062\\n\", \"122740849 8646067 70003215 -100 -80 70\\n\", \"475875319 333393831 284835031 22 7 90332975949346\\n\", \"323544442 39059198 2970015 92 17 98\\n\", \"73221379 4311914 992324 65 -40 705623357422685593\\n\", \"7310962 7564 6333485 -45 41 81980903005818\\n\", \"804 658 177 -95 37 9\\n\", \"885849694 703278210 46391 33 23 965949118732\\n\", \"1710 654 941 -81 -37 1281183940\\n\", \"3 2 2 -100 -100 2\\n\", \"2 2 2 -36 94 9429569334\\n\", \"717485513 5935 3 -5 -67 28\\n\", \"672939 589365 391409 -54 -70 205083640\\n\", \"620330674 603592488 3 38 94 34309127789188\\n\", \"1000000000 1 1 1 1 1000000000000000000\\n\", \"185144 100489 52 32 -21 5752324832726786\\n\", \"487599125 469431740 316230350 -77 57 1\\n\", \"321575625 2929581 31407414 -40 -44 1519191219474\\n\", \"2663 1508 4358 75 -4 794927060433551549\\n\", \"642762664 1095286391 1 -47 82 8\\n\", \"147834 6 2565 2 -35 166779\\n\", \"95 58 7 -36 -100 5\\n\", \"923 452 145 -95 -55 273135237285890\\n\", \"225361 91 47131957 -94 -54 5588994022550344\\n\", \"568980902 147246752 87068387 -17 106 677739653\\n\", \"230182675 73108597 42152975 -60 -8 93667970058209518\\n\", \"976890548 675855343 716 -11 46 796041265897304\\n\", \"38 10 36 19 30 5836208\\n\", \"546978166 115293871 313560296 -33 54 335478541730507422\\n\", \"560010572 4172512 514044248 -78 13 393\\n\", \"85 37 69 47 47 131\\n\", \"1000000000 1 2 -100 -100 2\\n\", \"53287047 36963416 50381 -49 -12 76558237\\n\", \"138971202 137695723 48931985 -28 -3 104208678900501\\n\", \"372903 106681 60090 54 -40 6188704\\n\", \"25699863 23288611 24796719 -45 31 437606836\\n\", \"61728 24280 17963 -19 85 652432745607745078\\n\", \"907122235 107269653 309181328 26 -99 242045007473044676\\n\", \"224 81 30 84 -13 8363\\n\", \"852525230 183629206 97088953 -12 98 9197937568\\n\", \"2 1 1 31 -2 2712360435504330\\n\", \"557911547 18 460221236 -58 -96 74518856\\n\", \"1000000000 1000000000 1000000001 100 -100 1000000000000000000\\n\", \"108774060 15274597 705602 -85 -94 6\\n\", \"878821580 82 7 30 -88 6797628981503799\\n\", \"155385515 404390162 67429 -91 10 178697004637242062\\n\", \"122740849 8646067 37990796 -100 -80 70\\n\", \"927291879 333393831 284835031 22 7 90332975949346\\n\", \"323544442 22921761 2970015 92 17 98\\n\", \"121427897 4311914 992324 65 -40 705623357422685593\\n\", \"3969458 7564 6333485 -45 41 81980903005818\\n\", \"804 658 177 -95 49 9\\n\", \"885849694 703278210 46391 59 23 965949118732\\n\", \"1710 851 941 -81 -37 1281183940\\n\", \"856171624 5935 3 -5 -67 28\\n\", \"672939 589365 391409 -54 -70 335066546\\n\", \"620330674 603592488 3 38 94 28927873097115\\n\", \"1000000000 1 1 1 2 1000000000000000000\\n\", \"185144 100489 52 32 -5 5752324832726786\\n\", \"5 1 1 0 1 2\\n\", \"487599125 469431740 316230350 -77 18 1\\n\", \"321575625 2929581 31407414 -40 -44 1229786479249\\n\", \"2663 751 4358 75 -4 794927060433551549\\n\", \"642762664 1095286391 1 -47 82 2\\n\", \"147834 6 2565 2 -35 70061\\n\", \"95 58 7 -36 -198 5\\n\", \"923 702 145 -95 -55 273135237285890\\n\", \"225361 91 47131957 -94 -54 4244131932700081\\n\", \"568980902 147246752 87068387 -17 106 162650338\\n\", \"230182675 73108597 42152975 -60 -8 17474146509129810\\n\", \"525118217 675855343 716 -11 46 796041265897304\\n\", \"546978166 115293871 313560296 -17 54 335478541730507422\\n\", \"1 0 1 -1 -1 2\\n\", \"38 10 36 38 30 5836208\\n\"], \"outputs\": [\"1 1\\n\", \"3 1\\n\", \"320939970 167740992\\n\", \"320222592 65760999\\n\", \"4973 5148\\n\", \"355500874 409658689\\n\", \"1 1\\n\", \"54423 144570\\n\", \"304849180 291538135\\n\", \"85 82\\n\", \"563 142\\n\", \"6742019 52104963\\n\", \"150920864 281916196\\n\", \"34918692 197804272\\n\", \"652954007 789518296\\n\", \"18 36\\n\", \"353006839 497349709\\n\", \"11882888 530616750\\n\", \"74 38\\n\", \"999999904 999999905\\n\", \"23368224 65407811\\n\", \"110585553 85995539\\n\", \"161485 86089\\n\", \"24072870 13015404\\n\", \"3174 1169\\n\", \"23731316 525833901\\n\", \"1 2\\n\", \"130 205\\n\", \"84737577 321684009\\n\", \"1 1\\n\", \"246089810 106240697\\n\", \"969796608 969796608\\n\", \"98184736 83340099\\n\", \"66039616 641057009\\n\", \"244834060 560206120\\n\", \"80795619 19413318\\n\", \"441571464 288459461\\n\", \"105890973 69794440\\n\", \"62692638 21726334\\n\", \"5246110 6302893\\n\", \"270 173\\n\", \"16593182 13087113\\n\", \"1568 945\\n\", \"1 1\\n\", \"1 1\\n\", \"71683921 71676253\\n\", \"503747 218115\\n\", \"200990066 258175045\\n\", \"168318977 168318977\\n\", \"56326 173503\\n\", \"279895503 126694247\\n\", \"120223512 198409074\\n\", \"389 1509\\n\", \"320528807 510768777\\n\", \"16002 56766\\n\", \"73 82\\n\", \"66 765\\n\", \"27230 88653\\n\", \"143912592 374499854\\n\", \"16750976 172064165\\n\", \"2626187 139190204\\n\", \"12 24\\n\", \"418606322 525783167\\n\", \"380399702 330296629\\n\", \"74 21\\n\", \"999999617 999999618\\n\", \"19953107 44768397\\n\", \"3332809 58377494\\n\", \"283847 227760\\n\", \"10347180 14352102\\n\", \"22898 11189\\n\", \"633770521 244700421\\n\", \"1 67\\n\", \"417513812 156658029\\n\", \"1 1\\n\", \"93759711 511822136\\n\", \"599261184 599261185\\n\", \"65363776 50794727\\n\", \"435298056 502362319\\n\", \"85912110 136087114\\n\", \"49959627 79305756\\n\", \"795972506 238859718\\n\", \"57661599 37702503\\n\", \"22445520 47409295\\n\", \"2625572 1982539\\n\", \"678 689\\n\", \"469992994 514074487\\n\", \"777 1667\\n\", \"219535425 219527757\\n\", \"262555 304876\\n\", \"438322854 50543531\\n\", \"138115585 138115585\\n\", \"133366 83543\\n\", \"3 5\\n\", \"279895503 126694208\\n\", \"119400263 144296725\\n\", \"56 1933\\n\", \"144091653 334330849\\n\", \"127171 50651\\n\", \"52 46\\n\", \"32 481\\n\", \"120860 200838\\n\", \"46382203 77863842\\n\", \"131451882 166442130\\n\", \"82039669 207099627\\n\", \"545631344 304908185\\n\", \"1 1\\n\", \"12 24\\n\"]}", "source": "primeintellect"}
|
Our bear's forest has a checkered field. The checkered field is an n × n table, the rows are numbered from 1 to n from top to bottom, the columns are numbered from 1 to n from left to right. Let's denote a cell of the field on the intersection of row x and column y by record (x, y). Each cell of the field contains growing raspberry, at that, the cell (x, y) of the field contains x + y raspberry bushes.
The bear came out to walk across the field. At the beginning of the walk his speed is (dx, dy). Then the bear spends exactly t seconds on the field. Each second the following takes place:
* Let's suppose that at the current moment the bear is in cell (x, y).
* First the bear eats the raspberry from all the bushes he has in the current cell. After the bear eats the raspberry from k bushes, he increases each component of his speed by k. In other words, if before eating the k bushes of raspberry his speed was (dx, dy), then after eating the berry his speed equals (dx + k, dy + k).
* Let's denote the current speed of the bear (dx, dy) (it was increased after the previous step). Then the bear moves from cell (x, y) to cell (((x + dx - 1) mod n) + 1, ((y + dy - 1) mod n) + 1).
* Then one additional raspberry bush grows in each cell of the field.
You task is to predict the bear's actions. Find the cell he ends up in if he starts from cell (sx, sy). Assume that each bush has infinitely much raspberry and the bear will never eat all of it.
Input
The first line of the input contains six space-separated integers: n, sx, sy, dx, dy, t (1 ≤ n ≤ 109; 1 ≤ sx, sy ≤ n; - 100 ≤ dx, dy ≤ 100; 0 ≤ t ≤ 1018).
Output
Print two integers — the coordinates of the cell the bear will end up in after t seconds.
Examples
Input
5 1 2 0 1 2
Output
3 1
Input
1 1 1 -1 -1 2
Output
1 1
Note
Operation a mod b means taking the remainder after dividing a by b. Note that the result of the operation is always non-negative. For example, ( - 1) mod 3 = 2.
In the first sample before the first move the speed vector will equal (3,4) and the bear will get to cell (4,1). Before the second move the speed vector will equal (9,10) and he bear will get to cell (3,1). Don't forget that at the second move, the number of berry bushes increased by 1.
In the second sample before the first move the speed vector will equal (1,1) and the bear will get to cell (1,1). Before the second move, the speed vector will equal (4,4) and the bear will get to cell (1,1). Don't forget that at the second move, the number of berry bushes increased by 1.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"124356983594583453458888889\\n\", \"4\\n\", \"464\\n\", \"13\\n\", \"2\\n\", \"64\\n\", \"85447\\n\", \"578487\\n\", \"2563\\n\", \"1\\n\", \"192329\\n\", \"51494\\n\", \"10\\n\", \"71752\\n\", \"26232\\n\", \"83\\n\", \"247\\n\", \"584660\\n\", \"7854\\n\", \"8\\n\", \"971836\\n\", \"52577\\n\", \"33\\n\", \"956\\n\", \"12\\n\", \"0\\n\", \"18\\n\", \"28\\n\", \"25\\n\", \"3\\n\", \"66\\n\", \"137471\\n\", \"1134974\\n\", \"76184\\n\", \"67673\\n\", \"94756\\n\", \"40485\\n\", \"67\\n\", \"132\\n\", \"654269\\n\", \"6087\\n\", \"7\\n\", \"1236642\\n\", \"72976\\n\", \"223\\n\", \"21\\n\", \"6\\n\", \"43\\n\", \"5\\n\", \"34\\n\", \"257934\\n\", \"349813\\n\", \"35\\n\", \"8904\\n\", \"75783\\n\", \"73482\\n\", \"27131\\n\", \"55\\n\", \"59\\n\", \"1068905\\n\", \"11577\\n\", \"9\\n\", \"1528132\\n\", \"40225\\n\", \"31\\n\", \"17\\n\", \"69\\n\", \"26\\n\", \"23\\n\", \"173406\\n\", \"41122\\n\", \"58\\n\", \"14041\\n\", \"144173\\n\", \"29723\\n\", \"24404\\n\", \"15\\n\", \"62\\n\", \"1580332\\n\", \"19688\\n\", \"19\\n\", \"1715856\\n\", \"20769\\n\", \"22\\n\", \"49\\n\", \"42\\n\", \"81233\\n\", \"1654\\n\", \"70\\n\", \"16473\\n\", \"247390\\n\", \"15942\\n\", \"5625\\n\", \"16\\n\", \"44\\n\", \"2960294\\n\", \"35307\\n\", \"11\\n\", \"2663305\\n\", \"17588\\n\", \"50\\n\", \"75\\n\", \"76\\n\", \"156310\\n\", \"2853\\n\", \"118\\n\", \"32707\\n\", \"416508\\n\", \"29615\\n\", \"2585\\n\", \"14\\n\", \"86\\n\", \"492120\\n\", \"30050\\n\", \"3158263\\n\", \"13625\\n\", \"87\\n\", \"121\\n\", \"117\\n\", \"226266\\n\", \"30\\n\"], \"outputs\": [\"0\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Fedya studies in a gymnasium. Fedya's maths hometask is to calculate the following expression:
(1n + 2n + 3n + 4n) mod 5
for given value of n. Fedya managed to complete the task. Can you? Note that given number n can be extremely large (e.g. it can exceed any integer type of your programming language).
Input
The single line contains a single integer n (0 ≤ n ≤ 10105). The number doesn't contain any leading zeroes.
Output
Print the value of the expression without leading zeros.
Examples
Input
4
Output
4
Input
124356983594583453458888889
Output
0
Note
Operation x mod y means taking remainder after division x by y.
Note to the first sample:
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"5\\n1 2 4 5 3\\n\", \"3\\n2118 2118 2118\\n\", \"5\\n763 763 763 763 763\\n\", \"10\\n5938 4836 5938 5938 4836 4836 2780 2780 1495 4836\\n\", \"10\\n4972 4972 4972 4858 4858 4972 4972 4972 4858 4972\\n\", \"5\\n3581 3581 305 305 3581\\n\", \"4\\n2440 2440 2440 2440\\n\", \"10\\n8097 8097 8097 8097 8097 8097 8097 8097 8097 8097\\n\", \"4\\n332 2714 2420 2714\\n\", \"4\\n1178 1178 2577 2577\\n\", \"10\\n1620 8260 1620 3994 3994 8260 8260 1620 1620 3994\\n\", \"5\\n4136 1826 4136 1826 1826\\n\", \"3\\n140 989 2895\\n\", \"10\\n6090 3360 6090 6313 1608 6313 4087 3360 1608 1608\\n\", \"3\\n2221 1976 2221\\n\", \"3\\n2118 2118 3573\\n\", \"5\\n763 763 763 122 763\\n\", \"10\\n5938 4836 5938 5938 4836 4836 2780 2051 1495 4836\\n\", \"10\\n4972 4972 9297 4858 4858 4972 4972 4972 4858 4972\\n\", \"4\\n2440 1779 2440 2440\\n\", \"10\\n8097 8097 8097 14160 8097 8097 8097 8097 8097 8097\\n\", \"10\\n1620 8260 1620 3994 3994 8260 8260 1620 1620 794\\n\", \"5\\n4136 1826 4136 1509 1826\\n\", \"10\\n6090 3360 6090 6313 1608 6313 3960 3360 1608 1608\\n\", \"10\\n4972 4972 9297 4858 3149 4972 4972 4972 4858 4972\\n\", \"10\\n8097 8097 8097 14160 8097 8097 8097 8097 8097 4894\\n\", \"10\\n6335 4836 5938 5938 4836 4836 2780 2051 1495 1044\\n\", \"10\\n4972 4972 9297 9120 3149 4972 4972 4972 4858 4972\\n\", \"10\\n8097 8097 8097 14160 8097 8097 8097 8097 9062 4894\\n\", \"10\\n6335 4836 5938 5938 4836 4081 2780 2051 1495 1044\\n\", \"10\\n8097 8097 8097 14160 8097 5098 8097 8097 9062 4894\\n\", \"5\\n5957 3581 305 305 3581\\n\", \"4\\n332 2714 4502 2714\\n\", \"4\\n1178 1178 205 2577\\n\", \"3\\n236 989 2895\\n\", \"3\\n2221 1152 2221\\n\", \"3\\n2118 3823 3573\\n\", \"5\\n763 763 1128 122 763\\n\", \"10\\n6335 4836 5938 5938 4836 4836 2780 2051 1495 4836\\n\", \"5\\n5957 3581 125 305 3581\\n\", \"4\\n2440 1779 2440 1853\\n\", \"4\\n332 4395 4502 2714\\n\", \"4\\n595 1178 205 2577\\n\", \"10\\n1164 8260 1620 3994 3994 8260 8260 1620 1620 794\\n\", \"5\\n4136 1826 4866 1509 1826\\n\", \"3\\n236 1912 2895\\n\", \"10\\n6090 4643 6090 6313 1608 6313 3960 3360 1608 1608\\n\", \"3\\n2221 1152 872\\n\", \"3\\n2118 5494 3573\\n\", \"5\\n763 1335 1128 122 763\\n\", \"5\\n5957 3581 125 197 3581\\n\", \"4\\n2440 1779 1190 1853\\n\", \"4\\n332 4395 2422 2714\\n\", \"4\\n595 1178 205 2157\\n\", \"10\\n1164 163 1620 3994 3994 8260 8260 1620 1620 794\\n\", \"5\\n4136 1826 6204 1509 1826\\n\", \"3\\n236 170 2895\\n\", \"10\\n6090 4643 6090 6313 1608 6313 975 3360 1608 1608\\n\", \"3\\n2221 1152 70\\n\", \"3\\n2118 513 3573\\n\", \"5\\n904 1335 1128 122 763\\n\", \"10\\n4972 4972 9297 9120 3149 9058 4972 4972 4858 4972\\n\", \"5\\n10529 3581 125 197 3581\\n\", \"4\\n2440 1779 1190 1057\\n\", \"4\\n332 4395 436 2714\\n\", \"4\\n595 1178 45 2157\\n\", \"10\\n1164 163 1620 3994 3994 8260 3820 1620 1620 794\\n\", \"5\\n4136 959 6204 1509 1826\\n\", \"3\\n236 93 2895\\n\", \"10\\n6090 5692 6090 6313 1608 6313 975 3360 1608 1608\\n\", \"3\\n2221 1152 39\\n\", \"3\\n2118 513 690\\n\", \"5\\n989 1335 1128 122 763\\n\", \"10\\n6335 4836 5938 1922 4836 4081 2780 2051 1495 1044\\n\", \"10\\n4972 4972 3215 9120 3149 9058 4972 4972 4858 4972\\n\", \"5\\n10529 3581 125 40 3581\\n\", \"4\\n1789 1779 1190 1057\\n\", \"10\\n8097 8097 8097 14160 8097 5098 8097 8097 273 4894\\n\"], \"outputs\": [\"7\\n\", \"3\\n\", \"10\\n\", \"21\\n\", \"28\\n\", \"8\\n\", \"6\\n\", \"45\\n\", \"5\\n\", \"6\\n\", \"19\\n\", \"8\\n\", \"3\\n\", \"19\\n\", \"3\\n\", \"3\\n\", \"8\\n\", \"20\\n\", \"28\\n\", \"5\\n\", \"45\\n\", \"21\\n\", \"7\\n\", \"19\\n\", \"27\\n\", \"38\\n\", \"18\\n\", \"32\\n\", \"26\\n\", \"17\\n\", \"23\\n\", \"8\\n\", \"5\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"8\\n\", \"20\\n\", \"7\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"19\\n\", \"7\\n\", \"3\\n\", \"19\\n\", \"3\\n\", \"3\\n\", \"8\\n\", \"7\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"21\\n\", \"7\\n\", \"3\\n\", \"19\\n\", \"3\\n\", \"3\\n\", \"7\\n\", \"27\\n\", \"7\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"20\\n\", \"7\\n\", \"3\\n\", \"19\\n\", \"3\\n\", \"3\\n\", \"7\\n\", \"17\\n\", \"27\\n\", \"7\\n\", \"5\\n\", \"27\\n\"]}", "source": "primeintellect"}
|
Everyone knows that long ago on the territory of present-day Berland there lived Bindian tribes. Their capital was surrounded by n hills, forming a circle. On each hill there was a watchman, who watched the neighbourhood day and night.
In case of any danger the watchman could make a fire on the hill. One watchman could see the signal of another watchman, if on the circle arc connecting the two hills there was no hill higher than any of the two. As for any two hills there are two different circle arcs connecting them, the signal was seen if the above mentioned condition was satisfied on at least one of the arcs. For example, for any two neighbouring watchmen it is true that the signal of one will be seen by the other.
An important characteristics of this watch system was the amount of pairs of watchmen able to see each other's signals. You are to find this amount by the given heights of the hills.
Input
The first line of the input data contains an integer number n (3 ≤ n ≤ 106), n — the amount of hills around the capital. The second line contains n numbers — heights of the hills in clockwise order. All height numbers are integer and lie between 1 and 109.
Output
Print the required amount of pairs.
Examples
Input
5
1 2 4 5 3
Output
7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"12 5 3\\n((()())(()))\\nRRDLD\\n\", \"8 8 8\\n(())()()\\nLLLLLLDD\\n\", \"8 4 5\\n(())()()\\nRDLD\\n\", \"88 33 12\\n(())((((())()((()())())())(((())())(())()())(()))((()())())())(((())()())(())()())()()()\\nLLLRRLRDRDRLDDLLRDLLDRLRDDLDRDLRR\\n\", \"14 8 13\\n((())())((()))\\nDLRLLRLR\\n\", \"28 13 16\\n(()()())(()()())(())(())()()\\nLRLDRRRRRLLLR\\n\", \"70 33 26\\n((()(())()())((())())(()())(())())((()((()())()())())()()(())())(()())\\nDLDRRRLRLDLRLLRDDRLRRLLLRDRLRLDRL\\n\", \"50 32 32\\n(()()())(())(())((()())())((())())((()())())(())()\\nLRLLLRDRRDLRRRLRLLDDRLLRDLRDLRLD\\n\", \"52 24 39\\n((()(()())(()())()())()())((()())(())())(())(()())()\\nDRRDLDRLRRLLRRDRRLDRRLLL\\n\", \"46 3 11\\n(()()(())())(()())((()((())())(()())(())())())\\nDDD\\n\", \"26 3 15\\n((())())(((())()()))(())()\\nRDL\\n\", \"38 8 26\\n((((())())(()))(()()))(((())())())()()\\nDDDLRLDR\\n\", \"30 18 15\\n(()((()()())()(())())())()()()\\nRRRLRRRLRRDLLLDRDR\\n\", \"48 33 11\\n((((())())((()()())())()()(()()))()(()())())()()\\nRLRDLDRLLLRRRLRDLRLDDRRDRLRRDRLRD\\n\", \"24 15 14\\n((()())()()())(())()()()\\nLDRRLDLDRRDDLRL\\n\", \"78 33 22\\n(((()((()()())())()()())((()())()())(())())(((((())())()())()())(())())())()()\\nRDRRRRRLDRDLDRLLLLDRDRRRDLDRDLLRD\\n\", \"58 3 22\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nLLR\\n\", \"34 8 20\\n(())((()())()((())())()()())()()()\\nRLLDLRRL\\n\", \"16 2 10\\n(((())())())()()\\nLD\\n\", \"96 37 18\\n((()()()())((((())()())())(())()())()()())(((())()(()(())())()()())(())())((()())()()())(()())()\\nDDLRRDDLDLRDDDRLDLRRDDDLLDRRRDDLDLLRL\\n\", \"66 55 24\\n(((())(((()())()()))(()())(()())())(())((()())())(()()())())()()()\\nRDLRLRRRLRDLRRLLDDRDRRDLRLDRRDRDLRDDLLRRDRDRLRRLLLDLRRR\\n\", \"84 18 78\\n(())(((()(()))()((((()())())(()())())()())((()())())())(((())(())())(())())())()()()\\nLLLRDDLRDRLDDLLRRL\\n\", \"32 6 19\\n((()())((())())())((())()(()))()\\nLDRLRR\\n\", \"68 34 8\\n((()(()())()())(()))((()())()())((()()())())(((())(()))(())()(())())\\nDLRRLRRRDLLDLLDDDLRRLRLRRRDDRLRRLL\\n\", \"56 43 9\\n(((((())())(()()))()()()())(()()(()))(()())(())())()()()\\nRLRLDLRLLRLRLDLLRLRRLLLRLRRLDLDRDLLRLRRLLDR\\n\", \"64 19 15\\n((((())((())())()())(())())(()())(()())())((()()())(())())()()()\\nDRRLRLRDDDDLLDRLRLD\\n\", \"36 11 36\\n(()()()()())((())())(()()())((())())\\nLDLRLLLLRLR\\n\", \"22 9 12\\n(()())((()()())())()()\\nRDLLLRDRL\\n\", \"6 4 1\\n()()()\\nDRRD\\n\", \"20 16 3\\n(()()())()(())()()()\\nLDRRRRRRLRLRLLLL\\n\", \"44 13 42\\n((()()())()()()())(((()()())())()())(()())()\\nLRRRLLDRDLDLR\\n\", \"62 34 43\\n(()((()())()()))(((())())()(()())(())())((())(()(()())()))()()\\nRLDDDDDDLRDLLRLDRLLDLRLDLLDRLLRRLL\\n\", \"82 16 6\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nRLLLLRRDDRRLRRRL\\n\", \"8 2 4\\n(())()()\\nRR\\n\", \"98 38 40\\n((()((((()))(())(()(())))))((())()())(())()())((((()())(((()()))()))()(())()()())())((()))(())()()\\nLRLRRDLDDRRLRDRDDLDRDLDRDLRLRLRLRLRLRR\\n\", \"10 3 3\\n(())((()))\\nDRD\\n\", \"90 44 6\\n(((((())()())(((()())())())()()))(()())((())()())(()())((())())(()()())())(())((())())()()\\nRLDLRRLLDRDDDLRDRRDLLRRDDDDLRLRDRLLDRDLRDDRR\\n\", \"40 22 35\\n(((()()()())()()())((())())()(())())()()\\nDRRLDRLRLLLDLLLDRLLRLD\\n\", \"54 22 3\\n(((()())(())()())((()())())())((())((()()())()())())()\\nLRLRDLRDLLRLDRLRRDRLRD\\n\", \"72 23 38\\n(((((()()())()())(((()()))(())())()(()())(()(())())))(())((())())())()()\\nRDLRLRRRDLLRDLRDLLRRLLD\\n\", \"94 48 47\\n(((()(())())(((())())())()())()()())((()()())(()(()()()())())())(()())(()(())(())()())(()())()\\nLLLLLLDLDRLLDLRRDLLLLRLLDLLRRDDRDRRLLRRDRRRDRLLD\\n\", \"86 11 62\\n(((())())(((()())())()()())(()())(()()())()())((()()())())(((())()())((())(()())())())\\nDLDLRLRLRRR\\n\", \"100 57 80\\n(((())(()))(()())())((((()()()())((())())()())(()((()())()()()))())()()())((())()((())()))((()))()()\\nLLRRLLLRLRLRLDLLRRRDDLRDDDLRLRLLLRLRRRLLDRLRDLLDLRLRLDDLR\\n\", \"80 31 30\\n(((()()())(((())())((()())()()())()()))(()()()())(()())(()())(())(())()()()())()\\nDDDLLDLDDLRLRLDDRDRRLDRDLLDRLRL\\n\", \"74 26 27\\n(((()()())())(())()())((()()(())())()())((()()())()())(()()())(()()())()()\\nLDRLLRLRLLDDDLDRRDRLLRDLRD\\n\", \"12 10 11\\n(())()()()()\\nDLRDLRDDLR\\n\", \"18 8 11\\n((()))(()()()())()\\nLLLRRRRD\\n\", \"42 7 29\\n(((())()(()())())(((()())())(()())())())()\\nDDRRRRD\\n\", \"4 2 2\\n()()\\nLD\\n\", \"76 51 69\\n(((())()())())(()()()()())(((((())(())())())())(((()(())())(()()())())()))()\\nLRLLRRLLLDRDDRLLDLRLRDRLRDLRLRLRLLDLRLRLLLDDLLRRDLD\\n\", \"10 7 3\\n(()())()()\\nRDLRDRD\\n\", \"92 51 30\\n(()(((()())(()())())())(()())()()()())((()()())(())(())(()((())()())())(())())((())()())()()\\nLRLRLLLLRRRLLRRLDLRLRRLRDLDLDLDDRRLRRRLLRDRLDDRLRRD\\n\", \"2 1 1\\n()\\nR\\n\", \"60 50 23\\n((((())(()())()())(()())()()()(()())())((())()())()())(())()\\nDRDLLDDLLLLDDRRDRDLLLRRRLRLDDDLRLLRRDLRLRRDDDRDRRL\\n\", \"14 8 13\\n((())()()(()))\\nDLRLLRLR\\n\", \"26 3 15\\n((())())(((())()()))(())()\\nLDR\\n\", \"78 33 22\\n(((()((()()())())()()())((()())()())(())())(((((())())()())()())(())())())()()\\nRDRRRRRLDRDDDRLLLLLRDRRRDLDRDLLRD\\n\", \"58 1 22\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nLLR\\n\", \"34 8 27\\n(())((()())()((())())()()())()()()\\nRLLDLRRL\\n\", \"32 6 19\\n((()())((())())())((())()(()))()\\nRRLRDL\\n\", \"68 34 12\\n((()(()())()())(()))((()())()())((()()())())(((())(()))(())()(())())\\nDLRRLRRRDLLDLLDDDLRRLRLRRRDDRLRRLL\\n\", \"20 16 2\\n(()()())()(())()()()\\nLDRRRRRRLRLRLLLL\\n\", \"82 11 6\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nRLLLLRRDDRRLRRRL\\n\", \"8 2 2\\n(())()()\\nRR\\n\", \"74 26 52\\n(((()()())())(())()())((()()(())())()())((()()())()())(()()())(()()())()()\\nLDRLLRLRLLDDDLDRRDRLLRDLRD\\n\", \"12 10 10\\n(())()()()()\\nDLRDLRDDLR\\n\", \"8 4 4\\n(())()()\\nRDLD\\n\", \"82 11 7\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nRLLLLRRDDRRLRRRL\\n\", \"82 11 7\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nLRRRLRRDDRRLLLLR\\n\", \"50 32 18\\n(()()())(())(())((()())())((())())((()())())(())()\\nLRLLLRDRRDLRRRLRLLDDRLLRDLRDLRLD\\n\", \"26 3 18\\n((())())(((())()()))(())()\\nRDL\\n\", \"38 8 26\\n((((())())(()))(()()))(((())())())()()\\nRDLRLDDD\\n\", \"24 15 11\\n((()())()()())(())()()()\\nLDRRLDLDRRDDLRL\\n\", \"34 8 13\\n(())((()())()((())())()()())()()()\\nRLLDLRRL\\n\", \"16 1 10\\n(((())())())()()\\nDL\\n\", \"66 55 16\\n(((())(((()())()()))(()())(()())())(())((()())())(()()())())()()()\\nRDLRLRRRLRDLRRLLDDRDRRDLRLDRRDRDLRDDLLRRDRDRLRRLLLDLRRR\\n\", \"84 18 78\\n(())(((()(()))()((((()())())(()())())()())((()())())())(((())(())())(())())())()()()\\nLLLRDRLRDRLDDLLDRL\\n\", \"68 34 7\\n((()(()())()())(()))((()())()())((()()())())(((())(()))(())()(())())\\nDLRRLRRRDLLDLLDDDLRRLRLRRRDDRLRRLL\\n\", \"40 22 35\\n(((()()()())()()())(((()())()(())())()))\\nDRRLDRLRLLLDLLLDRLLRLD\\n\", \"92 51 18\\n(()(((()())(()())())())(()())()()()())((()()())(())(())(()((())()())())(())())((())()())()()\\nLRLRLLLLRRRLLRRLDLRLRRLRDLDLDLDDRRLRRRLLRDRLDDRLRRD\\n\", \"60 50 23\\n((((())(()())()())(()())()()()(()())())((())()())()())(())()\\nDRDLLDDLLLLDDRRDRDLLLRRRLRLDDDLRLLRRDLRLRRDDDRRDRL\\n\", \"74 26 52\\n(((()()())())((()()())((()()(())())()())((()()())()())(()()())(()()())()))\\nLDRLLRLRLLDDDLDRRDRLLRDLRD\\n\", \"82 11 8\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nLRRRLRRDDRRLLLLR\\n\", \"50 32 22\\n(()()())(())(())((()())())((())())((()())())(())()\\nLRLLLRDRRDLRRRLRLLDDRLLRDLRDLRLD\\n\", \"24 15 18\\n((()())()()())(())()()()\\nLDRRLDLDRRDDLRL\\n\", \"82 11 8\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nRLLLLRRDDRRLRRRL\\n\", \"34 8 21\\n(())((()())()((())())()()())()()()\\nRLLDLRRL\\n\", \"68 28 8\\n((()(()())()())(()))((()())()())((()()())())(((())(()))(())()(())())\\nDLRRLRRRDLLDLLDDDLRRLRLRRRDDRLRRLL\\n\", \"72 23 16\\n(((((()()())()())(((()()))(())())()(()())(()(())())))(())((())())())()()\\nRDLRLRRRDLLRDLRDLLRRLLD\\n\", \"86 11 42\\n(((())())(((()())())()()())(()())(()()())()())((()()())())(((())()())((())(()())())())\\nDLDLRLRLRRR\\n\", \"80 31 30\\n(((()()())(((())())((()())()()())()()))(()()()())(()())(()())(())(())()()()())()\\nDDLLLDLDDLRLRLDDRDRRLDRDDLDRLRL\\n\", \"18 8 11\\n((()))(()()()())()\\nDRRRRLLL\\n\", \"78 33 9\\n(((()((()()())())()()())((()())()())(())())(((((())())()())()())(())())())()()\\nRDRRRRRLDRDDDRLLLLLRDRRRDLDRDLLRD\\n\", \"26 3 18\\n((())())(((())()()))(())()\\nLDR\\n\", \"82 14 7\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nLRRRLRRDDRRLLLLR\\n\", \"58 3 43\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nLLR\\n\", \"12 10 5\\n(())()()()()\\nDLRDLRDDLR\\n\", \"58 2 22\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nLLR\\n\", \"58 3 43\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nRLL\\n\", \"16 2 10\\n(((())())())()()\\nDL\\n\", \"88 33 12\\n(())((((())()((()())())())(((())())(())()())(()))()((())())())(((())()())(())()())()()()\\nLLLRRLRDRDRLDDLLRDLLDRLRDDLDRDLRR\\n\", \"58 0 22\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nLLR\\n\", \"58 1 22\\n((((())()())())((())())(())())(((())()()())(())()())()(())\\nLRL\\n\", \"82 11 11\\n(((())())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\nRLLLLRRDDRRLRRRL\\n\", \"24 15 11\\n((()()))(()())(())()()()\\nLDRRLDLDRRDDLRL\\n\"], \"outputs\": [\"(()(()))\\n\", \"()()\\n\", \"()\\n\", \"(())()()\\n\", \"((())())()\\n\", \"(()()())(()())(())(())()()\\n\", \"(()())\\n\", \"(()()())(())(())((()()))\\n\", \"((()(()())(()())()())()())((()())(()))()()\\n\", \"((()((())())(()())(())())())\\n\", \"((())())(((())()))(())()\\n\", \"((((())())(()))(()()))(())()()\\n\", \"()()\\n\", \"(()(()())())()()\\n\", \"()\\n\", \"((((((())())()())()())(())())())()()\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"(())((()())()((()))()()())()()()\\n\", \"(())()()\\n\", \"((()()()))((()())()()())(()())()\\n\", \"()()()()\\n\", \"(())\\n\", \"((())()(()))()\\n\", \"((()())()())((()()())())(((())(()))(())()(())())\\n\", \"()()()\\n\", \"()()()\\n\", \"(()()()()())((())())(()()())((()))\\n\", \"(()())((())())()()\\n\", \"()\\n\", \"(()())()(())()()()\\n\", \"((()()())()()()())(((()()())())())\\n\", \"(())\\n\", \"((())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"(())()()\\n\", \"()()()\\n\", \"()\\n\", \"()()\\n\", \"(())()\\n\", \"(()())()\\n\", \"()()\\n\", \"((())()())(()())()\\n\", \"(((())())(((()())())()()())(()())(()()())()())((()()())())((()())((())(()())())())\\n\", \"(((())(()))(()())())\\n\", \"()\\n\", \"()()()\\n\", \"(())\\n\", \"((()))(()()())()\\n\", \"(((())()(()())())(((()())()))())\\n\", \"()\\n\", \"(((())()()))\\n\", \"()\\n\", \"(()()())()()\\n\", \"()\\n\", \"(()())(())()\\n\", \"((())()())\\n\", \"((())())((()()))(())()\\n\", \"(((()((()()())())())())(((((())())()())()())(())())())()()\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"(())((()())()((())())()())()()()\\n\", \"((()())((())())())(()()(()))()\\n\", \"()(()()())((()()())())(((())(()))(())()(())())\\n\", \"()(())()()()\\n\", \"((())(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"(())()()\\n\", \"(((()()())())(())()())((()()(())())()())()(()()())()()\\n\", \"(())\\n\", \"()\\n\", \"(()(())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"(((())())())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"(()()())((())())((()())())(())()\\n\", \"((())())()(())()\\n\", \"((((())())(()))(()()))(())()()\\n\", \"((()()))()()()\\n\", \"(())((()())((())())()()())()()()\\n\", \"(((())()))()()\\n\", \"(((()))())()()()\\n\", \"(())(((()(()))()((((()())())(()())())()())((()())())())(((())(())())(())))\\n\", \"(())((()())()())((()()())())(((())(()))(())()(())())\\n\", \"(((()()()())()()())())\\n\", \"(()()()()())((()()())(())(())(()((())()())())(())())((())()())()()\\n\", \"(()())(())()\\n\", \"(((()()())())((()()())((()()(())())()())()(()()())()))\\n\", \"(((())())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"(()()())(())(())()\\n\", \"((()())()()())\\n\", \"((())()())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"(())((()())()((()))()()())()()()\\n\", \"((()())()())((()()())())(((())(()))(())()(())())\\n\", \"(()(())((())())())()()\\n\", \"(((())())(((()())())()()())(()())())((()()())())(((())()())((())(()())())())\\n\", \"((()())(()())(())(())()()()())()\\n\", \"((()))(()()())()\\n\", \"((())(((((())())()())()())(())())())()()\\n\", \"((())())(((())()))(())()\\n\", \"(((())())())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"(())\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"(((())()))()()\\n\", \"(())()()\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"((((())()())())((())())(())())(((())()()())(())()())()(())\\n\", \"(((())())())(((()()((()()))())()(())())(()())(())((())())()()())(()()()())()\\n\", \"((()()))()()()\\n\"]}", "source": "primeintellect"}
|
Recently Polycarp started to develop a text editor that works only with correct bracket sequences (abbreviated as CBS).
Note that a bracket sequence is correct if it is possible to get a correct mathematical expression by adding "+"-s and "1"-s to it. For example, sequences "(())()", "()" and "(()(()))" are correct, while ")(", "(()" and "(()))(" are not. Each bracket in CBS has a pair. For example, in "(()(()))":
* 1st bracket is paired with 8th,
* 2d bracket is paired with 3d,
* 3d bracket is paired with 2d,
* 4th bracket is paired with 7th,
* 5th bracket is paired with 6th,
* 6th bracket is paired with 5th,
* 7th bracket is paired with 4th,
* 8th bracket is paired with 1st.
Polycarp's editor currently supports only three operations during the use of CBS. The cursor in the editor takes the whole position of one of the brackets (not the position between the brackets!). There are three operations being supported:
* «L» — move the cursor one position to the left,
* «R» — move the cursor one position to the right,
* «D» — delete the bracket in which the cursor is located, delete the bracket it's paired to and all brackets between them (that is, delete a substring between the bracket in which the cursor is located and the one it's paired to).
After the operation "D" the cursor moves to the nearest bracket to the right (of course, among the non-deleted). If there is no such bracket (that is, the suffix of the CBS was deleted), then the cursor moves to the nearest bracket to the left (of course, among the non-deleted).
There are pictures illustrated several usages of operation "D" below.
<image>
All incorrect operations (shift cursor over the end of CBS, delete the whole CBS, etc.) are not supported by Polycarp's editor.
Polycarp is very proud of his development, can you implement the functionality of his editor?
Input
The first line contains three positive integers n, m and p (2 ≤ n ≤ 500 000, 1 ≤ m ≤ 500 000, 1 ≤ p ≤ n) — the number of brackets in the correct bracket sequence, the number of operations and the initial position of cursor. Positions in the sequence are numbered from left to right, starting from one. It is guaranteed that n is even.
It is followed by the string of n characters "(" and ")" forming the correct bracket sequence.
Then follow a string of m characters "L", "R" and "D" — a sequence of the operations. Operations are carried out one by one from the first to the last. It is guaranteed that the given operations never move the cursor outside the bracket sequence, as well as the fact that after all operations a bracket sequence will be non-empty.
Output
Print the correct bracket sequence, obtained as a result of applying all operations to the initial sequence.
Examples
Input
8 4 5
(())()()
RDLD
Output
()
Input
12 5 3
((()())(()))
RRDLD
Output
(()(()))
Input
8 8 8
(())()()
LLLLLLDD
Output
()()
Note
In the first sample the cursor is initially at position 5. Consider actions of the editor:
1. command "R" — the cursor moves to the position 6 on the right;
2. command "D" — the deletion of brackets from the position 5 to the position 6. After that CBS takes the form (())(), the cursor is at the position 5;
3. command "L" — the cursor moves to the position 4 on the left;
4. command "D" — the deletion of brackets from the position 1 to the position 4. After that CBS takes the form (), the cursor is at the position 1.
Thus, the answer is equal to ().
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 2 9\\n3 4 8 9\\n3 2 1 4\\n\", \"6 1 5\\n1 1 1 1 1 1\\n2 3 5 4 1 6\\n\", \"5 1 5\\n1 1 1 1 1\\n3 1 5 4 2\\n\", \"6 3 7\\n6 7 5 5 5 5\\n2 1 4 3 5 6\\n\", \"5 1 5\\n1 1 1 1 1\\n1 2 3 4 5\\n\", \"2 1 1000000000\\n1000000000 1\\n2 1\\n\", \"50 10 15\\n13 14 12 14 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 10 14 11 11 10 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"5 1 7\\n1 4 4 6 5\\n5 2 1 4 3\\n\", \"50 1 50\\n6 20 27 26 46 35 41 41 4 12 48 13 20 5 35 7 37 3 18 17 22 42 28 1 30 46 38 38 42 29 33 42 8 45 22 40 11 33 12 15 16 49 30 19 29 40 5 12 32 22\\n47 27 35 40 31 26 42 19 11 49 37 3 41 34 36 30 16 44 12 4 46 20 14 39 32 25 18 1 21 6 2 17 48 7 5 24 29 33 50 43 8 15 28 23 22 13 45 38 10 9\\n\", \"1 1000000000 1000000000\\n1000000000\\n1\\n\", \"3 5 100\\n10 50 100\\n3 2 1\\n\", \"2 1 1000000000\\n1000000000 1\\n1 2\\n\", \"30 100 200\\n102 108 122 116 107 145 195 145 119 110 187 196 140 174 104 190 193 181 118 127 157 111 139 175 173 191 181 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"5 10 100\\n12 14 15 11 13\\n4 2 1 5 3\\n\", \"5 1 5\\n1 1 1 1 1\\n2 3 1 5 4\\n\", \"10 1 10\\n9 2 9 5 5 2 6 8 2 8\\n2 10 1 6 7 8 5 3 9 4\\n\", \"11 5 11\\n9 8 7 5 7 5 9 5 10 5 7\\n3 4 6 9 5 11 2 10 1 8 7\\n\", \"10 8 10\\n8 10 10 9 8 10 10 10 10 10\\n9 5 6 8 10 2 7 3 1 4\\n\", \"5 1 5\\n0 1 1 1 1\\n1 2 3 4 5\\n\", \"5 1 10\\n1 4 4 6 5\\n5 2 1 4 3\\n\", \"2 1 1010000000\\n1000000000 1\\n1 2\\n\", \"30 100 200\\n102 108 112 116 107 145 195 145 119 110 187 196 140 174 104 190 193 181 118 127 157 111 139 175 173 191 181 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"5 1 5\\n1 1 1 2 1\\n3 1 5 4 2\\n\", \"5 1 7\\n1 4 4 6 6\\n5 2 1 4 3\\n\", \"1 1000000000 1000000100\\n1000000000\\n1\\n\", \"3 5 100\\n5 50 100\\n3 2 1\\n\", \"10 1 10\\n9 2 9 5 5 2 10 8 2 8\\n2 10 1 6 7 8 5 3 9 4\\n\", \"11 5 11\\n9 8 7 5 10 5 9 5 10 5 7\\n3 4 6 9 5 11 2 10 1 8 7\\n\", \"10 1 10\\n8 10 10 9 8 10 10 10 10 10\\n9 5 6 8 10 2 7 3 1 4\\n\", \"30 100 200\\n102 108 112 116 107 145 195 145 119 110 187 196 140 174 104 190 193 181 169 127 157 111 139 175 173 191 181 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"5 1 7\\n1 4 4 4 6\\n5 2 1 4 3\\n\", \"6 5 13\\n11 5 5 5 8 7\\n2 1 4 3 5 6\\n\", \"6 3 7\\n6 7 5 5 5 4\\n2 1 4 3 5 6\\n\", \"3 1 100\\n10 50 100\\n3 2 1\\n\", \"10 1 10\\n9 2 9 5 10 2 6 8 2 8\\n2 10 1 6 7 8 5 3 9 4\\n\", \"6 3 13\\n6 7 5 5 5 5\\n2 1 4 3 5 6\\n\", \"10 8 10\\n8 10 10 9 8 10 10 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 1 5\\n2 1 1 1 1 1\\n2 3 5 4 1 6\\n\", \"10 8 10\\n7 10 10 9 8 10 10 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"10 8 10\\n7 10 10 9 8 10 10 14 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 3 7\\n6 7 5 5 8 5\\n2 1 4 3 5 6\\n\", \"5 1 5\\n1 1 1 1 2\\n1 2 3 4 5\\n\", \"2 1 1000000000\\n1000000010 1\\n2 1\\n\", \"50 10 15\\n13 14 12 14 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 10 14 11 11 17 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"50 1 50\\n6 20 27 26 46 35 41 41 4 12 48 13 20 5 35 7 37 3 18 17 22 42 28 1 30 46 38 38 42 29 33 42 8 45 22 17 11 33 12 15 16 49 30 19 29 40 5 12 32 22\\n47 27 35 40 31 26 42 19 11 49 37 3 41 34 36 30 16 44 12 4 46 20 14 39 32 25 18 1 21 6 2 17 48 7 5 24 29 33 50 43 8 15 28 23 22 13 45 38 10 9\\n\", \"30 100 200\\n102 108 122 4 107 145 195 145 119 110 187 196 140 174 104 190 193 181 118 127 157 111 139 175 173 191 181 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"5 1 2\\n1 1 1 1 1\\n2 3 1 5 4\\n\", \"5 2 5\\n1 1 1 1 1\\n3 1 5 4 2\\n\", \"2 1 1010010000\\n1000000000 1\\n1 2\\n\", \"10 8 2\\n8 10 10 9 8 10 10 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 1 5\\n0 1 1 1 1 1\\n2 3 5 4 1 6\\n\", \"5 1 0\\n1 1 1 2 1\\n3 1 5 4 2\\n\", \"6 3 7\\n11 7 5 5 8 5\\n2 1 4 3 5 6\\n\", \"50 10 15\\n13 14 12 14 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 0 14 11 11 17 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"50 1 50\\n6 20 27 26 46 35 41 41 4 12 48 13 20 5 35 7 37 3 18 17 22 42 28 1 30 46 38 38 42 29 33 42 8 45 22 17 11 33 12 15 16 49 30 19 29 40 5 12 7 22\\n47 27 35 40 31 26 42 19 11 49 37 3 41 34 36 30 16 44 12 4 46 20 14 39 32 25 18 1 21 6 2 17 48 7 5 24 29 33 50 43 8 15 28 23 22 13 45 38 10 9\\n\", \"1 1000000000 1000000100\\n1000000001\\n1\\n\", \"30 100 200\\n102 108 122 4 107 145 195 145 40 110 187 196 140 174 104 190 193 181 118 127 157 111 139 175 173 191 181 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"5 1 2\\n1 1 1 1 2\\n2 3 1 5 4\\n\", \"10 8 2\\n8 16 10 9 8 10 10 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 1 5\\n0 2 1 1 1 1\\n2 3 5 4 1 6\\n\", \"6 3 7\\n11 12 5 5 8 5\\n2 1 4 3 5 6\\n\", \"50 10 15\\n10 14 12 14 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 0 14 11 11 17 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"5 1 9\\n1 4 4 4 6\\n5 2 1 4 3\\n\", \"50 1 50\\n6 20 27 26 46 35 41 41 4 12 48 13 20 5 34 7 37 3 18 17 22 42 28 1 30 46 38 38 42 29 33 42 8 45 22 17 11 33 12 15 16 49 30 19 29 40 5 12 7 22\\n47 27 35 40 31 26 42 19 11 49 37 3 41 34 36 30 16 44 12 4 46 20 14 39 32 25 18 1 21 6 2 17 48 7 5 24 29 33 50 43 8 15 28 23 22 13 45 38 10 9\\n\", \"30 100 200\\n102 108 122 4 107 145 195 145 40 110 187 196 140 174 106 190 193 181 118 127 157 111 139 175 173 191 181 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"5 1 2\\n0 1 1 1 2\\n2 3 1 5 4\\n\", \"10 12 2\\n8 16 10 9 8 10 10 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 1 3\\n0 2 1 1 1 1\\n2 3 5 4 1 6\\n\", \"6 5 7\\n11 12 5 5 8 5\\n2 1 4 3 5 6\\n\", \"50 10 15\\n10 14 12 20 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 0 14 11 11 17 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"5 1 2\\n-1 1 1 1 2\\n2 3 1 5 4\\n\", \"10 12 2\\n8 16 10 9 3 10 10 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 5 7\\n11 12 5 5 8 7\\n2 1 4 3 5 6\\n\", \"50 10 15\\n10 14 12 20 12 15 13 10 11 11 15 10 14 11 14 12 20 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 0 14 11 11 17 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"6 5 7\\n11 5 5 5 8 7\\n2 1 4 3 5 6\\n\", \"6 5 13\\n11 5 5 5 8 13\\n2 1 4 3 5 6\\n\", \"6 5 13\\n11 5 5 9 8 13\\n2 1 4 3 5 6\\n\", \"50 10 15\\n13 14 12 14 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 12 15 14 15 13 15 13 10 12 10 15 15 10 14 11 11 10 14 11 12 13 12 10 11 20 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"50 1 50\\n6 20 27 26 46 35 41 45 4 12 48 13 20 5 35 7 37 3 18 17 22 42 28 1 30 46 38 38 42 29 33 42 8 45 22 40 11 33 12 15 16 49 30 19 29 40 5 12 32 22\\n47 27 35 40 31 26 42 19 11 49 37 3 41 34 36 30 16 44 12 4 46 20 14 39 32 25 18 1 21 6 2 17 48 7 5 24 29 33 50 43 8 15 28 23 22 13 45 38 10 9\\n\", \"10 8 10\\n8 10 10 17 8 10 10 10 10 10\\n9 5 6 8 10 2 7 3 1 4\\n\", \"6 1 5\\n1 0 1 1 1 1\\n2 3 5 4 1 6\\n\", \"5 1 5\\n0 1 1 1 2\\n1 2 3 4 5\\n\", \"10 8 10\\n7 10 10 9 8 10 10 11 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"5 1 5\\n1 2 1 1 2\\n1 2 3 4 5\\n\", \"50 10 15\\n13 14 12 14 12 15 13 10 11 11 15 10 14 11 14 12 11 10 10 13 11 13 2 15 14 15 13 15 13 10 12 10 15 15 10 14 11 11 17 14 11 12 13 12 10 11 13 15 14 11\\n20 10 25 13 29 6 24 47 37 39 2 44 12 33 9 26 35 49 46 19 38 23 30 5 16 4 21 7 18 45 28 43 1 8 48 15 36 40 50 11 32 27 22 31 42 41 17 3 14 34\\n\", \"2 1 1000010000\\n1000000000 1\\n1 2\\n\", \"30 100 200\\n102 108 112 116 107 145 195 145 119 110 187 196 140 174 104 190 193 181 169 127 157 111 139 175 173 191 353 105 142 166\\n30 26 20 23 27 15 2 14 21 25 6 1 17 10 29 5 3 7 22 19 13 24 18 9 11 4 8 28 16 12\\n\", \"10 8 2\\n8 10 10 9 8 10 17 10 10 15\\n9 5 6 8 10 2 7 3 1 4\\n\", \"1 1000000000 1000000101\\n1000000001\\n1\\n\"], \"outputs\": [\"2 2 2 9 \", \"-1\", \"3 1 5 4 2 \", \"3 3 4 3 5 6 \", \"1 2 3 4 5 \", \"-1\", \"-1\", \"2 2 1 6 4 \", \"-1\", \"1000000000 \", \"5 5 5 \", \"1 1 \", \"100 100 100 100 100 101 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 101 100 100 100 \", \"10 10 10 10 10 \", \"2 3 1 5 4 \", \"2 3 1 2 3 1 2 2 2 3 \", \"6 6 7 8 6 10 5 9 5 7 8 \", \"-1\", \"-1\\n\", \"2 2 1 6 4\\n\", \"1 1\\n\", \"100 102 100 107 102 101 100 100 108 103 100 100 100 100 101 100 100 100 108 100 100 103 100 100 100 100 101 101 100 100\\n\", \"3 1 5 5 2\\n\", \"2 2 1 6 5\\n\", \"1000000000\\n\", \"5 5 5\\n\", \"2 3 1 2 3 1 6 2 2 3\\n\", \"6 6 7 8 9 10 5 9 5 7 8\\n\", \"7 5 6 7 8 2 7 3 1 4\\n\", \"100 102 100 107 102 101 100 100 108 103 100 100 100 100 101 100 100 100 159 100 100 103 100 100 100 100 101 101 100 100\\n\", \"2 2 1 4 5\\n\", \"12 5 8 7 12 12\\n\", \"3 3 4 3 5 5\\n\", \"1 1 1\\n\", \"2 3 1 2 8 1 2 2 2 3\\n\", \"3 3 4 3 5 6\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1 1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1000000000\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2 2 1 4 5\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1 1\\n\", \"-1\\n\", \"-1\\n\", \"1000000000\\n\"]}", "source": "primeintellect"}
|
Dasha logged into the system and began to solve problems. One of them is as follows:
Given two sequences a and b of length n each you need to write a sequence c of length n, the i-th element of which is calculated as follows: ci = bi - ai.
About sequences a and b we know that their elements are in the range from l to r. More formally, elements satisfy the following conditions: l ≤ ai ≤ r and l ≤ bi ≤ r. About sequence c we know that all its elements are distinct.
<image>
Dasha wrote a solution to that problem quickly, but checking her work on the standard test was not so easy. Due to an error in the test system only the sequence a and the compressed sequence of the sequence c were known from that test.
Let's give the definition to a compressed sequence. A compressed sequence of sequence c of length n is a sequence p of length n, so that pi equals to the number of integers which are less than or equal to ci in the sequence c. For example, for the sequence c = [250, 200, 300, 100, 50] the compressed sequence will be p = [4, 3, 5, 2, 1]. Pay attention that in c all integers are distinct. Consequently, the compressed sequence contains all integers from 1 to n inclusively.
Help Dasha to find any sequence b for which the calculated compressed sequence of sequence c is correct.
Input
The first line contains three integers n, l, r (1 ≤ n ≤ 105, 1 ≤ l ≤ r ≤ 109) — the length of the sequence and boundaries of the segment where the elements of sequences a and b are.
The next line contains n integers a1, a2, ..., an (l ≤ ai ≤ r) — the elements of the sequence a.
The next line contains n distinct integers p1, p2, ..., pn (1 ≤ pi ≤ n) — the compressed sequence of the sequence c.
Output
If there is no the suitable sequence b, then in the only line print "-1".
Otherwise, in the only line print n integers — the elements of any suitable sequence b.
Examples
Input
5 1 5
1 1 1 1 1
3 1 5 4 2
Output
3 1 5 4 2
Input
4 2 9
3 4 8 9
3 2 1 4
Output
2 2 2 9
Input
6 1 5
1 1 1 1 1 1
2 3 5 4 1 6
Output
-1
Note
Sequence b which was found in the second sample is suitable, because calculated sequence c = [2 - 3, 2 - 4, 2 - 8, 9 - 9] = [ - 1, - 2, - 6, 0] (note that ci = bi - ai) has compressed sequence equals to p = [3, 2, 1, 4].
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 3 3\\n1 8 4\\n\", \"4 3 5\\n2 7 7 7\\n\", \"3 2 3\\n1 8 4\\n\", \"15 8 10\\n216175135 15241965 611723934 987180005 151601897 403701727 533996295 207637446 875331635 46172555 604086315 350146655 401084142 156540458 982110455\\n\", \"2 2 100000\\n0 1\\n\", \"3 2 3\\n1 2 3\\n\", \"4 3 3\\n5 1 4 7\\n\", \"4 2 6\\n5 5 5 5\\n\", \"108 29 72\\n738 619 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 202 10 533 635 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 288 381 142 500 72 297 359 230 773 216 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 377591123 938158786 682031413 804153975 89006697 275945670 735510539\\n\", \"5 5 9\\n8 17 26 35 44\\n\", \"11 4 3\\n0 1 0 1 1 0 0 0 0 0 0\\n\", \"13 4 4\\n1 1 0 3 2 4 1 0 3 4 2 4 3\\n\", \"3 2 4\\n1 2 3\\n\", \"6 3 4\\n5 9 10 6 7 8\\n\", \"5 2 10\\n4 5 6 19 29\\n\", \"7 7 1\\n0 0 0 0 0 0 0\\n\", \"5 2 4\\n1 2 2 2 2\\n\", \"4 4 3\\n4 7 2 5\\n\", \"5 3 3\\n3 6 4 7 10\\n\", \"5 2 9\\n8 8 8 8 8\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 358 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 614 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 711 395 336 358 472 133 324 527 599 5 845 920 989 494 358 70 882\\n\", \"5 4 2\\n1 3 6 10 12\\n\", \"9 9 5\\n389149775 833127990 969340400 364457730 48649145 316121525 640054660 924273385 973207825\\n\", \"5 5 1\\n6 4 6 0 4\\n\", \"8 8 1\\n314088413 315795280 271532387 241073087 961218399 884234132 419866508 286799253\\n\", \"12 2 1\\n512497388 499105388 575265677 864726520 678272195 667107176 809432109 439696443 770034376 873126825 690514828 541499950\\n\", \"9 3 1\\n506004039 471451660 614118177 518013571 43210072 454727076 285905913 543002174 298515615\\n\", \"3 2 2\\n1 2 4\\n\", \"8 3 5\\n1 2 3 4 1 2 3 4\\n\", \"4 3 10\\n0 1 11 11\\n\", \"8 2 6\\n750462183 165947982 770714338 368445737 363145692 966611485 376672869 678687947\\n\", \"3 3 3\\n1 3 6\\n\", \"15 8 10\\n216175135 15241965 611723934 987180005 151601897 403701727 21233984 207637446 875331635 46172555 604086315 350146655 401084142 156540458 982110455\\n\", \"3 2 5\\n1 2 3\\n\", \"4 3 3\\n1 1 4 7\\n\", \"4 2 6\\n5 5 5 3\\n\", \"108 29 72\\n738 619 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 202 10 533 635 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 216 576 144 244 437 772 483 51\\n\", \"3 2 4\\n1 2 6\\n\", \"7 7 1\\n0 0 0 0 0 0 1\\n\", \"5 2 4\\n1 0 2 2 2\\n\", \"5 2 14\\n8 8 8 8 8\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 358 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 711 395 336 358 472 133 324 527 599 5 845 920 989 494 358 70 882\\n\", \"5 4 1\\n6 4 6 0 4\\n\", \"8 8 1\\n345529665 315795280 271532387 241073087 961218399 884234132 419866508 286799253\\n\", \"12 2 1\\n512497388 499105388 575265677 864726520 678272195 667107176 809432109 439696443 770034376 1102399289 690514828 541499950\\n\", \"9 3 1\\n506004039 471451660 614118177 518013571 43210072 454727076 285905913 543002174 551164804\\n\", \"3 2 2\\n1 2 8\\n\", \"8 2 6\\n750462183 165947982 770714338 368445737 617714211 966611485 376672869 678687947\\n\", \"4 3 6\\n2 7 7 7\\n\", \"4 3 3\\n1 1 1 7\\n\", \"108 29 72\\n738 619 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 202 10 533 635 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 101 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 377591123 145372775 682031413 804153975 89006697 215152188 735510539\\n\", \"6 3 4\\n5 9 20 6 9 8\\n\", \"7 7 1\\n0 0 0 0 0 0 2\\n\", \"5 2 4\\n1 0 2 1 2\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 471 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 711 395 336 358 472 133 324 527 599 5 845 920 989 494 358 70 882\\n\", \"5 4 1\\n6 0 6 0 4\\n\", \"8 8 1\\n436061587 315795280 271532387 241073087 961218399 884234132 419866508 286799253\\n\", \"12 2 1\\n512497388 84485487 575265677 864726520 678272195 667107176 809432109 439696443 770034376 1102399289 690514828 541499950\\n\", \"3 2 1\\n1 2 8\\n\", \"4 4 6\\n5 5 5 5\\n\", \"7 7 1\\n0 0 0 1 0 0 2\\n\", \"5 2 4\\n1 0 2 0 2\\n\", \"5 5 1\\n6 0 6 0 4\\n\", \"8 8 1\\n436061587 315795280 271532387 241073087 961218399 884234132 419866508 331568173\\n\", \"7 7 1\\n0 0 1 1 0 0 2\\n\", \"5 5 1\\n11 0 6 0 4\\n\", \"8 2 1\\n436061587 315795280 271532387 241073087 961218399 884234132 419866508 331568173\\n\", \"4 3 1\\n2 1 1 1\\n\", \"7 7 1\\n0 0 1 0 0 0 2\\n\", \"4 3 1\\n0 1 1 1\\n\", \"8 2 1\\n436061587 521025489 430066373 241073087 961218399 884234132 419866508 331568173\\n\", \"8 4 6\\n344417267 377591123 938158786 682031413 804153975 89006697 215152188 735510539\\n\", \"5 5 9\\n8 17 6 35 44\\n\", \"6 3 4\\n5 9 20 6 7 8\\n\", \"4 4 3\\n4 7 0 5\\n\", \"5 8 2\\n1 3 6 10 12\\n\", \"4 3 10\\n0 2 11 11\\n\", \"3 6 3\\n1 8 4\\n\", \"15 8 10\\n216175135 15241965 611723934 1805887181 151601897 403701727 21233984 207637446 875331635 46172555 604086315 350146655 401084142 156540458 982110455\\n\", \"4 4 6\\n5 5 5 3\\n\", \"5 5 9\\n8 17 6 52 44\\n\", \"4 4 3\\n4 4 0 5\\n\", \"5 8 2\\n1 3 6 10 3\\n\", \"4 3 10\\n0 4 11 11\\n\", \"3 6 3\\n1 16 4\\n\", \"4 3 6\\n2 7 7 11\\n\", \"15 8 10\\n216175135 15241965 611723934 1805887181 151601897 403701727 21233984 207637446 875331635 46172555 604086315 350146655 382718000 156540458 982110455\\n\", \"4 3 1\\n1 1 1 7\\n\", \"108 29 72\\n738 619 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 202 10 533 867 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 101 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 270053066 145372775 682031413 804153975 89006697 215152188 735510539\\n\", \"5 5 13\\n8 17 6 52 44\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 471 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 622 395 336 358 472 133 324 527 599 5 845 920 989 494 358 70 882\\n\", \"5 8 2\\n1 3 6 16 3\\n\", \"12 2 1\\n512497388 84485487 575265677 864726520 678272195 667107176 809432109 439696443 1226389642 1102399289 690514828 541499950\\n\", \"4 3 10\\n0 3 11 11\\n\", \"3 6 3\\n2 16 4\\n\", \"4 3 6\\n3 7 7 11\\n\", \"15 8 10\\n216175135 15241965 611723934 1805887181 151601897 403701727 21233984 207637446 875331635 46172555 604086315 136933161 382718000 156540458 982110455\\n\", \"4 3 1\\n1 1 1 1\\n\", \"108 29 72\\n738 619 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 393 10 533 867 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 101 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 270053066 145372775 682031413 804153975 161704458 215152188 735510539\\n\", \"5 3 4\\n1 0 2 1 2\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 471 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 622 395 336 358 472 133 324 527 599 5 845 920 1863 494 358 70 882\\n\", \"12 2 1\\n512497388 84485487 575265677 864726520 678272195 559161962 809432109 439696443 1226389642 1102399289 690514828 541499950\\n\", \"4 3 13\\n0 3 11 11\\n\", \"3 6 3\\n0 16 4\\n\", \"15 8 10\\n216175135 28113835 611723934 1805887181 151601897 403701727 21233984 207637446 875331635 46172555 604086315 136933161 382718000 156540458 982110455\\n\", \"108 29 72\\n738 192 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 393 10 533 867 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 101 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 235408254 145372775 682031413 804153975 161704458 215152188 735510539\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 471 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 622 395 336 358 472 133 324 527 599 5 845 920 191 494 358 70 882\\n\", \"8 2 1\\n436061587 315795280 430066373 241073087 961218399 884234132 419866508 331568173\\n\", \"4 3 13\\n0 3 6 11\\n\", \"15 8 10\\n216175135 14110726 611723934 1805887181 151601897 403701727 21233984 207637446 875331635 46172555 604086315 136933161 382718000 156540458 982110455\\n\", \"108 29 72\\n738 192 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 393 10 533 867 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 689 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 101 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 450727593 145372775 682031413 804153975 161704458 215152188 735510539\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 471 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 1211 748 934 714 672 712 614 587 589 846 260 593 85 839 257 622 395 336 358 472 133 324 527 599 5 845 920 191 494 358 70 882\\n\", \"4 3 13\\n0 3 4 11\\n\", \"108 29 72\\n738 192 711 235 288 288 679 36 785 233 706 71 216 144 216 1419 338 583 495 648 144 432 72 720 541 288 158 328 154 393 10 533 867 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 689 432 601 0 449 576 743 352 333 504 504 369 228 422 381 142 500 72 297 359 230 773 101 576 144 244 437 772 483 51\\n\", \"8 4 6\\n344417267 694654191 145372775 682031413 804153975 161704458 215152188 735510539\\n\", \"101 25 64\\n451 230 14 53 7 520 709 102 678 471 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 711 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 1211 748 934 714 672 712 614 587 589 846 260 593 85 839 257 622 395 336 358 472 133 324 527 599 5 845 920 191 494 186 70 882\\n\"], \"outputs\": [\"No\\n\", \"Yes\\n2 7 7\\n\", \"Yes\\n1 4\\n\", \"Yes\\n216175135 15241965 987180005 533996295 875331635 46172555 604086315 350146655\\n\", \"No\\n\", \"No\\n\", \"Yes\\n1 4 7\\n\", \"Yes\\n5 5\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 288 72\\n\", \"No\\n\", \"Yes\\n8 17 26 35 44\\n\", \"Yes\\n0 0 0 0\\n\", \"Yes\\n0 4 0 4\\n\", \"No\\n\", \"No\\n\", \"Yes\\n19 29\\n\", \"Yes\\n0 0 0 0 0 0 0\\n\", \"Yes\\n2 2\\n\", \"No\\n\", \"Yes\\n4 7 10\\n\", \"Yes\\n8 8\\n\", \"Yes\\n230 102 678 358 166 870 230 230 166 230 742 358 806 870 614 806 102 102 358 742 678 486 806 934 614\\n\", \"No\\n\", \"Yes\\n389149775 833127990 969340400 364457730 48649145 316121525 640054660 924273385 973207825\\n\", \"Yes\\n6 4 6 0 4\\n\", \"Yes\\n314088413 315795280 271532387 241073087 961218399 884234132 419866508 286799253\\n\", \"Yes\\n512497388 499105388\\n\", \"Yes\\n506004039 471451660 614118177\\n\", \"Yes\\n2 4\\n\", \"No\\n\", \"Yes\\n1 11 11\\n\", \"Yes\\n165947982 363145692\\n\", \"No\\n\", \"Yes\\n216175135 15241965 987180005 875331635 46172555 604086315 350146655 982110455\\n\", \"No\\n\", \"Yes\\n1 1 4\\n\", \"Yes\\n5 5\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 216\\n\", \"Yes\\n2 6\\n\", \"Yes\\n0 0 0 0 0 0 1\\n\", \"Yes\\n2 2\\n\", \"Yes\\n8 8\\n\", \"Yes\\n230 102 678 358 166 870 230 230 166 230 742 358 806 870 806 102 102 358 742 678 486 806 934 614 358\\n\", \"Yes\\n6 4 6 0\\n\", \"Yes\\n345529665 315795280 271532387 241073087 961218399 884234132 419866508 286799253\\n\", \"Yes\\n512497388 499105388\\n\", \"Yes\\n506004039 471451660 614118177\\n\", \"Yes\\n2 8\\n\", \"Yes\\n750462183 617714211\\n\", \"Yes\\n7 7 7\\n\", \"Yes\\n1 1 1\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 576\\n\", \"Yes\\n344417267 377591123 145372775 735510539\\n\", \"Yes\\n5 9 9\\n\", \"Yes\\n0 0 0 0 0 0 2\\n\", \"Yes\\n1 1\\n\", \"Yes\\n230 102 678 166 870 230 230 166 230 742 358 806 870 806 102 102 358 742 678 486 806 934 614 358 358\\n\", \"Yes\\n6 0 6 0\\n\", \"Yes\\n436061587 315795280 271532387 241073087 961218399 884234132 419866508 286799253\\n\", \"Yes\\n512497388 84485487\\n\", \"Yes\\n1 2\\n\", \"Yes\\n5 5 5 5\\n\", \"Yes\\n0 0 0 1 0 0 2\\n\", \"Yes\\n0 0\\n\", \"Yes\\n6 0 6 0 4\\n\", \"Yes\\n436061587 315795280 271532387 241073087 961218399 884234132 419866508 331568173\\n\", \"Yes\\n0 0 1 1 0 0 2\\n\", \"Yes\\n11 0 6 0 4\\n\", \"Yes\\n436061587 315795280\\n\", \"Yes\\n2 1 1\\n\", \"Yes\\n0 0 1 0 0 0 2\\n\", \"Yes\\n0 1 1\\n\", \"Yes\\n436061587 521025489\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n1 1 1\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 576\\n\", \"No\\n\", \"No\\n\", \"Yes\\n230 102 678 166 870 230 230 166 230 742 358 806 870 806 102 102 358 742 678 486 806 934 614 358 358\\n\", \"No\\n\", \"Yes\\n512497388 84485487\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n1 1 1\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 576\\n\", \"No\\n\", \"No\\n\", \"Yes\\n230 102 678 166 870 230 230 166 230 742 358 806 870 806 102 102 358 742 678 486 806 934 614 358 358\\n\", \"Yes\\n512497388 84485487\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 576\\n\", \"No\\n\", \"Yes\\n230 102 678 166 870 230 230 166 230 742 358 806 870 806 102 102 358 742 678 486 806 934 614 358 358\\n\", \"Yes\\n436061587 315795280\\n\", \"No\\n\", \"No\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 576\\n\", \"No\\n\", \"Yes\\n230 102 678 166 870 230 230 166 230 742 358 806 870 806 102 102 358 742 678 486 806 934 614 358 358\\n\", \"No\\n\", \"Yes\\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 72 576\\n\", \"No\\n\", \"No\\n\"]}", "source": "primeintellect"}
|
You are given a multiset of n integers. You should select exactly k of them in a such way that the difference between any two of them is divisible by m, or tell that it is impossible.
Numbers can be repeated in the original multiset and in the multiset of selected numbers, but number of occurrences of any number in multiset of selected numbers should not exceed the number of its occurrences in the original multiset.
Input
First line contains three integers n, k and m (2 ≤ k ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — number of integers in the multiset, number of integers you should select and the required divisor of any pair of selected integers.
Second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the numbers in the multiset.
Output
If it is not possible to select k numbers in the desired way, output «No» (without the quotes).
Otherwise, in the first line of output print «Yes» (without the quotes). In the second line print k integers b1, b2, ..., bk — the selected numbers. If there are multiple possible solutions, print any of them.
Examples
Input
3 2 3
1 8 4
Output
Yes
1 4
Input
3 3 3
1 8 4
Output
No
Input
4 3 5
2 7 7 7
Output
Yes
2 7 7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"RRUULLDD\\n\", \"LLUUUR\\n\", \"DDUL\\n\", \"LLLLLLLLRRRRDDDDDDDUUUUUU\\n\", \"UULLDLUR\\n\", \"URRRLULUURURLRLLLLULLRLRURLULRLULLULRRUU\\n\", \"RDRLL\\n\", \"RRRRRRRRRRRDDDDDDDDDDDDDDDDDDDRRRRRRRRRRRRRRRRRRRUUUUUUUUUUUUUUUUUUULLLLLLLLLLLLLLLLLLUUUUUUUUUUU\\n\", \"DDDLLLLLLLDDDDDDDRRRRRRRUUUUUURRR\\n\", \"DDDDLLLDDDRRRUURRRR\\n\", \"L\\n\", \"LUUDU\\n\", \"RRUULLD\\n\", \"LLLLLLLLLLLLLLLLLLLLLLLLLLRUUUUUUUUUUUUUUUUUUUUUUUUU\\n\", \"RRDL\\n\", \"DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLDDDDRRRRUUURRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\\n\", \"UUUDU\\n\", \"RR\\n\", \"RDLUR\\n\", \"DDDDDDDLLDDRRURRRRRRR\\n\", \"LUUUULLLLDDDDRRRD\\n\", \"ULURL\\n\", \"DDR\\n\", \"DLURUUU\\n\", \"ULD\\n\", \"RDRDDD\\n\", \"LLDDLDLLDDDLLLDLLLLLUU\\n\", \"UURUURRUUU\\n\", \"DRDRD\\n\", \"RRLR\\n\", \"RURRRRLURRRURRUURRRRRRRRDDULULRRURRRDRRRRRRRRRRLDR\\n\", \"URRRRRURRURUURRRRRDDDDLDDDRDDDDLLDLL\\n\", \"RRDD\\n\", \"DDDDDDDDDDDDUUUUUUUUUUUURRRRRRRRRRRRRLLLLLLLLLLLLLLL\\n\", \"DL\\n\", \"UUUURDLLLL\\n\", \"UUULLLLRDD\\n\", \"LULULL\\n\", \"LRUD\\n\", \"DLDLDDRR\\n\", \"RLRRRRRDRRDRRRRDLRRRRRRRDLRLDDLRRRRLDLDRDRRRRDRDRDRDLRRURRLRRRRDRRRRRRRRLDDRLRRDRRRRRRRDRDRLDRDDDRDR\\n\", \"RUL\\n\", \"DLUR\\n\", \"DDLDRRR\\n\", \"DDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRRRRRRRRRRRUUUUUUUUUUUUUUUUUUUUUUUU\\n\", \"LD\\n\", \"DDDDRDDLDDDDDDDRDDLD\\n\", \"UDR\\n\", \"LULU\\n\", \"DDDR\\n\", \"RRRUUULLLDD\\n\", \"R\\n\", \"DDDDDDDDDDLLLLLLLLLLLDDDDDDDDDDDRRRRRRRRRRRUUUUUUUUUURRRRRRRRRR\\n\", \"RRRRRRRRRRRURLLLLLLLLLLLL\\n\", \"UL\\n\", \"UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUURDRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\\n\", \"LLDLLLLLRRRRDDLDDDDUUUUUU\\n\", \"RRDDDD\\n\", \"RULDLLUU\\n\", \"URRRLULUULURLRLLLRULLRLRURLULRLULLULRRUU\\n\", \"LDRRL\\n\", \"LDRR\\n\", \"RDULR\\n\", \"LDUUULLLLDDDURRRD\\n\", \"LRULU\\n\", \"LUD\\n\", \"UUURRUURUU\\n\", \"RLRR\\n\", \"RDLRRRRRRRRRRDRRRURRLULUDDRRRRRRRRUURRURRRULRRRRUR\\n\", \"DDRR\\n\", \"LLLLLLLLLLLLLLLRRRRRRRRRRRRRUUUUUUUUUUUUDDDDDDDDDDDD\\n\", \"UDULLLLRDU\\n\", \"LURD\\n\", \"DLDLRDRD\\n\", \"RLU\\n\", \"DRUL\\n\", \"DRLDRRD\\n\", \"DLDDRDDDDDDDLDDRDDDD\\n\", \"URD\\n\", \"ULLU\\n\", \"DRDD\\n\", \"LLLLLLLLLLLLRURRRRRRRRRRR\\n\", \"DDLLUURR\\n\", \"RUUULL\\n\", \"LRRDL\\n\", \"RLUDR\\n\", \"DRRRUDDDLLLLUUUDL\\n\", \"URLLU\\n\", \"DDDDRR\\n\", \"UDRLLLLUDU\\n\", \"DRDRLDLD\\n\", \"DDRD\\n\", \"URLUL\\n\", \"LULRU\\n\", \"DULLULUR\\n\", \"RLUULRD\\n\", \"UUURULD\\n\", \"DLU\\n\", \"LLDLLDDDDRDDDLDDDDRRRRRUURURRURRRRRU\\n\", \"RDDR\\n\", \"RDRDDDRDLRDRDRRRRRRRDRRLRDDLRRRRRRRRDRRRRLRRURRLDRDRDRDRRRRDRDLDLRRRRLDDLRLDRRRRRRRLDRRRRDRRDRRRRRLR\\n\", \"DUR\\n\", \"LLUU\\n\", \"RDDD\\n\", \"UUUUUUDDDDLDDRRRRLLLLLDLL\\n\", \"RULULLDU\\n\", \"URRRLULUULURLRLRLRULLRLRURLULLLULLULRRUU\\n\", \"LRRD\\n\", \"LRU\\n\", \"DURL\\n\", \"DRRDLRD\\n\", \"DRU\\n\", \"DLDLUURR\\n\", \"UULLR\\n\", \"DRLRLDDD\\n\", \"ULRUL\\n\", \"RDU\\n\", \"UDLLULUR\\n\", \"UURRLULLULLLULRURLRLLURLRLRLRULUULULRRRU\\n\", \"URL\\n\", \"RLDLUUDR\\n\", \"UULRL\\n\"], \"outputs\": [\"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"OK\\n\", \"OK\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\", \"BUG\\n\"]}", "source": "primeintellect"}
|
The whole world got obsessed with robots,and to keep pace with the progress, great Berland's programmer Draude decided to build his own robot. He was working hard at the robot. He taught it to walk the shortest path from one point to another, to record all its movements, but like in many Draude's programs, there was a bug — the robot didn't always walk the shortest path. Fortunately, the robot recorded its own movements correctly. Now Draude wants to find out when his robot functions wrong. Heh, if Draude only remembered the map of the field, where he tested the robot, he would easily say if the robot walked in the right direction or not. But the field map was lost never to be found, that's why he asks you to find out if there exist at least one map, where the path recorded by the robot is the shortest.
The map is an infinite checkered field, where each square is either empty, or contains an obstruction. It is also known that the robot never tries to run into the obstruction. By the recorded robot's movements find out if there exist at least one such map, that it is possible to choose for the robot a starting square (the starting square should be empty) such that when the robot moves from this square its movements coincide with the recorded ones (the robot doesn't run into anything, moving along empty squares only), and the path from the starting square to the end one is the shortest.
In one movement the robot can move into the square (providing there are no obstrutions in this square) that has common sides with the square the robot is currently in.
Input
The first line of the input file contains the recording of the robot's movements. This recording is a non-empty string, consisting of uppercase Latin letters L, R, U and D, standing for movements left, right, up and down respectively. The length of the string does not exceed 100.
Output
In the first line output the only word OK (if the above described map exists), or BUG (if such a map does not exist).
Examples
Input
LLUUUR
Output
OK
Input
RRUULLDD
Output
BUG
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
{"tests": "{\"inputs\": [\"4 2\\n\", \"1000 1001\\n\", \"6 3\\n\", \"630719418 9872663\\n\", \"963891449 582938127\\n\", \"1000000000 999999999\\n\", \"0 2\\n\", \"481994122 678374097\\n\", \"779351061 773124120\\n\", \"141148629 351661795\\n\", \"771581370 589752968\\n\", \"422447052 772330542\\n\", \"225821895 880886365\\n\", \"7 0\\n\", \"318405810 783948974\\n\", \"424836699 793451637\\n\", \"81601559 445618240\\n\", \"1 0\\n\", \"807976599 442159843\\n\", \"3 0\\n\", \"1000000000 1\\n\", \"16155311 406422145\\n\", \"543930839 974134967\\n\", \"2 1\\n\", \"1 1\\n\", \"48564714 743566477\\n\", \"303352912 928083702\\n\", \"3 2\\n\", \"10 1\\n\", \"495662991 921268861\\n\", \"81452244 81452247\\n\", \"540157163 340043363\\n\", \"0 0\\n\", \"599704233 541054210\\n\", \"602093880 930771525\\n\", \"777777 0\\n\", \"690266488 579479730\\n\", \"2 0\\n\", \"67932690 202723476\\n\", \"948838551 727072855\\n\", \"403079076 313173543\\n\", \"0 1\\n\", \"185642801 65403588\\n\", \"831128440 790763814\\n\", \"1000000000 1000000000\\n\", \"247579518 361164458\\n\", \"188032448 86524683\\n\", \"365289629 223844571\\n\", \"1 2\\n\", \"661640950 836815080\\n\", \"453462237 167520068\\n\", \"2 2\\n\", \"341379754 9872663\\n\", \"1000000000 801551372\\n\", \"1079372212 582938127\\n\", \"481994122 1051460840\\n\", \"779351061 270243771\\n\", \"280175792 351661795\\n\", \"683455942 589752968\\n\", \"320053668 772330542\\n\", \"150739752 880886365\\n\", \"173294004 783948974\\n\", \"424836699 1500222727\\n\", \"81601559 270746194\\n\", \"3 1\\n\", \"807976599 38208693\\n\", \"6 0\\n\", \"1000000000 2\\n\", \"11622315 406422145\\n\", \"816835446 974134967\\n\", \"0 3\\n\", \"4981920 743566477\\n\", \"116145104 928083702\\n\", \"4 4\\n\", \"12 1\\n\", \"801877297 921268861\\n\", \"52836002 81452247\\n\", \"371403100 340043363\\n\", \"599704233 627896327\\n\", \"602093880 1725716026\\n\", \"845781566 579479730\\n\", \"67932690 402621179\\n\", \"1194133285 727072855\\n\", \"105283375 313173543\\n\", \"0 4\\n\", \"257520786 65403588\\n\", \"831128440 1019994035\\n\", \"1000001000 1000000000\\n\", \"331860270 361164458\\n\", \"265535936 86524683\\n\", \"222215468 223844571\\n\", \"4 0\\n\", \"240957380 836815080\\n\", \"698752893 167520068\\n\", \"-1 2\\n\", \"8 2\\n\", \"1001 1001\\n\", \"6 6\\n\", \"341379754 11528620\\n\", \"1079372212 230318370\\n\", \"0000000000 801551372\\n\", \"415555623 1051460840\\n\", \"1373065343 270243771\\n\", \"280175792 664336459\\n\", \"1014175846 589752968\\n\", \"320053668 611986504\\n\", \"150739752 1221247878\\n\", \"173294004 1120105588\\n\", \"424836699 1344072001\\n\", \"81601559 120447100\\n\", \"807976599 67038754\\n\", \"12 0\\n\", \"1000001000 2\\n\", \"2859579 406422145\\n\", \"816835446 1252616623\\n\", \"-1 3\\n\", \"4981920 1217858910\\n\", \"116145104 1715599612\\n\", \"5 4\\n\", \"6 1\\n\", \"913858962 921268861\\n\", \"23680683 81452247\\n\", \"15261865 340043363\\n\", \"599704233 472902709\\n\", \"72804371 402621179\\n\", \"115421479 313173543\\n\", \"1 4\\n\", \"257520786 115804182\\n\", \"831128440 765470542\\n\", \"1000011000 1000000000\\n\", \"255058418 361164458\\n\", \"265535936 77253423\\n\", \"222215468 162826288\\n\", \"0 -2\\n\", \"240957380 565747307\\n\", \"590096559 167520068\\n\", \"1 3\\n\", \"8 0\\n\", \"1011 1001\\n\", \"0 6\\n\", \"341379754 7734001\\n\", \"844444797 230318370\\n\", \"0100000000 801551372\\n\", \"415555623 296408105\\n\", \"1373065343 416085600\\n\", \"280175792 862787462\\n\", \"1014175846 449318755\\n\", \"320053668 486000247\\n\", \"150739752 37821131\\n\", \"274276677 1120105588\\n\", \"686242317 1344072001\\n\", \"120195654 120447100\\n\"], \"outputs\": [\"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\"]}", "source": "primeintellect"}
|
Imp likes his plush toy a lot.
<image>
Recently, he found a machine that can clone plush toys. Imp knows that if he applies the machine to an original toy, he additionally gets one more original toy and one copy, and if he applies the machine to a copied toy, he gets two additional copies.
Initially, Imp has only one original toy. He wants to know if it is possible to use machine to get exactly x copied toys and y original toys? He can't throw toys away, and he can't apply the machine to a copy if he doesn't currently have any copies.
Input
The only line contains two integers x and y (0 ≤ x, y ≤ 109) — the number of copies and the number of original toys Imp wants to get (including the initial one).
Output
Print "Yes", if the desired configuration is possible, and "No" otherwise.
You can print each letter in arbitrary case (upper or lower).
Examples
Input
6 3
Output
Yes
Input
4 2
Output
No
Input
1000 1001
Output
Yes
Note
In the first example, Imp has to apply the machine twice to original toys and then twice to copies.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n6 12 8\\n\\nSAMPLE\", \"15\\n163004418 141715548 168024392 150391828 194860227 992288235 933539839 120817690 26026774 465544095 363334937 708292303 29566466 171450602 452807812\", \"15\\n163004418 74928250 168024392 150391828 194860227 992288235 933539839 120817690 26026774 465544095 363334937 708292303 29566466 171450602 452807812\", \"3\\n6 12 8\\n\\nTAMPLE\", \"15\\n163004418 74928250 168024392 150391828 194860227 992288235 933539839 120817690 26026774 465544095 363334937 708292303 29566466 58453081 452807812\", \"3\\n6 8 8\\n\\nTAMPLE\", \"15\\n163004418 74928250 168024392 150391828 194860227 992288235 933539839 189011517 26026774 465544095 363334937 708292303 29566466 58453081 452807812\", \"3\\n6 8 13\\n\\nTAMPLE\", \"15\\n163004418 74928250 168024392 150391828 194860227 992288235 933539839 189011517 26026774 465544095 28287208 708292303 29566466 58453081 452807812\", \"15\\n163004418 74928250 168024392 177359443 194860227 992288235 933539839 189011517 26026774 465544095 28287208 708292303 29566466 58453081 452807812\", \"15\\n163004418 74928250 168024392 177359443 194860227 992288235 933539839 189011517 13004007 465544095 28287208 708292303 29566466 58453081 452807812\", \"15\\n163004418 74928250 168024392 177359443 194860227 992288235 933539839 189011517 13004007 338067987 28287208 708292303 29566466 58453081 452807812\", \"15\\n163004418 74928250 39825296 177359443 194860227 992288235 933539839 189011517 13004007 338067987 28287208 708292303 29566466 58453081 452807812\", \"3\\n6 9 13\\n\\nPEMMTA\", \"15\\n163004418 74928250 39825296 177359443 194860227 992288235 933539839 189011517 13004007 635166616 28287208 708292303 29566466 58453081 452807812\", \"3\\n12 9 13\\n\\nPEMMTA\", \"15\\n163004418 74928250 39825296 177359443 194860227 992288235 933539839 189011517 13004007 635166616 28287208 1375450021 29566466 58453081 452807812\", \"3\\n12 18 13\\n\\nPEMMTA\", \"15\\n163004418 74928250 39825296 177359443 194860227 992288235 933539839 189011517 13004007 635166616 28287208 1375450021 29566466 35248323 452807812\", \"3\\n8 18 13\\n\\nPEMMTA\", \"15\\n163004418 38521049 39825296 177359443 194860227 992288235 933539839 189011517 13004007 635166616 28287208 1375450021 29566466 35248323 452807812\", \"3\\n13 18 13\\n\\nPEMMTA\", \"15\\n163004418 38521049 39825296 177359443 194860227 992288235 933539839 189011517 13004007 635166616 28287208 1375450021 29566466 61954944 452807812\", \"15\\n163004418 38521049 39825296 177359443 194860227 992288235 933539839 189011517 13004007 635166616 28287208 1375450021 29566466 61954944 304175045\", \"3\\n13 18 5\\n\\nPAMMTE\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 933539839 189011517 13004007 635166616 28287208 1375450021 29566466 61954944 304175045\", \"3\\n13 18 8\\n\\nPAMMTE\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 933539839 189011517 13004007 773888530 28287208 1375450021 29566466 61954944 304175045\", \"3\\n15 18 8\\n\\nPAMMTE\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 933539839 189011517 13004007 773888530 30584252 1375450021 29566466 61954944 304175045\", \"3\\n15 31 8\\n\\nPAMMTE\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 933539839 189011517 13004007 773888530 30584252 1375450021 53594109 61954944 304175045\", \"3\\n4 31 8\\n\\nPAMMTE\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 933539839 189011517 13004007 773888530 26651319 1375450021 53594109 61954944 304175045\", \"3\\n4 31 11\\n\\nPAMMTE\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 933539839 189011517 13004007 773888530 26651319 1375450021 16750179 61954944 304175045\", \"15\\n163004418 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 13004007 773888530 26651319 1375450021 16750179 61954944 304175045\", \"3\\n4 31 19\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 13004007 773888530 26651319 1375450021 16750179 61954944 304175045\", \"3\\n6 31 19\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 17792019 773888530 26651319 1375450021 16750179 61954944 304175045\", \"3\\n6 43 19\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 3991116 773888530 26651319 1375450021 16750179 61954944 304175045\", \"3\\n6 43 22\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 3991116 773888530 26651319 1375450021 16750179 13001780 304175045\", \"3\\n6 38 22\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 3991116 773888530 28535948 1375450021 16750179 13001780 304175045\", \"3\\n6 13 22\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 3991116 773888530 28535948 1375450021 16750179 13001780 443389407\", \"15\\n81840199 38521049 39825296 177359443 194860227 1010453773 788056580 189011517 3991116 773888530 28535948 1375450021 16750179 11153465 443389407\", \"3\\n3 8 22\\n\\nPAEMTM\", \"15\\n81840199 38521049 39825296 53459194 194860227 1010453773 788056580 189011517 3991116 773888530 28535948 1375450021 16750179 11153465 443389407\", \"15\\n81840199 38521049 39825296 53459194 194860227 1010453773 788056580 55544116 3991116 773888530 28535948 1375450021 16750179 11153465 443389407\", \"15\\n81840199 38521049 39825296 53459194 194860227 1010453773 788056580 55544116 3991116 773888530 28535948 2005804741 16750179 11153465 443389407\", \"15\\n81840199 38521049 39825296 53459194 194860227 1010453773 788056580 69122384 3991116 773888530 28535948 2005804741 16750179 11153465 443389407\", \"3\\n3 12 2\\n\\nMTMEBP\", \"15\\n81840199 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 3991116 773888530 28535948 2005804741 16750179 11153465 443389407\", \"3\\n3 23 2\\n\\nMTMEBP\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 3991116 773888530 28535948 2005804741 16750179 11153465 443389407\", \"3\\n3 30 2\\n\\nMTMEBP\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 3991116 773888530 28535948 2586503336 16750179 11153465 443389407\", \"3\\n0 30 2\\n\\nMTMEBP\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 7937262 773888530 28535948 2586503336 16750179 11153465 443389407\", \"3\\n0 23 2\\n\\nMTMEBP\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 7937262 1388776890 28535948 2586503336 16750179 11153465 443389407\", \"3\\n1 23 2\\n\\nMTMEBP\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 28535948 2586503336 16750179 11153465 443389407\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 28535948 2586503336 14899799 11153465 443389407\", \"3\\n1 23 0\\n\\nPBEMTM\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 28535948 2586503336 5013554 11153465 443389407\", \"15\\n44693860 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 28535948 2586503336 5013554 17897200 443389407\", \"15\\n31675483 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 28535948 2586503336 5013554 17897200 443389407\", \"3\\n1 24 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 28535948 2586503336 1595072 17897200 443389407\", \"3\\n0 24 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 39825296 37631842 194860227 1010453773 788056580 69122384 11041582 1388776890 13343808 2586503336 1595072 17897200 443389407\", \"3\\n0 37 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 39825296 37631842 194860227 1010453773 788056580 128040031 11041582 1388776890 13343808 2586503336 1595072 17897200 443389407\", \"3\\n0 23 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 36844753 37631842 194860227 1010453773 788056580 128040031 11041582 1388776890 13343808 2586503336 1595072 17897200 443389407\", \"15\\n31675483 38521049 36844753 37631842 194860227 1010453773 788056580 128040031 11041582 1388776890 13343808 2586503336 483713 17897200 443389407\", \"3\\n0 33 0\\n\\nMSMEBP\", \"15\\n31675483 38521049 36844753 37631842 194860227 1010453773 788056580 128040031 11041582 1388776890 13343808 2298598414 483713 17897200 443389407\", \"3\\n0 33 -1\\n\\nMSMEBP\", \"15\\n31675483 38521049 36844753 37631842 200453315 1010453773 788056580 128040031 11041582 1388776890 13343808 2298598414 483713 17897200 443389407\", \"15\\n31675483 38521049 36844753 37631842 200453315 1010453773 788056580 128040031 11041582 1388776890 13343808 2298598414 483713 17897200 255388287\", \"3\\n0 7 -2\\n\\nMSMEBP\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 128040031 11041582 1388776890 13343808 2298598414 483713 17897200 255388287\", \"3\\n0 7 -3\\n\\nMSMEBP\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 128040031 11041582 1388776890 16974122 2298598414 483713 17897200 255388287\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 128040031 11041582 1388776890 16974122 2298598414 204013 17897200 255388287\", \"3\\n0 11 -3\\n\\nPBEMSM\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 156098427 11041582 1388776890 16974122 2298598414 204013 17897200 255388287\", \"3\\n0 11 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 156098427 11041582 1388776890 16974122 2298598414 204013 17897200 127558375\", \"3\\n0 10 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 156098427 11041582 2294550939 16974122 2298598414 204013 17897200 127558375\", \"3\\n0 9 0\\n\\nPBEMSM\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 156098427 11041582 2294550939 16974122 2298598414 204013 17897200 40441511\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 156098427 11041582 2294550939 25719822 2298598414 204013 17897200 40441511\", \"3\\n0 15 0\\n\\nSBEMPM\", \"15\\n31675483 38521049 36844753 37631842 200453315 1410687204 788056580 156098427 11041582 2294550939 25719822 2298598414 29342 17897200 40441511\"], \"outputs\": [\"160\\n\", \"987375170\\n\", \"622751009\\n\", \"160\\n\", \"487467724\\n\", \"136\\n\", \"281909584\\n\", \"176\\n\", \"750188527\\n\", \"343691192\\n\", \"518626021\\n\", \"391662334\\n\", \"563714013\\n\", \"182\\n\", \"715183057\\n\", \"206\\n\", \"343021835\\n\", \"260\\n\", \"942378759\\n\", \"244\\n\", \"199013241\\n\", \"264\\n\", \"908578754\\n\", \"314678897\\n\", \"200\\n\", \"999282682\\n\", \"224\\n\", \"508309543\\n\", \"232\\n\", \"316921337\\n\", \"310\\n\", \"999222436\\n\", \"266\\n\", \"376179506\\n\", \"290\\n\", \"819565248\\n\", \"428770162\\n\", \"354\\n\", \"634215376\\n\", \"362\\n\", \"868155672\\n\", \"434\\n\", \"298189822\\n\", \"458\\n\", \"933439614\\n\", \"428\\n\", \"200007528\\n\", \"278\\n\", \"304735863\\n\", \"183790252\\n\", \"236\\n\", \"229626737\\n\", \"945154696\\n\", \"200945899\\n\", \"299481996\\n\", \"100\\n\", \"11148612\\n\", \"166\\n\", \"405534699\\n\", \"208\\n\", \"482674925\\n\", \"196\\n\", \"750952984\\n\", \"154\\n\", \"570461441\\n\", \"158\\n\", \"876354063\\n\", \"659974107\\n\", \"142\\n\", \"826315485\\n\", \"496466482\\n\", \"203379205\\n\", \"148\\n\", \"144518333\\n\", \"144\\n\", \"696398231\\n\", \"222\\n\", \"576645839\\n\", \"138\\n\", \"910213501\\n\", \"450673398\\n\", \"198\\n\", \"728314713\\n\", \"190\\n\", \"639774164\\n\", \"957146018\\n\", \"26\\n\", \"942852625\\n\", \"18\\n\", \"817237582\\n\", \"739004206\\n\", \"42\\n\", \"428410011\\n\", \"66\\n\", \"506301632\\n\", \"60\\n\", \"616833773\\n\", \"54\\n\", \"35315491\\n\", \"772602278\\n\", \"90\\n\", \"739934770\\n\"]}", "source": "primeintellect"}
|
Limak is an old brown bear.
He often goes bowling with his friends.
For rolling a ball one gets a score - a non-negative integer number of points.
Score for the i-th roll is multiplied by i and scores are summed up.
For example, for rolls with scores 7, 10, 5 the total score is equal to 7×1 + 10×2 + 5×3 = 42.
Limak made N rolls and got a score Ai for the i-th of them.
Unfortunately, the bowling club's computer system isn't stable today.
Any rolls can be erased!
Then, the total score is calculated as if there were only non-erased rolls.
There are 2^N possible sequences of remaining (non-erased) rolls.
Limak is curious about various statistics of this situation.
He asks you for one thing.
Find the sum of total scores of all 2^N possible sequences of remaining rolls.
Print it modulo 10^9+7.
Input format
The first line contains a single integer N.
The second line contains N non-negative integers A1, A2, ..., AN.
Output format
In a single line print modulo 10^9+7 the sum of total scores of possible remaining sequences.
Constraints
1 ≤ N ≤ 200,000
0 ≤ Ai ≤ 10^9
SAMPLE INPUT
3
6 12 8
SAMPLE OUTPUT
160
Explanation
There are eight possible remaining subsequences.
{} - 0
{6} - 6
{12} - 12
{8} - 8
{6, 12} - 30
{6, 8} - 22
{12, 8} - 28
{6, 12, 8} - 54
0 + 6 + 12 + 8 + 30 + 22 + 28 + 54 = 160
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"a2b3c2a1\\n4\\n2\\n5\\n1\\n8\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n4\\n5\\n1\\n8\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n6\\n5\\n1\\n16\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n6\\n9\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n2\\n9\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n2\\n2\\n2\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n2\\n10\\n1\\n8\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n6\\n10\\n1\\n8\\n\\nSAMPLE\", \"a2b4c2a1\\n4\\n2\\n9\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n6\\n5\\n2\\n4\\n\\nSAMPLE\", \"a2b4c2a1\\n4\\n4\\n9\\n1\\n16\\n\\nELSMAP\", \"a2b4c2a1\\n4\\n4\\n9\\n1\\n4\\n\\nELSMAP\", \"a2b3c2a1\\n2\\n2\\n13\\n2\\n8\\n\\nSAPDLM\", \"a2b4c2a1\\n4\\n2\\n4\\n1\\n4\\n\\nEMSMAP\", \"a2b3c2a1\\n2\\n4\\n13\\n2\\n8\\n\\nS@PDLM\", \"a2b3c2a1\\n2\\n8\\n13\\n0\\n8\\n\\nMLEP@S\", \"a2b3c2a1\\n3\\n8\\n13\\n1\\n8\\n\\nS@PFLM\", \"a2b3c2a1\\n4\\n3\\n5\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n1\\n6\\n9\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n2\\n2\\n2\\n6\\n\\nPAMSLE\", \"b2b3c2a1\\n4\\n2\\n11\\n2\\n10\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n8\\n13\\n1\\n8\\n\\nMLFP@S\", \"a2b3c2a1\\n3\\n4\\n13\\n1\\n8\\n\\nS@PFLM\", \"a2b3c2a1\\n3\\n14\\n11\\n1\\n5\\n\\nMFLP@S\", \"a2b3c2a1\\n3\\n8\\n19\\n4\\n5\\n\\nMFLP@S\", \"a2b3c2a1\\n4\\n4\\n5\\n1\\n2\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n8\\n5\\n1\\n32\\n\\nSAMPLE\", \"a2a3c2a1\\n1\\n2\\n3\\n2\\n16\\n\\nLAMSPE\", \"a2b4c2a1\\n4\\n2\\n13\\n1\\n7\\n\\nELSMAP\", \"b2b3c2a1\\n4\\n2\\n11\\n2\\n2\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n2\\n25\\n4\\n8\\n\\nSAPDLM\", \"a2b3c2a1\\n2\\n10\\n13\\n1\\n8\\n\\nMLEP@S\", \"a2b3c2a1\\n3\\n1\\n13\\n1\\n8\\n\\nS@PFLM\", \"a2b3c2a1\\n3\\n5\\n19\\n4\\n5\\n\\nMFLP@S\", \"a2b4c2a1\\n4\\n2\\n8\\n1\\n7\\n\\nELSMAP\", \"a2a3c2a1\\n4\\n1\\n1\\n2\\n2\\n\\nLAMSPE\", \"a2b3c2a1\\n4\\n11\\n18\\n1\\n8\\n\\nMLFP@S\", \"a2b3c2a1\\n3\\n2\\n5\\n1\\n5\\n\\nAPMSLE\", \"c2b4a2a1\\n4\\n7\\n9\\n1\\n2\\n\\nELPMAS\", \"b2b4c2a1\\n4\\n3\\n5\\n2\\n4\\n\\nPAMSME\", \"a2b3c2a1\\n4\\n5\\n19\\n4\\n1\\n\\nMFLP@S\", \"a2b3c2a1\\n2\\n8\\n4\\n0\\n5\\n\\nS@PFLM\", \"a2b3c2a1\\n4\\n5\\n7\\n4\\n1\\n\\nMFLP@S\", \"a2b3c2a1\\n2\\n14\\n4\\n0\\n10\\n\\nS@PFLM\", \"a2b3c2a1\\n1\\n7\\n4\\n0\\n10\\n\\nS@QFKM\", \"a2b3c2a1\\n4\\n2\\n5\\n2\\n8\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n6\\n1\\n1\\n16\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n11\\n5\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n6\\n5\\n4\\n16\\n\\nAPMSLE\", \"a2b3c2a1\\n3\\n8\\n8\\n1\\n8\\n\\nMFLP@S\", \"a2b3c2a1\\n3\\n8\\n4\\n1\\n5\\n\\nMFLP@S\", \"a2a3c2a1\\n2\\n1\\n2\\n2\\n16\\n\\nPAMSLE\", \"a2b4c2a1\\n4\\n2\\n4\\n4\\n4\\n\\nPAMSME\", \"a2b4c2a1\\n4\\n8\\n9\\n1\\n4\\n\\nELPMAS\", \"a2b3c2a1\\n4\\n4\\n25\\n4\\n8\\n\\nSAPDLM\", \"a2b3c2a1\\n4\\n8\\n19\\n4\\n5\\n\\nMFLP@S\", \"a2b4c2a1\\n2\\n2\\n8\\n1\\n5\\n\\nELSMAP\", \"c2b4a2a1\\n3\\n7\\n9\\n1\\n2\\n\\nELPMAS\", \"a2b4c1a1\\n4\\n9\\n5\\n1\\n4\\n\\nELRMAP\", \"b2b4c2a1\\n3\\n3\\n5\\n2\\n4\\n\\nPAMSME\", \"a2b3c2a1\\n4\\n5\\n19\\n1\\n1\\n\\nMFLP@S\", \"a2b4c2a1\\n3\\n1\\n1\\n1\\n16\\n\\nLAMTPE\", \"a2b3b2a1\\n2\\n8\\n4\\n0\\n10\\n\\nS@PFLM\", \"a2b2c2a0\\n1\\n14\\n16\\n1\\n11\\n\\nMFLP@S\", \"b2b4c2a2\\n4\\n3\\n9\\n3\\n4\\n\\nPAMRME\", \"b3a3c2a2\\n4\\n6\\n5\\n3\\n8\\n\\nPAMRME\", \"a2b3c2a1\\n3\\n8\\n2\\n1\\n12\\n\\nMLFP@S\", \"a2b4c2a1\\n3\\n2\\n4\\n4\\n4\\n\\nPAMSME\", \"a2b3c2a1\\n4\\n2\\n1\\n1\\n8\\n\\nSAMDLP\", \"a2b3c2a1\\n4\\n4\\n25\\n8\\n8\\n\\nSAPDLM\", \"a2b3c2a1\\n4\\n1\\n10\\n4\\n10\\n\\nPALSLE\", \"c2b4a2a1\\n2\\n7\\n9\\n2\\n4\\n\\nELPMAS\", \"a2b3c2a1\\n4\\n11\\n18\\n2\\n3\\n\\nMLFP@S\", \"a2b3c2a1\\n4\\n11\\n18\\n1\\n13\\n\\nMLFP@S\", \"a2b3c2a0\\n3\\n11\\n4\\n1\\n22\\n\\nMFLP@S\", \"a2b3c2a1\\n4\\n2\\n13\\n4\\n1\\n\\nMFLP@S\", \"a2b3c2a1\\n2\\n14\\n2\\n0\\n12\\n\\nS@QFLM\", \"b3a4c2a2\\n4\\n11\\n1\\n2\\n8\\n\\nMAMRPE\", \"a2b4c2a1\\n4\\n2\\n9\\n3\\n9\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n9\\n5\\n5\\n16\\n\\nAPMSLE\", \"a2b4c2a1\\n4\\n4\\n3\\n1\\n8\\n\\nEMSMAP\", \"a2b3c2a1\\n4\\n8\\n13\\n4\\n11\\n\\nMLFS@P\", \"a2b4c2a1\\n4\\n4\\n9\\n2\\n8\\n\\nFSLNAP\", \"a2b3b3a1\\n2\\n2\\n8\\n-1\\n0\\n\\nS@PELM\", \"b3a4c2a2\\n4\\n11\\n1\\n2\\n2\\n\\nMAMRPE\", \"a2b3c3a1\\n3\\n2\\n7\\n2\\n2\\n\\nSAPDLM\", \"a2b4c2a1\\n4\\n1\\n9\\n4\\n4\\n\\nELPLAS\", \"b2a3c2a1\\n2\\n8\\n7\\n0\\n8\\n\\nS@PFLM\", \"a2b3c2a1\\n4\\n8\\n13\\n8\\n11\\n\\nMLFS@P\", \"a2b3c2a1\\n4\\n11\\n3\\n2\\n3\\n\\nMLFP@S\", \"a2b3c1a1\\n4\\n3\\n7\\n4\\n2\\n\\nMFLP@T\", \"a2b3c2a2\\n2\\n9\\n4\\n1\\n7\\n\\nS@PFLM\", \"a2c2b2a0\\n4\\n5\\n16\\n2\\n16\\n\\nMFKP@R\", \"a2b3c2a1\\n4\\n2\\n5\\n1\\n2\\n\\nAPMSLE\", \"a2b4c2a1\\n3\\n4\\n3\\n1\\n9\\n\\nEMSMAP\", \"a2b3c2a1\\n4\\n6\\n5\\n1\\n8\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n6\\n5\\n1\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n2\\n9\\n2\\n16\\n\\nPAMSLE\", \"a2a3c2a1\\n4\\n2\\n2\\n2\\n16\\n\\nPAMSLE\", \"a2b3c2a1\\n4\\n6\\n5\\n2\\n16\\n\\nSAMPLE\", \"a2b3c2a1\\n4\\n6\\n5\\n1\\n16\\n\\nAPMSLE\"], \"outputs\": [\"a\\nb\\na\\nc\\n\", \"b\\nb\\na\\nc\\n\", \"b\\nb\\na\\n-1\\n\", \"b\\n-1\\na\\n-1\\n\", \"a\\n-1\\na\\n-1\\n\", \"a\\na\\na\\n-1\\n\", \"a\\n-1\\na\\nc\\n\", \"b\\n-1\\na\\nc\\n\", \"a\\nc\\na\\n-1\\n\", \"b\\nb\\na\\nb\\n\", \"b\\nc\\na\\n-1\\n\", \"b\\nc\\na\\nb\\n\", \"a\\n-1\\n\", \"a\\nb\\na\\nb\\n\", \"b\\n-1\\n\", \"c\\n-1\\n\", \"c\\n-1\\na\\n\", \"a\\nb\\na\\n-1\\n\", \"b\\n\", \"a\\na\\na\\nb\\n\", \"b\\n-1\\nb\\n-1\\n\", \"c\\n-1\\na\\nc\\n\", \"b\\n-1\\na\\n\", \"-1\\n-1\\na\\n\", \"c\\n-1\\nb\\n\", \"b\\nb\\na\\na\\n\", \"c\\nb\\na\\n-1\\n\", \"a\\n\", \"a\\n-1\\na\\nb\\n\", \"b\\n-1\\nb\\nb\\n\", \"a\\n-1\\nb\\nc\\n\", \"-1\\n-1\\n\", \"a\\n-1\\na\\n\", \"b\\n-1\\nb\\n\", \"a\\nc\\na\\nb\\n\", \"a\\na\\na\\na\\n\", \"-1\\n-1\\na\\nc\\n\", \"a\\nb\\na\\n\", \"b\\nc\\na\\na\\n\", \"b\\nb\\nb\\nb\\n\", \"b\\n-1\\nb\\na\\n\", \"c\\nb\\n\", \"b\\nc\\nb\\na\\n\", \"-1\\nb\\n\", \"c\\n\", \"a\\nb\\na\\nc\\n\", \"b\\na\\na\\n-1\\n\", \"-1\\nb\\na\\n-1\\n\", \"b\\nb\\nb\\n-1\\n\", \"c\\nc\\na\\n\", \"c\\nb\\na\\n\", \"a\\na\\n\", \"a\\nb\\nb\\nb\\n\", \"c\\nc\\na\\nb\\n\", \"b\\n-1\\nb\\nc\\n\", \"c\\n-1\\nb\\nb\\n\", \"a\\nc\\n\", \"b\\nc\\na\\n\", \"-1\\nb\\na\\nb\\n\", \"b\\nb\\nb\\n\", \"b\\n-1\\na\\na\\n\", \"a\\na\\na\\n\", \"b\\nb\\n\", \"-1\\n\", \"b\\nc\\nb\\nb\\n\", \"b\\na\\na\\nb\\n\", \"c\\na\\na\\n\", \"a\\nb\\nb\\n\", \"a\\na\\na\\nc\\n\", \"b\\n-1\\nc\\nc\\n\", \"a\\n-1\\nb\\n-1\\n\", \"b\\nc\\n\", \"-1\\n-1\\na\\na\\n\", \"-1\\n-1\\na\\n-1\\n\", \"-1\\nb\\na\\n\", \"a\\n-1\\nb\\na\\n\", \"-1\\na\\n\", \"c\\na\\na\\nb\\n\", \"a\\nc\\na\\nc\\n\", \"-1\\nb\\nb\\n-1\\n\", \"b\\na\\na\\nc\\n\", \"c\\n-1\\nb\\n-1\\n\", \"b\\nc\\na\\nc\\n\", \"a\\nb\\n\", \"c\\na\\na\\na\\n\", \"a\\nc\\na\\n\", \"a\\nc\\nb\\nb\\n\", \"c\\nc\\n\", \"c\\n-1\\nc\\n-1\\n\", \"-1\\na\\na\\na\\n\", \"a\\nc\\nb\\na\\n\", \"c\\na\\n\", \"c\\n-1\\na\\n-1\\n\", \"a\\nb\\na\\na\\n\", \"b\\na\\na\\n\", \"b\\nb\\na\\nc\\n\", \"b\\nb\\na\\n-1\\n\", \"a\\n-1\\na\\n-1\\n\", \"a\\na\\na\\n-1\\n\", \"b\\nb\\na\\n-1\\n\", \"b\\nb\\na\\n-1\\n\"]}", "source": "primeintellect"}
|
Ma5termind and Subway are bored of their normal life.They want to do something interesting so that they can enjoy their last sem of college life.As usual Ma5termind comes up with a simple and interesting game.
Ma5termind gives Subway a compressed string. A compressed String is composed of characters and numbers.Every character in a compressed string contains a number. Ex a3b1c2 it represents aaabcc. Other compressed string could be a22b2a1 , z5c2x36. Each number in the compressed string indicates the number of times the corresponding character occurs in the string. The final string is 1 indexed. Ma5termind wants Subway to sort the compressed string and tell him the kth character in the sorted compressed string.Since subway got speed Ma5termind asks him various such questions.
Help Subway in answering Ma5termind's question.
Input:
The first line contains the compressed string.This is followed by Q that indicates the number of questions Ma5termind shoots on Subway.Follows Q lines each line contain an integer K.
Output:
For every question output the Kth character if it exists else print -1 .
Constraints:
2 ≤ Length of Compressed String ≤ 10^4
1 ≤ Length of Final String ≤ 10^18
1 ≤ Q ≤ 10^5
1 ≤ K ≤ 10^18
Every character in the string is lowercase English letter.
Note:
The number for a character may contain leading zeroes.
SAMPLE INPUT
a2b3c2a1
4
2
5
1
8
SAMPLE OUTPUT
a
b
a
c
Explanation
The final sorted string is aaabbbcc.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"3 0\\n1000000000 1000000000 1000000000\", \"8 9\\n7 9 3 2 3 8 4 6\", \"3 1\\n4 1 5\", \"3 0\\n1000000000 1000000000 1010000000\", \"8 8\\n7 9 3 2 3 8 4 6\", \"3 1\\n0 1 5\", \"3 0\\n1000000000 1000000000 1110000000\", \"3 0\\n1100000000 1000000000 1110000000\", \"3 0\\n1100000000 1000000001 1110000000\", \"3 0\\n1100000000 1000000001 1110001000\", \"3 0\\n1100000001 1000000001 1110001000\", \"8 0\\n4 9 5 2 3 6 5 6\", \"8 1\\n4 9 5 2 3 6 5 6\", \"3 0\\n1000000100 1000000000 1000000000\", \"3 0\\n1000000000 1000000000 1010010000\", \"3 0\\n0 1 5\", \"3 0\\n1000000000 1000000000 0110000000\", \"3 0\\n0100000000 1000000001 1110000000\", \"3 0\\n1100000001 1000000001 0110001000\", \"8 0\\n4 16 5 2 3 6 5 6\", \"8 1\\n4 9 9 2 3 6 5 6\", \"3 0\\n1100000011 1000000000 1110000000\", \"3 0\\n1000000000 1100000000 0110000000\", \"3 0\\n0000000000 1000000001 1110000000\", \"8 0\\n4 16 5 1 3 6 5 6\", \"8 1\\n4 9 9 2 3 4 5 6\", \"8 2\\n7 6 3 2 3 8 7 6\", \"3 0\\n1100000011 1010000000 1110000000\", \"3 0\\n0000000000 1100000000 0110000000\", \"3 0\\n0000000000 1000000001 0110000000\", \"8 1\\n4 9 9 2 6 4 5 6\", \"3 0\\n1100000011 1010100000 1110000000\", \"3 0\\n0000000000 0100000000 0110000000\", \"8 0\\n4 22 5 1 3 6 6 6\", \"8 2\\n7 6 3 2 0 14 7 6\", \"3 0\\n0000000001 0100000000 0110000000\", \"8 1\\n4 9 9 0 6 4 16 6\", \"8 2\\n7 6 3 1 0 23 7 6\", \"8 1\\n4 9 8 0 3 4 16 6\", \"8 2\\n7 6 3 1 0 23 10 5\", \"8 2\\n7 6 2 1 0 23 10 5\", \"8 2\\n4 9 8 0 3 4 11 6\", \"8 2\\n7 6 2 1 0 23 0 5\", \"8 2\\n7 2 2 1 0 23 0 5\", \"8 2\\n7 2 2 1 0 23 0 6\", \"8 2\\n7 2 2 2 0 23 0 6\", \"8 0\\n6 9 8 0 3 4 8 6\", \"8 2\\n7 2 2 2 0 1 0 6\", \"8 2\\n0 2 2 2 0 1 0 1\", \"3 0\\n1000000000 1000000000 1000001000\", \"3 1\\n4 1 6\", \"3 0\\n1000000000 1000000100 1110000000\", \"8 5\\n7 9 5 2 3 8 4 6\", \"3 0\\n1100000000 1000000000 1110000010\", \"3 0\\n1100000000 1000000001 1010000000\", \"3 0\\n1100000000 1000000001 1110011000\", \"8 0\\n4 12 5 2 3 6 5 6\", \"8 1\\n4 9 5 2 0 6 5 6\", \"3 0\\n1000000100 1000010000 1000000000\", \"3 0\\n1000000000 1000010000 1010010000\", \"3 0\\n0110000000 1000000001 1110000000\", \"3 0\\n1100000001 1000000001 0010001000\", \"8 0\\n2 16 5 2 3 6 5 6\", \"3 0\\n1100010011 1000000000 1110000000\", \"3 0\\n1000000000 1100100000 0110000000\", \"3 1\\n0000000000 1100000000 0110000000\", \"8 0\\n4 16 5 1 3 6 6 8\", \"8 1\\n4 9 9 2 6 4 5 12\", \"3 0\\n1000000011 1010100000 1110000000\", \"3 0\\n0000000100 0100000000 0110000000\", \"8 0\\n4 22 5 1 3 6 7 6\", \"3 0\\n0000000001 0100010000 0110000000\", \"8 2\\n2 6 3 1 0 23 7 6\", \"8 2\\n7 2 3 1 0 23 10 6\", \"8 2\\n7 6 2 1 0 23 1 5\", \"8 2\\n6 9 8 0 2 4 8 6\", \"8 0\\n6 9 5 0 3 4 8 6\", \"3 0\\n1000000000 1001000100 1110000000\", \"3 1\\n1100000000 1000000000 1110000010\", \"3 0\\n1100000000 1001000001 1010000000\", \"3 0\\n1100000000 1000000001 1110010000\", \"3 1\\n1000000100 1000010000 1000000000\", \"3 0\\n1100000000 1000000000 0110000100\", \"3 0\\n1000000010 1100100000 0110000000\", \"3 0\\n0000000000 1000000100 1110000000\", \"8 1\\n4 9 9 2 3 4 1 7\", \"3 1\\n0000000010 1100000000 0110000000\", \"8 0\\n4 16 5 0 3 6 6 8\", \"8 2\\n7 7 3 2 3 14 7 9\", \"3 0\\n1000000011 1010100001 1110000000\", \"3 0\\n0000000100 0100010000 0110000000\", \"8 0\\n4 22 10 1 3 6 7 6\", \"8 2\\n4 2 3 1 0 23 10 6\", \"8 2\\n6 6 3 0 0 23 10 5\", \"8 1\\n4 9 6 0 3 4 13 6\", \"8 2\\n7 6 2 2 0 23 2 5\", \"8 2\\n4 6 2 1 0 23 1 5\", \"8 0\\n2 9 5 0 3 4 8 6\", \"3 0\\n1000000000 1101000100 1110000000\", \"3 1\\n1000000000 1000000000 1110000010\", \"3 0\\n0100000000 1001000001 1010000000\", \"3 1\\n1000001100 1000010000 1000000000\", \"3 0\\n1110000000 1000000000 0110000100\"], \"outputs\": [\"3000000000\", \"0\", \"5\", \"3010000000\\n\", \"0\\n\", \"1\\n\", \"3110000000\\n\", \"3210000000\\n\", \"3210000001\\n\", \"3210001001\\n\", \"3210001002\\n\", \"40\\n\", \"31\\n\", \"3000000100\\n\", \"3010010000\\n\", \"6\\n\", \"2110000000\\n\", \"2210000001\\n\", \"2210001002\\n\", \"47\\n\", \"35\\n\", \"3210000011\\n\", \"2210000000\\n\", \"2110000001\\n\", \"46\\n\", \"33\\n\", \"27\\n\", \"3220000011\\n\", \"1210000000\\n\", \"1110000001\\n\", \"36\\n\", \"3220100011\\n\", \"210000000\\n\", \"53\\n\", \"24\\n\", \"210000001\\n\", \"38\\n\", \"23\\n\", \"34\\n\", \"22\\n\", \"21\\n\", \"25\\n\", \"14\\n\", \"10\\n\", \"11\\n\", \"12\\n\", \"44\\n\", \"7\\n\", \"4\\n\", \"3000001000\\n\", \"5\\n\", \"3110000100\\n\", \"9\\n\", \"3210000010\\n\", \"3110000001\\n\", \"3210011001\\n\", \"43\\n\", \"28\\n\", \"3000010100\\n\", \"3010020000\\n\", \"2220000001\\n\", \"2110001002\\n\", \"45\\n\", \"3210010011\\n\", \"2210100000\\n\", \"110000000\\n\", \"49\\n\", \"39\\n\", \"3120100011\\n\", \"210000100\\n\", \"54\\n\", \"210010001\\n\", \"18\\n\", \"19\\n\", \"15\\n\", \"26\\n\", \"41\\n\", \"3111000100\\n\", \"2100000000\\n\", \"3111000001\\n\", \"3210010001\\n\", \"2000000100\\n\", \"2210000100\\n\", \"2210100010\\n\", \"2110000100\\n\", \"30\\n\", \"110000010\\n\", \"48\\n\", \"29\\n\", \"3120100012\\n\", \"210010100\\n\", \"59\\n\", \"16\\n\", \"20\\n\", \"32\\n\", \"17\\n\", \"13\\n\", \"37\\n\", \"3211000100\\n\", \"2000000000\\n\", \"2111000001\\n\", \"2000001100\\n\", \"2220000100\\n\"]}", "source": "primeintellect"}
|
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"CSS\\nCSR\", \"RRR\\nSSS\", \"SSR\\nSSR\", \"CSS\\nBSR\", \"SRR\\nSSR\", \"SSR\\nRTS\", \"STR\\nSTR\", \"RSR\\nSSS\", \"SSC\\nBSR\", \"RSR\\nSSR\", \"SSR\\nRSS\", \"SSC\\nRSB\", \"RTR\\nSSR\", \"CSS\\nRSB\", \"RTR\\nSTR\", \"SSR\\nRTR\", \"CSR\\nRSB\", \"SRS\\nRTR\", \"CSR\\nBSR\", \"STR\\nRTS\", \"SRT\\nRTR\", \"CSR\\nBRS\", \"SUR\\nRTS\", \"SST\\nRTR\", \"CTR\\nBRS\", \"TUR\\nRTS\", \"STT\\nRTR\", \"CTR\\nBRR\", \"TUQ\\nRTS\", \"TTS\\nRTR\", \"CTQ\\nBRR\", \"QUT\\nRTS\", \"TTS\\nRTS\", \"CTP\\nBRR\", \"QVT\\nRTS\", \"TTR\\nRTS\", \"CTP\\nRRB\", \"QUT\\nRST\", \"TTR\\nSTS\", \"PTC\\nRRB\", \"TUQ\\nRST\", \"UTR\\nSTS\", \"PTC\\nBRR\", \"TVQ\\nRST\", \"UTR\\nSUS\", \"PTB\\nBRR\", \"QVT\\nRST\", \"TTR\\nSUS\", \"PBT\\nBRR\", \"QVT\\nTSR\", \"TTR\\nSUR\", \"PBU\\nBRR\", \"QVT\\nTRR\", \"TTR\\nRUS\", \"PBU\\nBRQ\", \"QVT\\nTQR\", \"TTS\\nSUS\", \"PBU\\nBQQ\", \"VQT\\nTQR\", \"STT\\nSUS\", \"PAU\\nBQQ\", \"VQT\\nRQT\", \"RTT\\nSUS\", \"PAU\\nQQB\", \"VRT\\nRQT\", \"RST\\nSUS\", \"APU\\nQQB\", \"VRT\\nRTQ\", \"TSR\\nSUS\", \"APU\\nBQQ\", \"VRS\\nRTQ\", \"TSR\\nSTS\", \"APV\\nQQB\", \"VRS\\nQTR\", \"STR\\nSTS\", \"APV\\nQPB\", \"VRS\\nQTS\", \"RTS\\nSTS\", \"APV\\nPQB\", \"VRS\\nRTS\", \"RTS\\nTTS\", \"AQV\\nPQB\", \"VRS\\nSTR\", \"RST\\nTTS\", \"VQA\\nPQB\", \"VSS\\nSTR\", \"RST\\nSTT\", \"VQA\\nPPB\", \"VSS\\nSRT\", \"TSR\\nSTT\", \"VQ@\\nPPB\", \"SSV\\nSRT\", \"TSR\\nTTS\", \"VQ@\\nPPA\", \"VSS\\nTRS\", \"USR\\nTTS\", \"VQ@\\nPAP\", \"VSS\\nTSR\", \"TSR\\nTTR\", \"VQ@\\nPAO\", \"SSV\\nTSR\", \"TSR\\nUTS\", \"VQ@\\nQAO\"], \"outputs\": [\"2\", \"0\", \"3\", \"1\\n\", \"2\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"3 3\\n...\\n.##\\n.##\", \"6 7\\n.####.#\\n....#.\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.#\\n....#.\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.$\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"2 3\\n...\\n.##\\n.##\", \"2 1\\n...\\n.##\\n.##\", \"2 7\\n####..$\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"1 5\\n.####.$\\n./..\\\".\\n-#....\\n.#....\\n.####.#\\n..#.$.\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n.####.#\\n..#.\\\".\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n.\\\"###.#\\n..#.\\\".\", \"5 7\\n.####.#\\n....#.\\n....#.\\n....#-\\n.####.#\\n....##\", \"5 7\\n.####.$\\n-...#.\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#.\\n.$###.#\\n....\\\"#\", \"5 7\\n####..$\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n.####.#\\n..#.#.\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n.\\\"###.#\\n...#\\\".\", \"5 7\\n.####.$\\n.#...-\\n....#.\\n....#.\\n.####.#\\n....##\", \"10 7\\n####..$\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n-#....\\n./..#.\\n.\\\"###.#\\n...#\\\".\", \"3 1\\n...\\n.##\\n.##\", \"10 7\\n.####.$\\n.#...-\\n....#.\\n....#.\\n.####.#\\n....##\", \"10 7\\n####..$\\n....#.\\n.#..-.\\n....#.\\n.####.#\\n....\\\"#\", \"10 7\\n.####.$\\n.#...-\\n....#.\\n.#....\\n.####.#\\n....##\", \"10 7\\n####..$\\n....#.\\n.#..-.\\n.../#.\\n.####.#\\n....\\\"#\", \"4 7\\n.####.$\\n.#...-\\n....#.\\n.#....\\n.####.#\\n....##\", \"10 7\\n####..$\\n....#.\\n.#..-.\\n.../#.\\n.####.#\\n#\\\"....\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n.#....\\n.####.#\\n....##\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n....#.\\n.####.#\\n....##\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n....##\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n....$#\", \"8 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n....$#\", \"5 7\\n.####.#\\n....$.\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.$\\n....#.\\n....#.\\n.#....\\n.####.#\\n....##\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#-\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n.#....\\n....#.\\n.####.#\\n...\\\".#\", \"5 7\\n.####.$\\n..-.#.\\n-#....\\n....#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n-...#.\\n-#....\\n....#.\\n.####.#\\n..#.\\\".\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n#.###\\\".\\n..#.\\\".\", \"2 3\\n...\\n.##\\n##.\", \"5 7\\n.####.#\\n....#.\\n....#.\\n....#,\\n.####.#\\n....##\", \"5 7\\n.####.$\\n-...#.\\n....#.\\n....#.\\n.####.#\\n##....\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#.\\n.$###.\\\"\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n-#....\\n....#.\\n#.####.\\n..#.#.\", \"3 7\\n.####.$\\n.#...-\\n....#.\\n....#.\\n.####.#\\n....##\", \"10 12\\n####..$\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n-#....\\n./..#.\\n.\\\"###.#\\n...#!.\", \"10 7\\n.###$.$\\n.#...-\\n....#.\\n....#.\\n.####.#\\n....##\", \"10 7\\n####..$\\n....#.\\n.#..-.\\n../.#.\\n.####.#\\n....\\\"#\", \"10 7\\n####..$\\n.....#\\n.#..-.\\n.../#.\\n.####.#\\n#\\\"....\", \"4 7\\n.####.%\\n.#....\\n....#.\\n.#....\\n.####.#\\n....##\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n##....\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n#$....\", \"8 6\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n....$#\", \"5 7\\n.####.#\\n....$/\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.$\\n....#.\\n....#.\\n.#....\\n.####.#\\n../.##\", \"5 7\\n.####.$\\n....#.\\n....#.\\n...-#.\\n.####.#\\n....\\\"#\", \"5 7\\n.####.$\\n....#.\\n.#....\\n....\\\".\\n.####.#\\n...\\\".#\", \"5 7\\n.####.$\\n..-.#.\\n-#....\\n....#.\\n#.####.\\n....\\\"#\", \"5 7\\n.####.$\\n-...#.\\n-#/...\\n....#.\\n.####.#\\n..#.\\\".\", \"5 13\\n.####.$\\n....#.\\n-#....\\n....#.\\n#.###\\\".\\n..#.\\\".\", \"5 7\\n.####.$\\n-...#.\\n....#.\\n....#.\\n.$###.#\\n##....\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#.\\n\\\".###$.\\n....\\\"#\", \"2 7\\n####..$\\n....#.\\n.#....\\n....#/\\n.####.#\\n....\\\"#\", \"3 7\\n.####.$\\n.#...-\\n../.#.\\n....#.\\n.####.#\\n....##\", \"10 7\\n$..####\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"10 7\\n.###$.$\\n.#...-\\n/...#.\\n....#.\\n.####.#\\n....##\", \"10 7\\n$..####\\n.....#\\n.#..-.\\n.../#.\\n.####.#\\n#\\\"....\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.####.#\\n##.../\", \"5 7\\n.####.#\\n/$....\\n....#.\\n....#.\\n.####.#\\n....##\", \"5 7\\n.####.$\\n.#....\\n.#....\\n....\\\".\\n.####.#\\n...\\\".#\", \"5 7\\n.####.$\\n..-.\\\".\\n-#....\\n....#.\\n#.####.\\n....\\\"#\", \"5 7\\n.####.$\\n-...#.\\n-#/...\\n....#.\\n.####-#\\n..#.\\\".\", \"5 8\\n.####.$\\n....#.\\n-#....\\n....#.\\n#.###\\\".\\n..#.\\\".\", \"2 7\\n.####.$\\n-...#.\\n....#.\\n....#.\\n.$###.#\\n##....\", \"5 7\\n.####.$\\n....#.\\n....#.\\n....#.\\n#.###$.\\n....\\\"#\", \"2 7\\n####..$\\n....#.\\n.#....\\n....#/\\n#.####.\\n....\\\"#\", \"3 7\\n.####.$\\n.#...-\\n/./.#.\\n....#.\\n.####.#\\n....##\", \"20 7\\n$..####\\n....#.\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"10 7\\n.###$.$\\n.#...-\\n/...#.\\n...-#.\\n.####.#\\n....##\", \"4 7\\n.####.%\\n.#...-\\n....#.\\n..-.#.\\n.##$#.#\\n##.../\", \"5 7\\n.####.#\\n/$....\\n....#.\\n.#....\\n.####.#\\n....##\", \"5 7\\n.####.$\\n.#....\\n.#....\\n....\\\".\\n.####.#\\n.-.\\\".#\", \"5 7\\n.####.$\\n..-.\\\".\\n-#....\\n....#.\\n#.#.###\\n....\\\"#\", \"5 7\\n.####.$\\n-...#.\\n-#/...\\n....#.\\n.##$#-#\\n..#.\\\".\", \"5 8\\n.####.$\\n....#.\\n-#....\\n....#.\\n#.###\\\"-\\n..#.\\\".\", \"20 7\\n$..####\\n....\\\".\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"14 7\\n.###$.$\\n.#...-\\n/...#.\\n...-#.\\n.####.#\\n....##\", \"5 7\\n.####.#\\n/$....\\n....#.\\n.#....\\n#.####.\\n....##\", \"5 7\\n.####.$\\n....#.\\n.#....\\n....\\\".\\n.####.#\\n.-.\\\".#\", \"5 12\\n.####.$\\n....#.\\n-#....\\n....#.\\n#.###\\\"-\\n..#.\\\".\", \"20 7\\n#..####\\n....\\\".\\n.#....\\n....#.\\n.####.#\\n....\\\"#\", \"14 14\\n.###$.$\\n.#...-\\n/...#.\\n...-#.\\n.####.#\\n....##\", \"5 7\\n#.####.\\n/$....\\n....#.\\n.#....\\n#.####.\\n....##\", \"5 7\\n.####.$\\n.....#\\n.#....\\n....\\\".\\n.####.#\\n.-.\\\".#\", \"20 7\\n#..####\\n....\\\".\\n.#....\\n../.#.\\n.####.#\\n....\\\"#\", \"14 14\\n.###$.$\\n.#...-\\n/...#.\\n...-#.\\n#.####.\\n....##\", \"8 7\\n#.####.\\n/$....\\n....#.\\n.#....\\n#.####.\\n....##\", \"6 7\\n#.####.\\n/$....\\n....#.\\n.#....\\n#.####.\\n....##\", \"6 7\\n#.####.\\n/$....\\n....#.\\n.$....\\n#.####.\\n....##\"], \"outputs\": [\"2\", \"4\", \"4\\n\", \"5\\n\", \"2\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"0\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\"]}", "source": "primeintellect"}
|
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 3 7\\n1\\n3\\n6\\n9\\n12\", \"3 3 4\\n5\\n6\\n7\", \"8 2 9\\n3\\n4\\n5\\n13\\n15\\n22\\n26\\n32\", \"7 5 3\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"3 3 4\\n9\\n6\\n7\", \"8 2 9\\n3\\n4\\n5\\n7\\n15\\n22\\n26\\n32\", \"3 3 4\\n0\\n6\\n7\", \"8 2 9\\n3\\n0\\n5\\n7\\n15\\n22\\n26\\n32\", \"5 3 2\\n1\\n3\\n6\\n9\\n12\", \"8 2 9\\n3\\n4\\n5\\n7\\n15\\n22\\n50\\n32\", \"8 2 9\\n3\\n0\\n5\\n7\\n11\\n22\\n26\\n32\", \"3 6 7\\n0\\n3\\n7\", \"3 5 4\\n5\\n6\\n10\", \"6 5 1\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"5 6 2\\n1\\n3\\n6\\n9\\n12\", \"3 6 7\\n1\\n3\\n7\", \"5 0 2\\n1\\n3\\n6\\n9\\n21\", \"7 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"6 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"3 6 4\\n0\\n6\\n7\", \"6 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n5\", \"3 6 4\\n0\\n10\\n7\", \"6 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n6\", \"3 6 4\\n0\\n18\\n7\", \"6 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n1\", \"3 6 7\\n0\\n18\\n7\", \"6 5 5\\n0\\n2\\n4\\n3\\n8\\n11\\n1\", \"3 6 7\\n0\\n23\\n7\", \"6 5 5\\n0\\n4\\n4\\n3\\n8\\n11\\n1\", \"3 2 7\\n0\\n23\\n7\", \"3 2 7\\n0\\n14\\n7\", \"3 2 7\\n0\\n26\\n7\", \"2 2 7\\n0\\n26\\n7\", \"2 2 7\\n0\\n17\\n7\", \"2 2 7\\n0\\n17\\n4\", \"2 2 7\\n0\\n33\\n4\", \"3 3 4\\n5\\n6\\n10\", \"7 7 3\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"3 3 5\\n9\\n6\\n7\", \"12 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"3 3 4\\n0\\n0\\n7\", \"6 5 5\\n0\\n2\\n8\\n7\\n8\\n11\\n15\", \"3 6 4\\n0\\n0\\n7\", \"9 5 5\\n0\\n2\\n4\\n7\\n8\\n11\\n5\", \"3 1 4\\n0\\n10\\n7\", \"6 5 5\\n1\\n2\\n4\\n7\\n8\\n11\\n6\", \"6 5 5\\n0\\n0\\n4\\n7\\n8\\n11\\n1\", \"2 6 7\\n0\\n18\\n7\", \"6 5 5\\n0\\n2\\n4\\n3\\n4\\n11\\n1\", \"6 5 5\\n0\\n4\\n4\\n3\\n8\\n12\\n1\", \"2 2 7\\n0\\n26\\n10\", \"2 2 7\\n0\\n21\\n7\", \"2 2 7\\n0\\n35\\n4\", \"5 3 2\\n1\\n3\\n6\\n9\\n21\", \"3 3 5\\n15\\n6\\n7\", \"8 2 9\\n3\\n4\\n7\\n7\\n15\\n22\\n50\\n32\", \"12 1 5\\n0\\n2\\n4\\n7\\n8\\n11\\n15\", \"3 3 5\\n0\\n0\\n7\", \"8 2 9\\n3\\n0\\n5\\n7\\n11\\n22\\n52\\n32\", \"6 5 5\\n0\\n2\\n8\\n7\\n8\\n8\\n15\", \"3 6 4\\n0\\n1\\n7\", \"9 0 5\\n0\\n2\\n4\\n7\\n8\\n11\\n5\", \"3 1 2\\n0\\n10\\n7\", \"11 5 5\\n1\\n2\\n4\\n7\\n8\\n11\\n6\", \"4 5 5\\n0\\n0\\n4\\n7\\n8\\n11\\n1\", \"4 6 7\\n0\\n18\\n7\", \"6 5 5\\n0\\n2\\n5\\n3\\n4\\n11\\n1\", \"2 6 7\\n0\\n3\\n7\", \"6 5 5\\n0\\n4\\n3\\n3\\n8\\n12\\n1\", \"2 2 7\\n0\\n26\\n4\", \"3 2 7\\n0\\n21\\n7\", \"2 4 7\\n0\\n35\\n4\", \"3 5 4\\n5\\n6\\n6\", \"3 3 5\\n24\\n6\\n7\", \"8 2 9\\n3\\n4\\n7\\n7\\n15\\n41\\n50\\n32\", \"12 1 5\\n0\\n2\\n4\\n7\\n8\\n0\\n15\", \"3 3 5\\n0\\n0\\n12\", \"8 2 9\\n3\\n0\\n5\\n7\\n11\\n22\\n15\\n32\", \"10 5 5\\n0\\n2\\n8\\n7\\n8\\n8\\n15\", \"6 6 4\\n0\\n1\\n7\", \"9 0 5\\n0\\n2\\n4\\n7\\n7\\n11\\n5\", \"3 1 3\\n0\\n10\\n7\", \"11 5 5\\n1\\n2\\n4\\n7\\n8\\n11\\n4\", \"4 5 5\\n0\\n0\\n4\\n3\\n8\\n11\\n1\", \"4 6 7\\n0\\n18\\n11\", \"6 5 5\\n0\\n2\\n5\\n5\\n4\\n11\\n1\", \"2 6 7\\n0\\n1\\n7\", \"3 5 5\\n0\\n4\\n3\\n3\\n8\\n12\\n1\", \"3 2 5\\n0\\n21\\n7\", \"4 4 7\\n0\\n35\\n4\", \"3 5 4\\n5\\n3\\n6\", \"4 3 5\\n24\\n6\\n7\", \"8 2 9\\n4\\n4\\n7\\n7\\n15\\n41\\n50\\n32\", \"12 1 5\\n0\\n2\\n4\\n7\\n14\\n0\\n15\", \"3 3 5\\n0\\n0\\n15\", \"10 8 5\\n0\\n2\\n8\\n7\\n8\\n8\\n15\", \"6 6 5\\n0\\n1\\n7\", \"9 0 5\\n0\\n2\\n4\\n7\\n9\\n11\\n5\", \"3 1 3\\n0\\n0\\n7\", \"11 5 5\\n1\\n2\\n4\\n7\\n13\\n11\\n4\", \"4 5 5\\n0\\n1\\n4\\n3\\n8\\n11\\n1\", \"4 3 7\\n0\\n18\\n11\", \"6 5 5\\n-1\\n2\\n5\\n5\\n4\\n11\\n1\", \"2 6 6\\n0\\n1\\n7\"], \"outputs\": [\"5\", \"0\", \"13\", \"4\", \"0\", \"8\", \"4\", \"16\", \"24\", \"6\", \"10\", \"2\", \"3\", \"14\", \"11\", \"1\", \"32\", \"0\", \"0\", \"4\", \"0\", \"4\", \"0\", \"4\", \"0\", \"4\", \"0\", \"4\", \"0\", \"4\", \"4\", \"4\", \"4\", \"4\", \"4\", \"4\", \"4\", \"0\", \"0\", \"0\", \"4\", \"0\", \"4\", \"0\", \"4\", \"0\", \"0\", \"4\", \"0\", \"0\", \"4\", \"4\", \"4\", \"24\", \"0\", \"0\", \"0\", \"4\", \"8\", \"0\", \"4\", \"0\", \"4\", \"0\", \"0\", \"0\", \"0\", \"2\", \"0\", \"4\", \"4\", \"4\", \"0\", \"0\", \"0\", \"0\", \"4\", \"8\", \"0\", \"0\", \"0\", \"4\", \"0\", \"0\", \"0\", \"0\", \"2\", \"0\", \"4\", \"0\", \"0\", \"0\", \"0\", \"0\", \"4\", \"0\", \"0\", \"0\", \"4\", \"0\", \"0\", \"0\", \"0\", \"2\"]}", "source": "primeintellect"}
|
There is a set consisting of N distinct integers. The i-th smallest element in this set is S_i. We want to divide this set into two sets, X and Y, such that:
* The absolute difference of any two distinct elements in X is A or greater.
* The absolute difference of any two distinct elements in Y is B or greater.
How many ways are there to perform such division, modulo 10^9 + 7? Note that one of X and Y may be empty.
Constraints
* All input values are integers.
* 1 ≦ N ≦ 10^5
* 1 ≦ A , B ≦ 10^{18}
* 0 ≦ S_i ≦ 10^{18}(1 ≦ i ≦ N)
* S_i < S_{i+1}(1 ≦ i ≦ N - 1)
Input
The input is given from Standard Input in the following format:
N A B
S_1
:
S_N
Output
Print the number of the different divisions under the conditions, modulo 10^9 + 7.
Examples
Input
5 3 7
1
3
6
9
12
Output
5
Input
7 5 3
0
2
4
7
8
11
15
Output
4
Input
8 2 9
3
4
5
13
15
22
26
32
Output
13
Input
3 3 4
5
6
7
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 1 2\\n1 2\\n3 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"5 1 2\\n1 2\\n1 3\\n1 4\\n4 5\\n2 1\\n1 3\\n1 5\\n5 4\", \"3 3 1\\n1 2\\n2 3\\n1 2\\n2 3\", \"4 1 2\\n1 2\\n1 3\\n1 4\\n2 1\\n2 3\\n1 4\", \"4 2 1\\n1 2\\n3 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"4 1 2\\n1 4\\n3 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"4 2 1\\n1 4\\n3 4\\n4 4\\n1 2\\n3 4\\n1 3\", \"4 2 1\\n1 2\\n3 6\\n2 4\\n1 2\\n2 4\\n1 3\", \"4 2 1\\n1 4\\n3 1\\n4 4\\n2 2\\n3 4\\n1 3\", \"5 1 2\\n1 2\\n1 3\\n1 4\\n6 5\\n2 1\\n1 3\\n1 5\\n5 4\", \"4 2 1\\n1 4\\n3 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"4 2 1\\n1 4\\n3 4\\n2 4\\n1 2\\n2 4\\n1 3\", \"4 2 1\\n1 2\\n3 4\\n2 4\\n1 2\\n2 4\\n1 3\", \"4 2 1\\n1 4\\n3 1\\n4 4\\n1 2\\n3 4\\n1 3\", \"4 1 2\\n1 2\\n3 4\\n3 4\\n1 2\\n3 4\\n1 3\", \"5 1 2\\n1 2\\n1 3\\n1 4\\n4 6\\n2 1\\n1 3\\n1 5\\n5 4\", \"4 2 1\\n1 4\\n3 3\\n4 4\\n1 2\\n3 4\\n1 3\", \"4 1 2\\n1 2\\n2 4\\n3 4\\n1 2\\n3 4\\n1 3\", \"4 2 1\\n1 4\\n3 3\\n4 4\\n1 2\\n5 4\\n1 3\", \"1 2 1\\n1 4\\n3 1\\n4 4\\n2 2\\n3 4\\n1 3\", \"1 2 1\\n1 4\\n3 1\\n4 2\\n2 2\\n3 4\\n1 3\", \"1 2 1\\n0 4\\n3 1\\n4 2\\n2 2\\n3 4\\n1 3\", \"4 0 2\\n1 2\\n3 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"3 3 1\\n2 2\\n2 3\\n1 2\\n2 3\", \"4 1 2\\n1 2\\n1 3\\n1 1\\n2 1\\n2 3\\n1 4\", \"4 4 1\\n1 2\\n3 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"4 1 2\\n1 4\\n3 4\\n3 4\\n1 2\\n3 4\\n1 3\", \"4 2 1\\n1 4\\n6 4\\n2 4\\n1 2\\n3 4\\n1 3\", \"4 2 2\\n1 4\\n3 1\\n4 4\\n1 2\\n3 4\\n1 3\", \"4 1 2\\n1 2\\n3 4\\n4 4\\n1 2\\n3 4\\n1 3\", \"4 0 2\\n1 2\\n2 4\\n3 4\\n1 2\\n3 4\\n1 3\", \"4 1 1\\n1 4\\n3 3\\n4 4\\n1 2\\n5 4\\n1 3\", \"1 2 1\\n1 4\\n3 1\\n4 4\\n2 2\\n1 4\\n1 3\", \"1 0 1\\n1 4\\n3 1\\n4 2\\n2 2\\n3 4\\n1 3\", \"1 2 1\\n0 4\\n3 1\\n4 2\\n2 2\\n3 3\\n1 3\", \"2 3 1\\n2 2\\n2 3\\n1 2\\n2 3\", \"4 4 1\\n1 2\\n3 4\\n2 6\\n1 2\\n3 4\\n1 3\", \"4 1 2\\n1 2\\n3 4\\n4 4\\n1 2\\n3 1\\n1 3\", \"4 0 2\\n1 2\\n1 4\\n3 4\\n1 2\\n3 4\\n1 3\", \"4 0 1\\n1 4\\n3 3\\n4 4\\n1 2\\n5 4\\n1 3\", \"1 2 1\\n1 4\\n3 0\\n4 4\\n2 2\\n1 4\\n1 3\", \"1 0 1\\n1 8\\n3 1\\n4 2\\n2 2\\n3 4\\n1 3\", \"1 2 1\\n0 4\\n3 1\\n4 2\\n2 4\\n3 3\\n1 3\", \"2 4 1\\n2 2\\n2 3\\n1 2\\n2 3\", \"4 4 1\\n1 2\\n3 8\\n2 6\\n1 2\\n3 4\\n1 3\", \"4 0 4\\n1 2\\n1 4\\n3 4\\n1 2\\n3 4\\n1 3\", \"4 0 0\\n1 4\\n3 3\\n4 4\\n1 2\\n5 4\\n1 3\", \"1 2 1\\n1 4\\n3 0\\n4 4\\n2 2\\n1 3\\n1 3\", \"1 0 1\\n1 8\\n3 2\\n4 2\\n2 2\\n3 4\\n1 3\", \"1 2 1\\n0 4\\n3 1\\n3 2\\n2 4\\n3 3\\n1 3\", \"2 4 1\\n2 2\\n0 3\\n1 2\\n2 3\", \"4 0 4\\n1 2\\n1 4\\n5 4\\n1 2\\n3 4\\n1 3\", \"1 0 1\\n1 8\\n3 2\\n4 2\\n4 2\\n3 4\\n1 3\", \"1 2 1\\n0 4\\n3 1\\n3 2\\n2 4\\n3 0\\n1 3\", \"2 8 1\\n2 2\\n0 3\\n1 2\\n2 3\", \"4 0 4\\n1 2\\n1 1\\n5 4\\n1 2\\n3 4\\n1 3\", \"1 0 1\\n2 8\\n3 2\\n4 2\\n4 2\\n3 4\\n1 3\", \"1 2 1\\n0 4\\n3 1\\n3 3\\n2 4\\n3 0\\n1 3\", \"2 8 1\\n2 2\\n-1 3\\n1 2\\n2 3\", \"4 0 4\\n1 2\\n1 1\\n5 3\\n1 2\\n3 4\\n1 3\", \"1 0 1\\n2 8\\n3 2\\n8 2\\n4 2\\n3 4\\n1 3\", \"1 2 2\\n0 4\\n3 1\\n3 3\\n2 4\\n3 0\\n1 3\", \"2 8 1\\n2 2\\n-1 6\\n1 2\\n2 3\", \"4 0 4\\n1 2\\n1 1\\n5 3\\n1 2\\n3 7\\n1 3\", \"2 0 1\\n2 8\\n3 2\\n8 2\\n4 2\\n3 4\\n1 3\", \"1 2 2\\n0 4\\n3 1\\n3 3\\n2 4\\n5 0\\n1 3\", \"2 0 1\\n2 8\\n3 2\\n8 2\\n4 2\\n3 4\\n1 6\", \"1 2 2\\n0 4\\n3 1\\n3 3\\n2 4\\n5 0\\n1 6\", \"2 0 1\\n2 8\\n3 1\\n8 2\\n4 2\\n3 4\\n1 6\", \"1 4 2\\n0 4\\n3 1\\n3 3\\n2 4\\n5 0\\n1 6\", \"2 0 1\\n2 8\\n3 0\\n8 2\\n4 2\\n3 4\\n1 6\", \"1 4 2\\n0 0\\n3 1\\n3 3\\n2 4\\n5 0\\n1 6\", \"2 0 1\\n2 8\\n3 0\\n8 2\\n1 2\\n3 4\\n1 6\", \"1 4 3\\n0 0\\n3 1\\n3 3\\n2 4\\n5 0\\n1 6\", \"2 0 1\\n2 8\\n3 0\\n8 2\\n0 2\\n3 4\\n1 6\", \"1 4 3\\n0 0\\n3 0\\n3 3\\n2 4\\n5 0\\n1 6\", \"2 0 1\\n2 8\\n3 0\\n8 2\\n0 1\\n3 4\\n1 6\", \"1 4 3\\n0 0\\n3 0\\n3 3\\n2 4\\n2 0\\n1 6\", \"2 0 1\\n2 8\\n6 0\\n8 2\\n0 1\\n3 4\\n1 6\", \"1 4 3\\n0 0\\n6 0\\n3 3\\n2 4\\n2 0\\n1 6\", \"2 0 1\\n2 8\\n6 0\\n8 2\\n0 1\\n3 4\\n1 0\", \"1 4 3\\n0 0\\n6 1\\n3 3\\n2 4\\n2 0\\n1 6\", \"2 0 1\\n2 8\\n11 0\\n8 2\\n0 1\\n3 4\\n1 0\", \"1 4 3\\n0 0\\n6 1\\n3 3\\n2 1\\n2 0\\n1 6\", \"2 0 1\\n2 8\\n11 0\\n8 2\\n0 0\\n3 4\\n1 0\", \"1 4 3\\n0 0\\n6 1\\n3 3\\n2 1\\n2 0\\n1 8\", \"2 0 1\\n4 8\\n11 0\\n8 2\\n0 0\\n3 4\\n1 0\", \"1 4 3\\n0 0\\n6 1\\n3 3\\n2 1\\n4 0\\n1 8\", \"2 0 2\\n4 8\\n11 0\\n8 2\\n0 0\\n3 4\\n1 0\", \"1 4 3\\n0 0\\n9 1\\n3 3\\n2 1\\n4 0\\n1 8\", \"2 0 4\\n4 8\\n11 0\\n8 2\\n0 0\\n3 4\\n1 0\", \"1 4 3\\n0 0\\n9 1\\n3 3\\n4 1\\n4 0\\n1 8\", \"2 1 4\\n4 8\\n11 0\\n8 2\\n0 0\\n3 4\\n1 0\", \"1 8 3\\n0 0\\n9 1\\n3 3\\n4 1\\n4 0\\n1 8\", \"1 8 3\\n-1 0\\n9 1\\n3 3\\n4 1\\n4 0\\n1 8\", \"1 8 3\\n-1 0\\n9 0\\n3 3\\n4 1\\n4 0\\n1 8\", \"1 8 3\\n-1 0\\n9 0\\n3 3\\n4 1\\n4 0\\n0 8\", \"1 8 3\\n-1 -1\\n9 0\\n3 3\\n4 1\\n4 0\\n0 8\", \"1 10 3\\n-1 -1\\n9 0\\n3 3\\n4 1\\n4 0\\n0 8\", \"1 10 3\\n-1 -1\\n9 0\\n3 3\\n4 1\\n4 0\\n-1 8\", \"1 10 3\\n-1 -2\\n9 0\\n3 3\\n4 1\\n4 0\\n-1 8\", \"1 10 3\\n-1 -2\\n9 0\\n3 3\\n1 1\\n4 0\\n-1 8\", \"1 10 3\\n-1 -2\\n0 0\\n3 3\\n1 1\\n4 0\\n-1 8\", \"1 10 3\\n-1 -2\\n0 0\\n3 3\\n1 1\\n4 0\\n0 8\", \"1 2 3\\n-1 -2\\n0 0\\n3 3\\n1 1\\n4 0\\n0 8\"], \"outputs\": [\"2\", \"6\", \"4\", \"4\", \"-1\", \"-1\\n\", \"2\\n\", \"4\\n\", \"0\\n\", \"6\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"-1\\n\", \"6\\n\", \"-1\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Sigma and Sugim are playing a game.
The game is played on a graph with N vertices numbered 1 through N. The graph has N-1 red edges and N-1 blue edges, and the N-1 edges in each color forms a tree. The red edges are represented by pairs of integers (a_i, b_i), and the blue edges are represented by pairs of integers (c_i, d_i).
Each player has his own piece. Initially, Sigma's piece is at vertex X, and Sugim's piece is at vertex Y.
The game is played in turns, where turns are numbered starting from turn 1. Sigma takes turns 1, 3, 5, ..., and Sugim takes turns 2, 4, 6, ....
In each turn, the current player either moves his piece, or does nothing. Here, Sigma can only move his piece to a vertex that is directly connected to the current vertex by a red edge. Similarly, Sugim can only move his piece to a vertex that is directly connected to the current vertex by a blue edge.
When the two pieces come to the same vertex, the game ends immediately. If the game ends just after the operation in turn i, let i be the total number of turns in the game.
Sigma's objective is to make the total number of turns as large as possible, while Sugim's objective is to make it as small as possible.
Determine whether the game will end in a finite number of turns, assuming both players plays optimally to achieve their respective objectives. If the answer is positive, find the number of turns in the game.
Constraints
* 2 ≦ N ≦ 200,000
* 1 ≦ X, Y ≦ N
* X \neq Y
* 1 ≦ a_i, b_i, c_i, d_i ≦ N
* The N-1 edges in each color (red and blue) forms a tree.
Input
The input is given from Standard Input in the following format:
N X Y
a_1 b_1
a_2 b_2
:
a_{N-1} b_{N-1}
c_1 d_1
c_2 d_2
:
c_{N-1} d_{N-1}
Output
If the game will end in a finite number of turns, print the number of turns. Otherwise, print `-1`.
Examples
Input
4 1 2
1 2
1 3
1 4
2 1
2 3
1 4
Output
4
Input
3 3 1
1 2
2 3
1 2
2 3
Output
4
Input
4 1 2
1 2
3 4
2 4
1 2
3 4
1 3
Output
2
Input
4 2 1
1 2
3 4
2 4
1 2
3 4
1 3
Output
-1
Input
5 1 2
1 2
1 3
1 4
4 5
2 1
1 3
1 5
5 4
Output
6
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\n#..S\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 14\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO.#.\\nX.\\nR-.#\\n\\n2 0\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#-..$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.\\\"#\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 4\\n\\n......E.X\\n\\n4 4\\n\\nO.#\\n/.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n#X#..\\n.EE#.\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#T..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.\\\"#\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##\\\"#######\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 3\\n##X#####\\n#....E.#\\n#####.\\\"#\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nF.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#T..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n6 8\\n##X#####\\n#....E.#\\n#####.\\\"#\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##\\\"#######\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N/.#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 3\\n##X#####\\n#....E.#\\n#####.\\\"#\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 4\\n\\nF.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\n#..S\\n\\n6 6\\n\\n..#X#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n..#X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\n#..S\\n\\n6 6\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n..#X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#./#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n6 6\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N-#\\n..#X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#./#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n6 6\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N-\\\"\\n..#X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#./#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n6 6\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N-\\\"\\n..#X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#./#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 10\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n1 6\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N-\\\"\\n..#X\\n####\\n5 7\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 0\\n######\\n#./#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 10\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#-#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..S\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n....E.#\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#..R\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n....E.#\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\nO..#\\n.X\\n#.-R\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n....E.#\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\n.X\\n#.-R\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n....E.#\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\n.X\\n#.-R\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\n.X\\nR-.#\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n1 8\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n1 14\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 14\\n\\n..#W#\\n.EE.#\\n#N\\n....#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 14\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 14\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\nX#####\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 14\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.##\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n.W/#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n#.EE.\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\n#..O\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EE.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 4\\n\\nN.$\\n..X\\n\\n5 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EF.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..#W#\\n.EF.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..$W#\\n.EF.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n.$#\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..$W#\\n.EF.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n5 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..$W#\\n.EF.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#-..$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..$W#\\n.EF.#\\n#N\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#-..$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO..#\\nX.\\nR-.#\\n\\n2 2\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#-..$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO.#.\\nX.\\nR-.#\\n\\n2 2\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#-..$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO.#.\\nX.\\nR-.#\\n\\n2 0\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n####X#\\n#.E....\\n#$.\\n.#-./$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO.#.\\nX.\\nR-.#\\n\\n2 0\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n#$##X#\\n#.E....\\n#$.\\n.#-./$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO.#.\\nX.\\nR-#.\\n\\n2 0\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n#$##X#\\n#.E....\\n#$.\\n.#-./$#\\n#..#.W.\\n.#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 1\\n\\nE.......X\\n\\n4 7\\n\\nN.$\\n..X\\n\\n10 5\\n\\nO.#.\\nX.\\nR-#.\\n\\n2 0\\n\\n..$W#\\n.EF.#\\nN#\\n...-#\\n\\n8 11\\n#$##X#\\n#.E....\\n#$.\\n.#-./$#\\n#..#.W.\\n-#.N#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n-1 0\", \"10 3\\n##########\\n#E.......X\\n##\\\"#######\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.\\\"#\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n#X#..\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n/.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n#X#..\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n/.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n#X#..\\n.EE#.\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"13 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#S..#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.O#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n6 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nW##.#.#\\n\\n-1 1\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 3\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..N\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS.-#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\n#..N\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nF.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n\\\"#.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n-.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW#$.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS.#.\\n\\n6 6\\n\\n#X#..\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nX.......E\\n\\n4 4\\n\\nO.#\\n/.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n#X#..\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 4\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n/.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n3 6\\n\\n#X#..\\n.EE#.\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"17 4\\n\\n......E.X\\n\\n4 4\\n\\nO.#\\n/.X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n#X#..\\n.EE#.\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"13 3\\n##########\\n#E.......X\\n##########\\n4 4\\n####\\n#N.#\\n#..X\\n####\\n5 5\\n#####\\n#N..#\\n###.X\\n#..S#\\n#####\\n6 6\\n######\\n#..#X#\\n#.EE.#\\n####N#\\n#....#\\n######\\n8 8\\n##X#####\\n#....E.#\\n#####.##\\n#.#...##\\n#.W.#..#\\n#.#.N#.X\\n#X##.#.#\\n########\\n0 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 10\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.O#.X\\nX##.#.#\\n\\n0 0\", \"10 3\\n\\nE.......X\\n\\n6 4\\n\\nN.#\\n..X\\n\\n10 5\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nX##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\nN..#\\n.X\\nS/.#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nN#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N#.X\\nW##.#.#\\n\\n-1 1\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 3\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n.W.#..#\\n.#.N$.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 5\\n\\n#..N\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...$#\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 1\\n\\nN..#\\n.X\\nS.-#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n.##\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nF.......X\\n\\n1 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS..#\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 3\\n\\n#..N\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n....#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.N#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nN.#\\n..X\\n\\n5 2\\n\\nN..#\\n.X\\nS#..\\n\\n6 6\\n\\n..#X#\\n.EE-#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n\\\"#.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\", \"10 3\\n\\nE.......X\\n\\n4 4\\n\\nO.#\\n-.X\\n\\n5 2\\n\\nN..#\\n.X\\nS$..\\n\\n6 6\\n\\n..#X#\\n.EE.#\\nO#\\n../.#\\n\\n8 8\\nX#####\\n....E.#\\n##.\\n.#...##\\n#..#.W.\\n.#.M#.X\\nW##.#.#\\n\\n-1 0\"], \"outputs\": [\"8\\nNA\\n9\\n16\\n10\", \"8\\nNA\\n9\\n16\\n10\", \"8\\nNA\\n9\\n16\\n23\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\n0\\n\", \"8\\nNA\\n9\\n16\\n10\\n\", \"2\\n\", \"8\\nNA\\n8\\n16\\n10\\n\", \"8\\nNA\\n9\\n16\\n8\\n\", \"0\\n\", \"8\\nNA\\n8\\n16\\n12\\n\", \"8\\nNA\\nNA\\n16\\n8\\n\", \"NA\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\n\", \"8\\nNA\\n9\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\nNA\\n\", \"8\\nNA\\n0\\n\", \"8\\nNA\\n0\\n\", \"8\\nNA\\n0\\n\", \"8\\nNA\\n0\\n\", \"8\\n\", \"8\\nNA\\n9\\n16\\n10\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\nNA\\n9\\n16\\n10\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"0\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"2\\n\", \"8\\nNA\\n9\\n16\\n10\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"0\\n\", \"8\\n\", \"8\\n\", \"8\\n\"]}", "source": "primeintellect"}
|
The huge maze The Squares has been newly completed in the famous theme park. Evacuation drills must be conducted under the guidance of the fire department, but the time required for the drills cannot be predicted due to the huge maze. Therefore, you decided to develop an evacuation drill simulator based on the following specifications.
As shown in Fig. 1, the giant maze is represented by W × H squares of horizontal W and vertical H. Each square is either a passage (white square), a wall (brown square), or an emergency exit (green square). The circles in the figure represent people, and the lowercase letters (E, W, S, N) in them represent the direction in which the person is facing (north, south, east, and west). The figure is drawn with the upward direction facing north.
<image>
Figure 1
People in the giant maze initially stand facing either north, south, east, or west. Each person attempts to move in 1-second increments at the same time, following the steps below.
1. Look at the right, front, left, and back squares in the direction you are currently facing, and turn to the first vacant aisle or emergency exit you find. If there is no such square, the direction will not change.
2. If the square in front of you is open and not in front of another person, move it. If there are multiple people with the same square in front of you, the selected one will move in the order of the people in that square, east, north, west, and south.
Those who arrive at the emergency exit after moving will evacuate safely and disappear from the maze.
Create a program that inputs the given huge maze and the location information of people and outputs the time when all people finish evacuating. If it takes more than 180 seconds to escape, output NA. Maze and person location information is given by the characters in rows H and columns W. The meaning of each character is as follows.
: Wall
.: Floor
X: Emergency exit
E: People facing east
N: People facing north
W: People facing west
S: People facing south
The boundary between the maze and the outside is either the wall # or the emergency exit X. In addition, there is always one or more people in the huge maze.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format:
W H
str1
str2
::
strH
The first line gives the horizontal size W of the maze and the vertical size H (1 ≤ W, H ≤ 30). The following H line is given the string stri (length W) that represents the i-th line of the maze.
The number of datasets does not exceed 50.
Output
For each input dataset, the time when all people finish evacuating is output on one line.
Examples
Input
10 3
##########
#E.......X
##########
4 4
####
#N.#
#..X
####
5 5
#####
#N..#
###.X
#S..#
#####
6 6
######
#..#X#
#.EE.#
####N#
#....#
######
8 8
##X#####
#....E.#
#####.##
#.#...##
#.W.#..#
#.#.N#.X
#X##.#.#
########
0 0
Output
8
NA
9
16
10
Input
10 3
E.......X
4 4
N.#
..X
5 5
N..#
.X
S..#
6 6
..#X#
.EE.#
N#
....#
8 8
X#####
....E.#
.##
.#...##
.W.#..#
.#.N#.X
X##.#.#
0 0
Output
8
NA
9
16
10
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n4\\n5\\n16\\n17\\n18\\n29\\n30\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n4\\n5\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n18\\n29\\n65\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n18\\n56\\n65\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n18\\n56\\n65\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n1\\n56\\n65\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n65\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n16\\n21\\n1\\n56\\n91\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n21\\n1\\n56\\n91\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n000\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n21\\n1\\n56\\n91\\n0 0\", \"3 50\\n011\\n1\\n100\\n3 50\\n100\\n000\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n21\\n1\\n56\\n91\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n0\\n8\\n5\\n16\\n34\\n18\\n56\\n65\\n0 0\", \"3 50\\n010\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n9\\n5\\n16\\n17\\n1\\n56\\n65\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 24\\n100\\n100\\n45\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n65\\n0 0\", \"3 50\\n010\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n12\\n5\\n16\\n17\\n1\\n56\\n65\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 24\\n100\\n100\\n45\\n10 10\\n1\\n2\\n3\\n8\\n5\\n6\\n21\\n1\\n56\\n65\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n100\\n0\\n10 10\\n1\\n2\\n3\\n9\\n5\\n16\\n35\\n1\\n63\\n91\\n0 0\", \"3 87\\n111\\n1\\n100\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n21\\n1\\n42\\n91\\n0 0\", \"3 50\\n101\\n0\\n100\\n3 50\\n100\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n29\\n53\\n0 0\", \"3 50\\n110\\n0\\n100\\n3 50\\n100\\n101\\n29\\n10 16\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n18\\n56\\n65\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n100\\n0\\n10 10\\n1\\n2\\n3\\n9\\n5\\n4\\n35\\n1\\n63\\n91\\n0 0\", \"3 87\\n111\\n1\\n100\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n12\\n1\\n42\\n91\\n0 0\", \"3 50\\n101\\n0\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n29\\n53\\n0 0\", \"3 87\\n111\\n1\\n100\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n12\\n1\\n19\\n91\\n0 0\", \"3 50\\n110\\n0\\n100\\n3 50\\n100\\n111\\n29\\n10 16\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n18\\n56\\n83\\n0 0\", \"3 49\\n110\\n1\\n101\\n3 50\\n110\\n100\\n34\\n10 10\\n1\\n1\\n5\\n8\\n5\\n25\\n21\\n1\\n56\\n65\\n0 0\", \"3 49\\n110\\n1\\n101\\n3 50\\n110\\n100\\n34\\n10 10\\n1\\n1\\n5\\n8\\n5\\n36\\n21\\n1\\n56\\n65\\n0 0\", \"3 49\\n110\\n1\\n101\\n3 96\\n110\\n100\\n34\\n10 10\\n1\\n1\\n5\\n8\\n5\\n36\\n21\\n1\\n62\\n65\\n0 0\", \"3 53\\n101\\n0\\n110\\n3 50\\n110\\n100\\n51\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n10\\n53\\n0 0\", \"3 53\\n101\\n0\\n010\\n3 50\\n110\\n100\\n51\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n10\\n53\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n4\\n5\\n2\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 42\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n10\\n5\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n0\\n8\\n5\\n27\\n17\\n18\\n56\\n65\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n100\\n7\\n10 10\\n1\\n2\\n3\\n10\\n5\\n16\\n35\\n1\\n56\\n91\\n0 0\", \"3 50\\n101\\n0\\n000\\n3 50\\n100\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n6\\n10 10\\n1\\n2\\n0\\n8\\n2\\n16\\n34\\n18\\n56\\n65\\n0 0\", \"3 50\\n010\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n12\\n5\\n16\\n17\\n1\\n56\\n76\\n0 0\", \"3 50\\n110\\n1\\n101\\n3 50\\n110\\n100\\n34\\n10 10\\n1\\n1\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n104\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 24\\n100\\n100\\n45\\n10 10\\n1\\n2\\n3\\n8\\n5\\n6\\n21\\n1\\n56\\n18\\n0 0\", \"3 87\\n111\\n1\\n000\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n12\\n1\\n42\\n91\\n0 0\", \"3 50\\n011\\n1\\n100\\n3 74\\n100\\n100\\n0\\n10 10\\n1\\n2\\n3\\n9\\n5\\n4\\n35\\n1\\n63\\n91\\n0 0\", \"3 87\\n111\\n1\\n100\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n14\\n5\\n20\\n12\\n1\\n19\\n91\\n0 0\", \"3 49\\n110\\n1\\n101\\n3 17\\n110\\n100\\n34\\n10 10\\n1\\n1\\n5\\n8\\n5\\n25\\n21\\n1\\n56\\n65\\n0 0\", \"3 53\\n101\\n0\\n100\\n3 11\\n110\\n100\\n51\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n10\\n53\\n0 0\", \"3 49\\n110\\n1\\n101\\n3 96\\n110\\n100\\n34\\n10 10\\n1\\n1\\n5\\n8\\n5\\n58\\n21\\n1\\n62\\n65\\n0 0\", \"3 53\\n101\\n0\\n110\\n3 50\\n110\\n100\\n41\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n10\\n53\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n46\\n10 10\\n1\\n2\\n3\\n5\\n5\\n16\\n17\\n18\\n29\\n65\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n3\\n8\\n8\\n16\\n5\\n18\\n56\\n65\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n8\\n10 10\\n1\\n2\\n5\\n0\\n5\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n100\\n1\\n100\\n3 50\\n100\\n010\\n50\\n10 10\\n1\\n2\\n3\\n8\\n2\\n16\\n17\\n18\\n56\\n65\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n2\\n0\\n8\\n5\\n27\\n17\\n18\\n56\\n104\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n72\\n10 10\\n1\\n0\\n3\\n11\\n5\\n16\\n17\\n18\\n24\\n65\\n0 0\", \"3 50\\n010\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n1\\n3\\n9\\n5\\n16\\n17\\n1\\n56\\n73\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 24\\n100\\n100\\n49\\n10 10\\n1\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n65\\n0 0\", \"3 50\\n101\\n0\\n000\\n3 50\\n100\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n17\\n18\\n29\\n22\\n0 0\", \"3 50\\n110\\n0\\n100\\n3 50\\n100\\n101\\n29\\n10 25\\n1\\n2\\n3\\n8\\n5\\n16\\n17\\n18\\n55\\n65\\n0 0\", \"3 87\\n111\\n1\\n000\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n12\\n1\\n59\\n91\\n0 0\", \"3 53\\n101\\n0\\n010\\n3 50\\n110\\n100\\n51\\n10 10\\n1\\n2\\n5\\n0\\n5\\n16\\n22\\n21\\n10\\n53\\n0 0\", \"3 82\\n100\\n1\\n100\\n3 50\\n100\\n100\\n50\\n10 10\\n1\\n3\\n3\\n8\\n5\\n16\\n17\\n18\\n17\\n65\\n0 0\", \"3 50\\n000\\n0\\n100\\n3 50\\n100\\n100\\n8\\n10 10\\n1\\n2\\n5\\n0\\n5\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n100\\n100\\n7\\n10 10\\n2\\n2\\n3\\n10\\n5\\n16\\n35\\n1\\n56\\n27\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n127\\n10 10\\n1\\n0\\n3\\n11\\n5\\n16\\n17\\n18\\n24\\n65\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n101\\n43\\n10 10\\n1\\n2\\n0\\n8\\n5\\n16\\n34\\n29\\n56\\n65\\n0 0\", \"3 50\\n101\\n0\\n000\\n3 50\\n100\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n17\\n25\\n29\\n22\\n0 0\", \"3 50\\n110\\n1\\n100\\n3 50\\n100\\n100\\n10\\n10 10\\n1\\n2\\n0\\n8\\n2\\n16\\n34\\n18\\n56\\n78\\n0 0\", \"3 50\\n110\\n1\\n101\\n3 50\\n010\\n100\\n34\\n10 10\\n1\\n1\\n5\\n8\\n0\\n16\\n21\\n2\\n56\\n65\\n0 0\", \"3 87\\n111\\n2\\n100\\n3 50\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n14\\n5\\n20\\n12\\n1\\n21\\n91\\n0 0\", \"3 22\\n110\\n1\\n101\\n3 17\\n110\\n101\\n34\\n10 10\\n1\\n1\\n5\\n8\\n5\\n25\\n21\\n1\\n56\\n65\\n0 0\", \"3 49\\n111\\n1\\n101\\n3 50\\n110\\n100\\n48\\n10 10\\n1\\n1\\n5\\n8\\n5\\n36\\n21\\n1\\n56\\n55\\n0 0\", \"3 53\\n101\\n0\\n100\\n3 11\\n110\\n100\\n98\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n10\\n53\\n0 0\", \"3 53\\n101\\n0\\n010\\n3 50\\n110\\n100\\n51\\n10 10\\n1\\n2\\n5\\n0\\n10\\n16\\n22\\n21\\n10\\n53\\n0 0\", \"3 53\\n110\\n0\\n000\\n3 50\\n110\\n100\\n51\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n10\\n39\\n0 0\", \"3 45\\n110\\n1\\n100\\n3 31\\n100\\n100\\n34\\n10 10\\n0\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n16\\n0 0\", \"3 50\\n000\\n0\\n100\\n3 50\\n100\\n100\\n8\\n10 10\\n1\\n2\\n5\\n0\\n5\\n16\\n17\\n18\\n56\\n53\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n000\\n100\\n7\\n10 10\\n2\\n2\\n3\\n10\\n5\\n16\\n35\\n1\\n56\\n27\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n127\\n10 10\\n1\\n0\\n3\\n11\\n5\\n27\\n17\\n18\\n24\\n65\\n0 0\", \"3 43\\n110\\n1\\n100\\n3 50\\n100\\n100\\n29\\n10 10\\n1\\n2\\n3\\n11\\n5\\n16\\n17\\n12\\n56\\n65\\n0 0\", \"3 15\\n110\\n1\\n100\\n3 50\\n110\\n100\\n34\\n10 20\\n1\\n1\\n4\\n8\\n5\\n14\\n21\\n1\\n56\\n65\\n0 0\", \"3 87\\n111\\n1\\n000\\n3 69\\n000\\n100\\n7\\n10 10\\n1\\n2\\n3\\n9\\n5\\n20\\n8\\n1\\n59\\n91\\n0 0\", \"3 87\\n111\\n2\\n100\\n3 50\\n000\\n100\\n3\\n10 10\\n1\\n2\\n3\\n2\\n2\\n20\\n12\\n1\\n33\\n91\\n0 0\", \"3 53\\n101\\n0\\n100\\n3 11\\n110\\n100\\n98\\n10 10\\n1\\n2\\n3\\n0\\n5\\n16\\n22\\n18\\n7\\n53\\n0 0\", \"3 50\\n110\\n2\\n100\\n3 50\\n000\\n100\\n59\\n10 10\\n1\\n2\\n3\\n8\\n8\\n16\\n5\\n18\\n56\\n65\\n0 0\", \"3 45\\n110\\n1\\n100\\n3 31\\n100\\n100\\n34\\n10 13\\n0\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n16\\n0 0\", \"3 52\\n100\\n0\\n100\\n3 42\\n100\\n110\\n0\\n10 10\\n1\\n2\\n3\\n10\\n3\\n16\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n110\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n8\\n8\\n17\\n18\\n29\\n53\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n100\\n100\\n127\\n10 9\\n1\\n0\\n3\\n11\\n5\\n27\\n17\\n18\\n24\\n65\\n0 0\", \"3 49\\n110\\n0\\n101\\n3 96\\n110\\n000\\n39\\n10 10\\n0\\n1\\n5\\n8\\n5\\n58\\n21\\n1\\n62\\n65\\n0 0\", \"3 45\\n110\\n1\\n100\\n3 31\\n100\\n100\\n34\\n10 13\\n0\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n32\\n0 0\", \"3 50\\n111\\n1\\n100\\n3 50\\n000\\n100\\n8\\n10 10\\n2\\n2\\n3\\n9\\n5\\n16\\n35\\n1\\n56\\n27\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n110\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n8\\n8\\n17\\n18\\n44\\n53\\n0 0\", \"3 43\\n110\\n1\\n100\\n3 50\\n100\\n100\\n20\\n10 10\\n1\\n2\\n3\\n11\\n5\\n16\\n17\\n12\\n64\\n65\\n0 0\", \"3 29\\n110\\n1\\n000\\n3 24\\n100\\n110\\n49\\n10 10\\n1\\n2\\n3\\n16\\n5\\n16\\n21\\n1\\n56\\n65\\n0 0\", \"3 50\\n010\\n1\\n100\\n3 50\\n100\\n100\\n19\\n10 10\\n1\\n2\\n3\\n12\\n5\\n16\\n6\\n0\\n54\\n105\\n0 0\", \"3 49\\n110\\n0\\n101\\n3 96\\n110\\n000\\n39\\n10 11\\n0\\n1\\n5\\n8\\n5\\n58\\n21\\n1\\n62\\n65\\n0 0\", \"3 50\\n110\\n2\\n000\\n3 50\\n000\\n100\\n68\\n10 10\\n1\\n2\\n3\\n8\\n8\\n16\\n5\\n18\\n56\\n65\\n0 0\", \"3 50\\n100\\n0\\n100\\n3 50\\n110\\n000\\n50\\n10 10\\n1\\n2\\n3\\n0\\n14\\n8\\n17\\n18\\n44\\n53\\n0 0\", \"3 45\\n110\\n1\\n100\\n3 31\\n110\\n000\\n34\\n10 13\\n0\\n2\\n3\\n8\\n5\\n16\\n21\\n1\\n56\\n32\\n0 0\", \"3 50\\n000\\n0\\n101\\n3 50\\n101\\n100\\n8\\n10 10\\n1\\n2\\n5\\n0\\n5\\n16\\n8\\n16\\n56\\n53\\n0 0\", \"3 52\\n100\\n0\\n100\\n3 42\\n100\\n111\\n0\\n10 10\\n1\\n2\\n3\\n10\\n3\\n1\\n17\\n18\\n29\\n105\\n0 0\", \"3 53\\n101\\n0\\n110\\n3 50\\n000\\n110\\n51\\n10 10\\n2\\n2\\n6\\n0\\n1\\n16\\n22\\n18\\n1\\n53\\n0 0\"], \"outputs\": [\"0.51\\n0.26\\n1.4766666666666667\", \"0.51\\n0.26\\n1.61\\n\", \"0.51\\n0.26\\n1.64333333333\\n\", \"0.51\\n0.26\\n1.54333333333\\n\", \"0.51\\n0.51\\n1.54333333333\\n\", \"0.51\\n0.51\\n1.31555555556\\n\", \"0.51\\n0.51\\n1.28777777778\\n\", \"0.51\\n0.51\\n1.36185185185\\n\", \"0.51\\n0.51\\n1.34333333333\\n\", \"0.51\\n1.01\\n1.34333333333\\n\", \"1.01\\n1.01\\n1.34333333333\\n\", \"0.51\\n1.51\\n1.61\\n\", \"0.51\\n0.26\\n1.47666666667\\n\", \"1.01\\n0.51\\n1.31555555556\\n\", \"0.51\\n0.385\\n1.28777777778\\n\", \"1.01\\n0.51\\n1.54333333333\\n\", \"0.51\\n0.385\\n1.12904761905\\n\", \"0.51\\n0.51\\n1.32481481481\\n\", \"0.51\\n1.01\\n1.36185185185\\n\", \"0.51\\n1.51\\n1.57\\n\", \"0.51\\n0.51\\n1.51\\n\", \"0.51\\n0.51\\n1.15285714286\\n\", \"0.51\\n1.01\\n1.38037037037\\n\", \"0.51\\n0.26\\n1.57\\n\", \"0.51\\n1.01\\n1.43592592593\\n\", \"0.51\\n0.51\\n1.57\\n\", \"0.51\\n0.51\\n1.26\\n\", \"0.51\\n0.51\\n1.23222222222\\n\", \"0.51\\n0.51\\n1.20444444444\\n\", \"1.51\\n0.26\\n1.61\\n\", \"1.01\\n0.26\\n1.61\\n\", \"0.51\\n0.26\\n1.37666666667\\n\", \"0.51\\n0.26\\n1.96\\n\", \"0.51\\n0.26\\n1.51\\n\", \"0.51\\n0.51\\n1.58777777778\\n\", \"1.01\\n1.51\\n1.61\\n\", \"0.51\\n0.51\\n1.47666666667\\n\", \"1.01\\n0.51\\n1.58142857143\\n\", \"0.51\\n0.51\\n1.37666666667\\n\", \"0.51\\n0.385\\n1.21\\n\", \"1.01\\n1.01\\n1.38037037037\\n\", \"1.01\\n0.51\\n1.15285714286\\n\", \"0.51\\n1.01\\n1.69888888889\\n\", \"0.51\\n0.843333333333\\n1.26\\n\", \"0.51\\n0.71\\n1.61\\n\", \"0.51\\n0.51\\n1.14888888889\\n\", \"1.51\\n0.51\\n1.61\\n\", \"0.51\\n0.51\\n1.64333333333\\n\", \"0.51\\n0.26\\n1.31555555556\\n\", \"0.51\\n0.51\\n1.61\\n\", \"0.51\\n1.51\\n1.54333333333\\n\", \"0.51\\n0.26\\n1.63\\n\", \"0.51\\n0.26\\n2.01\\n\", \"1.01\\n0.51\\n1.34333333333\\n\", \"0.51\\n0.26\\n1.28777777778\\n\", \"1.01\\n1.51\\n1.31\\n\", \"0.51\\n0.51\\n1.01\\n\", \"1.01\\n1.01\\n1.36185185185\\n\", \"1.01\\n0.26\\n1.57\\n\", \"0.51\\n0.26\\n1.67666666667\\n\", \"1.01\\n0.51\\n1.61\\n\", \"0.51\\n0.51\\n1.53\\n\", \"0.51\\n0.01\\n2.01\\n\", \"0.51\\n0.51\\n1.44333333333\\n\", \"1.01\\n1.51\\n1.21\\n\", \"0.51\\n0.51\\n1.52428571429\\n\", \"0.51\\n1.01\\n1.28777777778\\n\", \"0.51\\n1.01\\n1.67666666667\\n\", \"1.21\\n0.843333333333\\n1.26\\n\", \"0.51\\n0.51\\n1.17666666667\\n\", \"0.51\\n0.31\\n1.61\\n\", \"1.01\\n0.26\\n1.91\\n\", \"1.01\\n0.26\\n1.47666666667\\n\", \"0.51\\n0.343333333333\\n1.37666666667\\n\", \"1.01\\n0.51\\n1.49\\n\", \"0.51\\n1.01\\n1.53\\n\", \"0.51\\n0.01\\n1.96833333333\\n\", \"0.51\\n0.51\\n1.885\\n\", \"1.15285714286\\n0.51\\n1.15285714286\\n\", \"1.01\\n1.01\\n1.1846031746\\n\", \"0.51\\n1.01\\n1.39888888889\\n\", \"0.51\\n0.31\\n1.37666666667\\n\", \"0.51\\n1.51\\n1.31555555556\\n\", \"0.51\\n0.343333333333\\n1.385\\n\", \"0.51\\n0.51\\n1.96\\n\", \"0.51\\n1.51\\n1.37666666667\\n\", \"0.51\\n0.01\\n1.93857142857\\n\", \"0.51\\n1.01\\n1.14888888889\\n\", \"0.51\\n0.343333333333\\n1.34333333333\\n\", \"0.51\\n1.01\\n1.31\\n\", \"0.51\\n1.51\\n1.31\\n\", \"0.51\\n0.51\\n1.84333333333\\n\", \"1.01\\n0.26\\n1.51\\n\", \"1.01\\n0.51\\n1.39333333333\\n\", \"0.51\\n1.01\\n1.14333333333\\n\", \"1.01\\n1.51\\n1.31555555556\\n\", \"0.51\\n1.51\\n1.53\\n\", \"0.51\\n1.67666666667\\n1.34333333333\\n\", \"1.01\\n0.51\\n1.27666666667\\n\", \"0.51\\n0.51\\n1.71\\n\", \"1.51\\n1.51\\n1.37666666667\\n\"]}", "source": "primeintellect"}
|
Dr. Grey is a data analyst, who visualizes various aspects of data received from all over the world everyday. He is extremely good at sophisticated visualization tools, but yet his favorite is a simple self-made histogram generator.
Figure 1 is an example of histogram automatically produced by his histogram.
<image>
A histogram is a visual display of frequencies of value occurrences as bars. In this example, values in the interval 0-9 occur five times, those in the interval 10-19 occur three times, and 20-29 and 30-39 once each.
Dr. Grey’s histogram generator is a simple tool. First, the height of the histogram is fixed, that is, the height of the highest bar is always the same and those of the others are automatically adjusted proportionately. Second, the widths of bars are also fixed. It can only produce a histogram of uniform intervals, that is, each interval of a histogram should have the same width (10 in the above example). Finally, the bar for each interval is painted in a grey color, where the colors of the leftmost and the rightmost intervals are black and white, respectively, and the darkness of bars monotonically decreases at the same rate from left to right. For instance, in Figure 1, the darkness levels of the four bars are 1, 2/3, 1/3, and 0, respectively.
In this problem, you are requested to estimate ink consumption when printing a histogram on paper. The amount of ink necessary to draw a bar is proportional to both its area and darkness.
Input
The input consists of multiple datasets, each of which contains integers and specifies a value table and intervals for the histogram generator, in the following format.
n w
v1
v2
.
.
vn
n is the total number of value occurrences for the histogram, and each of the n lines following the first line contains a single value. Note that the same value may possibly occur multiple times.
w is the interval width. A value v is in the first (i.e. leftmost) interval if 0 ≤ v < w, the second one if w ≤ v < 2w, and so on. Note that the interval from 0 (inclusive) to w (exclusive) should be regarded as the leftmost even if no values occur in this interval. The last (i.e. rightmost) interval is the one that includes the largest value in the dataset.
You may assume the following.
1 ≤ n ≤ 100
10 ≤ w ≤ 50
0 ≤ vi ≤ 100 for 1 ≤ i ≤ n
You can also assume that the maximum value is no less than w. This means that the histogram has more than one interval. The end of the input is indicated by a line containing two zeros.
Output
For each dataset, output a line containing the amount of ink consumed in printing the histogram.
One unit of ink is necessary to paint one highest bar black. Assume that 0.01 units of ink per histogram is consumed for various purposes except for painting bars such as drawing lines and characters (see Figure 1). For instance, the amount of ink consumed in printing the histogram in Figure 1 is:
<image>
Each output value should be in a decimal fraction and may have an error less than 10-5 .
Example
Input
3 50
100
0
100
3 50
100
100
50
10 10
1
2
3
4
5
16
17
18
29
30
0 0
Output
0.51
0.26
1.4766666666666667
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
{"tests": "{\"inputs\": [\"2 3\\n1.0 1.0\\n-1.0 0.0\\n0.5 0.5\", \"4 3\\n1.0 1.0 0.0 0.0\\n-1.0 0.0 -1.0 0.0\\n0.5 0.5 0.5 0.5\", \"1 1\\n1.0\", \"2 3\\n1.2834290847607077 1.0\\n-1.0 0.0\\n0.5 0.5\", \"4 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.0 -1.0 0.0\\n0.5 0.5 0.5 0.5\", \"2 1\\n1.0\", \"2 3\\n1.2834290847607077 1.0\\n-1.0 0.27668724595465666\\n0.5 0.5\", \"8 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.0 -1.0 0.0\\n0.5 0.5 0.5 0.5\", \"2 3\\n1.88381284250856 1.0\\n-1.0 0.27668724595465666\\n0.5 0.5\", \"8 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.0 -0.10583714601690064 0.0\\n0.5 0.5 0.5 0.5\", \"8 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n0.5 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n0.5 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n0.5 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n1.009961934531147 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 0.5\", \"9 3\\n1.4619505731749123 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 0.5\", \"9 3\\n1.4619505731749123 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.0 0.9556232910993283 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.0 0.9867872732115789 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-0.444296057332376 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-0.444296057332376 0.5585633480145408 0.2979049796742458 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.2979049796742458 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 2.159150879281688 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 2.159150879281688 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.242875309278145 2.159150879281688 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.242875309278145 2.159150879281688 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 2.607472070212129 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 2.607472070212129 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 1.5575047644285314 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 2.607472070212129 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 2.418961926998407 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 2.418961926998407 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 1.9231774516178177 0.5153809858809549\\n0.5015226314102327 2.418961926998407 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 1.9231774516178177 0.5153809858809549\\n0.5015226314102327 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 2.7430876831712183 0.5153809858809549\\n0.5015226314102327 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"16 3\\n2.242875309278145 3.4628197115619836 2.7430876831712183 0.5153809858809549\\n0.5015226314102327 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"16 3\\n2.242875309278145 3.4628197115619836 2.7430876831712183 0.5153809858809549\\n0.5015226314102327 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 2.050694060753176 1.2838449227433606\", \"16 4\\n2.242875309278145 3.4628197115619836 2.8105250026221755 0.5153809858809549\\n0.5015226314102327 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 2.050694060753176 1.2838449227433606\", \"16 4\\n2.242875309278145 3.4628197115619836 2.8105250026221755 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 2.050694060753176 1.2838449227433606\", \"16 4\\n2.9498357179035515 3.4628197115619836 2.8105250026221755 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 2.050694060753176 1.2838449227433606\", \"16 4\\n2.9498357179035515 3.940737376487606 2.8105250026221755 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 2.050694060753176 1.2838449227433606\", \"16 4\\n2.9498357179035515 3.940737376487606 2.8105250026221755 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.050694060753176 1.2838449227433606\", \"16 4\\n3.578857615358075 3.940737376487606 2.8105250026221755 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.050694060753176 1.2838449227433606\", \"16 4\\n3.578857615358075 3.940737376487606 2.8105250026221755 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 4\\n3.578857615358075 3.940737376487606 3.6529376741127564 0.5153809858809549\\n0.8717542191150367 2.4349144722266685 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n3.578857615358075 3.940737376487606 3.6529376741127564 0.5153809858809549\\n0.8717542191150367 2.900143966130924 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n3.578857615358075 3.940737376487606 3.6529376741127564 0.5153809858809549\\n1.6075936644217126 2.900143966130924 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n3.578857615358075 4.2767255255124255 3.6529376741127564 0.5153809858809549\\n1.6075936644217126 2.900143966130924 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n3.578857615358075 4.2767255255124255 3.6529376741127564 0.5153809858809549\\n2.4138177998865378 2.900143966130924 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n3.578857615358075 4.2767255255124255 3.6529376741127564 0.5153809858809549\\n2.4138177998865378 2.900143966130924 0.6044093106720025 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n4.138680503349344 4.2767255255124255 3.6529376741127564 0.5153809858809549\\n2.4138177998865378 2.900143966130924 0.6044093106720025 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n4.138680503349344 4.2767255255124255 3.6529376741127564 0.5153809858809549\\n2.4138177998865378 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n4.138680503349344 4.2767255255124255 3.8075192246119176 0.5153809858809549\\n2.4138177998865378 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n4.138680503349344 4.875700439855141 3.8075192246119176 0.5153809858809549\\n2.4138177998865378 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.2838449227433606\", \"16 8\\n4.138680503349344 4.875700439855141 3.8075192246119176 0.5153809858809549\\n2.4138177998865378 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.823240882935031\", \"16 8\\n4.138680503349344 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.4138177998865378 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.823240882935031\", \"16 15\\n4.138680503349344 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.543076978184359 1.823240882935031\", \"16 15\\n4.138680503349344 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.569801477398121 1.823240882935031\", \"16 15\\n4.138680503349344 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.569801477398121 2.212051505432021\", \"16 9\\n4.138680503349344 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.863137758264881 2.212051505432021\", \"16 9\\n4.501715377052143 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.863137758264881 2.212051505432021\", \"16 9\\n4.501715377052143 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 0.5815158140795751 2.863137758264881 2.3377338794728457\", \"16 9\\n4.501715377052143 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 2.900143966130924 1.2668306673398737 1.0790706578914466\\n2.696467865949769 1.319735907903989 2.863137758264881 2.3377338794728457\", \"16 9\\n4.501715377052143 4.875700439855141 3.8075192246119176 1.063384662894167\\n2.441335972156807 3.7963445001769083 1.2668306673398737 1.0790706578914466\\n2.696467865949769 1.319735907903989 2.863137758264881 2.3377338794728457\", \"2 3\\n1.2592421940740615 1.0\\n-1.0 0.0\\n0.5 0.5\", \"4 3\\n1.3318667984159749 1.0 0.0 0.0\\n-1.0 0.0 -1.0 0.0\\n0.5 0.5 0.5 0.5\", \"2 3\\n1.3776954246339783 1.0\\n-1.0 0.0\\n0.5 0.5\", \"4 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.5818152957507576 -1.0 0.0\\n0.5 0.5 0.5 0.5\", \"2 3\\n1.2834290847607077 1.0\\n-1.0 0.27668724595465666\\n0.5 0.6088208797308303\", \"8 3\\n1.0 1.0 0.0 0.5908142265864281\\n-1.0 0.0 -1.0 0.0\\n0.5 0.5 0.5 0.5\", \"2 3\\n1.88381284250856 1.0\\n-1.0 0.27668724595465666\\n1.4236167396284127 0.5\", \"8 3\\n1.0 1.0 0.0 0.40562788475787737\\n-1.0 0.0 -0.10583714601690064 0.0\\n0.5 0.5325570747293088 0.5 0.5\", \"8 3\\n1.0 1.6947651231403524 0.0 0.40562788475787737\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n0.5 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.2365413241160469 0.40562788475787737\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n0.5 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n0.5 1.228733925706154 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.0\\n1.009961934531147 1.0185558115147835 0.5 0.5\", \"9 3\\n1.0 1.0 0.0 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5489649307715825 0.5 0.5\", \"9 3\\n1.0 1.2849868926754513 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 0.5 0.5\", \"9 3\\n1.0 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.9718021893152318\\n1.009961934531147 0.5 1.0322563221228453 0.5\", \"9 3\\n2.0485047612979095 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 0.5\", \"9 3\\n1.4619505731749123 1.6153238946611106 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.0 0.6091921440739713 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.458405378702372 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.0 0.9556232910993283 0.5153809858809549\\n-1.0 0.5585633480145408 0.2842652662769395 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.6815024255265658 0.9867872732115789 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 1.2972962779724448\\n1.009961934531147 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-1.0 0.5585633480145408 -0.10583714601690064 0.931699357335547\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.616666997882088 0.9867872732115789 0.5153809858809549\\n-0.444296057332376 0.5585633480145408 -0.10583714601690064 0.8344522878606784\\n2.3763614574906606 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 2.218003507906506 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.2979049796742458 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 1.9811197935482272 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"11 3\\n2.1570051989707055 2.159150879281688 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 0.8344522878606784\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.1570051989707055 2.159150879281688 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n2.290619321879634 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.242875309278145 2.159150879281688 0.9867872732115789 0.5153809858809549\\n1.337190570603469 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.0322563221228453 1.2838449227433606\", \"9 3\\n2.242875309278145 2.607472070212129 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 0.5585633480145408 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.8575254961510084 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 2.607472070212129 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 1.5575047644285314 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.6013083998305917\", \"9 3\\n2.9332731340207063 2.607472070212129 0.9867872732115789 0.5153809858809549\\n0.5015226314102327 2.418961926998407 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 0.9867872732115789 1.3159124051612174\\n0.5015226314102327 2.418961926998407 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 2.914362876102388 0.5153809858809549\\n0.5015226314102327 2.418961926998407 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 1.9231774516178177 0.5153809858809549\\n0.5015226314102327 2.506516958770912 0.6044093106720025 1.0790706578914466\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\", \"9 3\\n2.242875309278145 3.4628197115619836 2.7430876831712183 0.5153809858809549\\n0.5015226314102327 2.4349144722266685 0.6044093106720025 1.8924328235097445\\n1.8516458934245779 0.5 1.7136907495766462 1.2838449227433606\"], \"outputs\": [\"1.0\", \"3.0\", \"1.0\", \"0.917925050\\n\", \"2.717772601\\n\", \"1.000000000\\n\", \"1.233852077\\n\", \"3.717772601\\n\", \"1.399302582\\n\", \"2.728974102\\n\", \"3.040967116\\n\", \"3.154395163\\n\", \"3.255478742\\n\", \"4.025501852\\n\", \"4.721812472\\n\", \"4.156966326\\n\", \"5.086648069\\n\", \"5.647867061\\n\", \"7.591417031\\n\", \"9.469121621\\n\", \"9.076243585\\n\", \"9.046124577\\n\", \"9.072139575\\n\", \"11.480708980\\n\", \"10.678107967\\n\", \"10.755653842\\n\", \"10.809779805\\n\", \"11.086343043\\n\", \"11.511974769\\n\", \"11.980057633\\n\", \"12.224726710\\n\", \"13.621770888\\n\", \"13.701754562\\n\", \"15.815582639\\n\", \"19.241138352\\n\", \"19.831531831\\n\", \"18.118835139\\n\", \"18.196266822\\n\", \"17.645724025\\n\", \"40.785381428\\n\", \"42.053991573\\n\", \"42.428512326\\n\", \"42.936942795\\n\", \"46.607983905\\n\", \"50.146274620\\n\", \"50.234435262\\n\", \"54.341126331\\n\", \"56.603020717\\n\", \"62.047923577\\n\", \"64.529950115\\n\", \"66.354352086\\n\", \"69.115322236\\n\", \"72.357481217\\n\", \"76.199827655\\n\", \"80.520282133\\n\", \"81.759831457\\n\", \"82.913080452\\n\", \"88.395154011\\n\", \"90.071103542\\n\", \"90.936272923\\n\", \"91.069877881\\n\", \"91.206516997\\n\", \"92.775481543\\n\", \"94.369159732\\n\", \"97.505924760\\n\", \"98.077752588\\n\", \"99.481294813\\n\", \"105.482691352\\n\", \"0.920347086\\n\", \"3.414468477\\n\", \"0.916387159\\n\", \"3.553469675\\n\", \"1.441912241\\n\", \"3.670981861\\n\", \"1.920707239\\n\", \"2.732846722\\n\", \"3.956848118\\n\", \"2.876307929\\n\", \"4.361615243\\n\", \"4.646403103\\n\", \"4.733437521\\n\", \"4.285361423\\n\", \"5.334736943\\n\", \"6.877261683\\n\", \"7.973585550\\n\", \"10.617413286\\n\", \"9.145848825\\n\", \"9.103174625\\n\", \"10.058806587\\n\", \"11.652462052\\n\", \"12.896609229\\n\", \"11.304253873\\n\", \"11.330735175\\n\", \"13.918841817\\n\", \"13.798401996\\n\", \"13.761280382\\n\", \"12.886405258\\n\", \"17.516120301\\n\", \"21.811010239\\n\", \"21.297539728\\n\", \"17.565178804\\n\", \"18.550085600\\n\", \"20.062632532\\n\"]}", "source": "primeintellect"}
|
You are recording a result of a secret experiment, which consists of a large set of N-dimensional vectors. Since the result may become very large, you are thinking of compressing it. Fortunately you already have a good compression method for vectors with small absolute values, all you have to do is to preprocess the vectors and make them small.
You can record the set of vectors in any order you like. Let's assume you process them in the order v_1, v_2,..., v_M. Each vector v_i is recorded either as is, or as a difference vector. When it is recorded as a difference, you can arbitrarily pick up an already chosen vector v_j (j<i) and a real value r. Then the actual vector value recorded is (v_i - r v_j). The values of r and j do not affect the compression ratio so much, so you don't have to care about them.
Given a set of vectors, your task is to write a program that calculates the minimum sum of the squared length of the recorded vectors.
Input
The input is like the following style.
N M
v_{1,1} v_{1,2} ... v_{1,N}
...
v_{M,1} v_{M,2} ... v_{M,N}
The first line contains two integers N and M (1 \leq N, M \leq 100), where N is the dimension of each vector, and M is the number of the vectors. Each of the following M lines contains N floating point values v_{i,j} (-1.0 \leq v_{i,j} \leq 1.0) which represents the j-th element value of the i-th vector.
Output
Output the minimum sum of the squared length of the recorded vectors. The output should not contain an absolute error greater than 10^{-6}.
Examples
Input
2 3
1.0 1.0
-1.0 0.0
0.5 0.5
Output
1.0
Input
1 1
1.0
Output
1.0
Input
4 3
1.0 1.0 0.0 0.0
-1.0 0.0 -1.0 0.0
0.5 0.5 0.5 0.5
Output
3.0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n?sum??mer\\nc??a??mp\", \"3\\nsnuje\\n????e\\nsnule\", \"2\\n?rum??mer\\nc??a??mp\", \"3\\nsnuje\\n????e\\neluns\", \"2\\n?rum??mer\\nc@?a??mp\", \"3\\nsunje\\n????e\\neluns\", \"2\\n?rum??mer\\ncA?a??mp\", \"3\\nsunje\\n@???e\\neluns\", \"2\\nrem??mur?\\ncA?a??mp\", \"3\\nsunje\\n@???e\\nsnule\", \"2\\nsem??mur?\\ncA?a??mp\", \"3\\njunse\\n@???e\\nsnule\", \"2\\nsem??mur?\\ncA?a>?mp\", \"3\\nesnuj\\n@???e\\nsnule\", \"2\\nsem??mur?\\npm?>a?Ac\", \"3\\nesnuj\\n@?e??\\nsnule\", \"2\\nsem??mur?\\npm?>a?Ab\", \"3\\nesnuj\\n@?f??\\nsnule\", \"2\\n?rum??mes\\npm?>a?Ab\", \"3\\nesnuj\\n@?f??\\nnsule\", \"2\\nr?um??mes\\npm?>a?Ab\", \"3\\nesnuj\\n@???f\\nnsule\", \"2\\nr?um??mes\\npm?a>?Ab\", \"3\\nnseuj\\n@???f\\nnsule\", \"2\\nrmu???mes\\npm?a>?Ab\", \"3\\nnseuj\\n@???e\\nnsule\", \"2\\nrmu???les\\npm?a>?Ab\", \"3\\nnseuj\\n@???d\\nnsule\", \"2\\nrmu???les\\npm?a>@Ab\", \"3\\nnseuj\\n@???d\\nelusn\", \"2\\nrmu???les\\npm>a>@Ab\", \"3\\nnseuj\\n@???e\\nelusn\", \"2\\nrmul???es\\npm>a>@Ab\", \"3\\nnseuj\\n@>??e\\nelusn\", \"2\\nrmul???es\\npm>a>@Ac\", \"3\\nnteuj\\n@>??e\\nelusn\", \"2\\nrmul???es\\n@m>a>pAc\", \"3\\nntetj\\n@>??e\\nelusn\", \"2\\nrmul???es\\n@m>`>pAc\", \"3\\nntetj\\n@??>e\\nelusn\", \"2\\nr?ul??mes\\n@m>`>pAc\", \"3\\nnsetj\\n@??>e\\nelusn\", \"2\\nr?ul??mes\\n@m>`>pcA\", \"3\\nnsetj\\n@???e\\nelusn\", \"2\\nr?ul??les\\n@m>`>pcA\", \"3\\nnsesj\\n@???e\\nelusn\", \"2\\nr?ul??les\\n@c>`>pmA\", \"3\\nnsesj\\n@???e\\nemusn\", \"2\\n?rul??les\\n@c>`>pmA\", \"3\\nnsesi\\n@???e\\nemusn\", \"2\\n?rul??les\\nmc>`>p@A\", \"3\\nntesi\\n@???e\\nemusn\", \"2\\nsel??lur?\\nmc>`>p@A\", \"3\\nntesi\\ne???@\\nemusn\", \"2\\nsel??mur?\\nmc>`>p@A\", \"3\\nnsesi\\ne???@\\nemusn\", \"2\\nsel??mur?\\nA@p>`>cm\", \"3\\nnsesi\\ne???@\\nenusn\", \"2\\nsel??mur?\\nAcp>`>@m\", \"3\\nnsesi\\n@???e\\nenusn\", \"2\\nsel??mur?\\nAcp>`m@>\", \"3\\nnsesi\\n@?@?e\\nenusn\", \"2\\nsel??mur?\\n>@m`>pcA\", \"3\\nnsesi\\n@?@?e\\nnsune\", \"2\\ntel??mur?\\n>@m`>pcA\", \"3\\nnsesi\\n@?A?e\\nnsune\", \"2\\ntel??mur?\\n>@m`Apc>\", \"3\\nnsesi\\ne?A?@\\nnsune\", \"2\\ntel??mur?\\n>@maApc>\", \"3\\nnsesi\\n??Ae@\\nnsune\", \"2\\ntel??mur?\\n>@caApm>\", \"3\\nnsfsi\\n??Ae@\\nnsune\", \"2\\ntel??mur?\\n>@campA>\", \"3\\nnsfsi\\n??Ae@\\nnnuse\", \"2\\ntel??mur?\\n>@campB>\", \"3\\nnsfsi\\n>?Ae@\\nnnuse\", \"2\\n?rum??let\\n>@campB>\", \"3\\nssfni\\n>?Ae@\\nnnuse\", \"2\\n?rvm??let\\n>@campB>\", \"3\\ntsfni\\n>?Ae@\\nnnuse\", \"2\\n?rvm??lft\\n>@campB>\", \"3\\ntsfni\\n>?Ae@\\nneusn\", \"2\\ntfl??mvr?\\n>@campB>\", \"3\\ntsfni\\n>?Ae@\\nneusm\", \"2\\ntfl??mvs?\\n>@campB>\", \"3\\nssfni\\n>?Ae@\\nneusm\", \"2\\ntfl??mvs?\\n>@campB=\", \"3\\nssfni\\n>@Ae@\\nneusm\", \"2\\ntfm??mvs?\\n>@campB=\", \"3\\nssfni\\n@eA@>\\nneusm\", \"2\\ntfn??mvs?\\n>@campB=\", \"3\\nrsfni\\n@eA@>\\nneusm\", \"2\\ntfn??mvs?\\n>@calpB=\", \"3\\ninfsr\\n@eA@>\\nneusm\", \"2\\ntfn??mvs?\\n>pcal@B=\", \"3\\ninfsr\\n>eA@@\\nneusm\", \"2\\ntfn??mws?\\n>pcal@B=\", \"3\\ninfsr\\n@@Ae>\\nneusm\", \"2\\ntfn??mvs?\\n>Bcal@p=\", \"3\\ninrsf\\n@@Ae>\\nneusm\", \"2\\ntfn??mvs?\\n>cBal@p=\", \"3\\ninrsf\\n@@Ae>\\nmsuen\"], \"outputs\": [\"703286064\", \"1\", \"715167440\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Sunuke-kun's dictionary contains the words s1, ..., sn, which consist of n lowercase letters. This satisfies s1 <... <sn when compared in lexicographical order. Unfortunately, some characters are faint and unreadable. Unreadable characters are represented by?. Find out how many ways to restore the dictionary by replacing? With lowercase letters, even with mod 1,000,000,007.
Constraints
* 1 ≤ n ≤ 50
* 1 ≤ | si | ≤ 20
* The characters that appear in si are lowercase letters or?
Input
n
s1
.. ..
sn
Output
Print the answer on one line.
Examples
Input
2
?sum??mer
c??a??mp
Output
703286064
Input
3
snuje
????e
snule
Output
1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n1 1\\n4 1\\n4 3\\n1 3\\n2\\n2 0 2 4\\n2 4 2 0\", \"4\\n1 1\\n4 1\\n4 3\\n1 3\\n2\\n2 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n4 1\\n4 3\\n0 3\\n2\\n2 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 2 5\\n0 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 2 0\\n0 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n0 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n1 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n1 4 2 1\", \"4\\n2 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n1 4 2 1\", \"4\\n2 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n1 1\\n4 1\\n4 3\\n1 2\\n2\\n2 0 2 4\\n2 4 2 0\", \"4\\n1 1\\n4 1\\n4 3\\n1 3\\n2\\n2 0 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 1\\n4 3\\n0 3\\n2\\n2 0 0 5\\n2 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n1 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 2 5\\n0 4 0 0\", \"4\\n1 1\\n8 2\\n4 3\\n0 3\\n2\\n2 0 2 0\\n0 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n-1 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 0\\n2\\n2 0 0 0\\n1 4 2 0\", \"4\\n2 1\\n4 2\\n4 5\\n0 3\\n2\\n2 0 0 0\\n1 4 2 1\", \"4\\n2 1\\n4 3\\n4 3\\n0 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n4 1\\n4 3\\n1 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n7 2\\n4 3\\n1 3\\n2\\n2 1 0 0\\n1 8 2 1\", \"4\\n1 1\\n4 1\\n4 3\\n1 2\\n2\\n2 0 2 4\\n2 4 3 0\", \"4\\n1 1\\n4 1\\n4 1\\n1 3\\n2\\n2 0 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 1\\n4 3\\n0 3\\n2\\n2 -1 0 5\\n2 4 2 0\", \"4\\n1 1\\n4 4\\n4 3\\n0 3\\n2\\n1 0 2 5\\n2 4 2 0\", \"4\\n1 0\\n4 2\\n4 3\\n0 0\\n2\\n2 0 0 0\\n1 4 2 0\", \"4\\n2 1\\n4 1\\n4 3\\n2 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n7 2\\n4 3\\n1 3\\n2\\n2 1 0 0\\n1 8 0 1\", \"4\\n2 2\\n4 2\\n4 3\\n1 3\\n2\\n4 1 0 1\\n1 8 2 1\", \"4\\n1 1\\n4 1\\n4 3\\n1 2\\n2\\n2 0 2 4\\n2 4 3 -1\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 -1 0 5\\n2 4 2 0\", \"4\\n1 1\\n4 2\\n4 6\\n0 3\\n2\\n2 0 2 5\\n0 4 -1 0\", \"4\\n1 0\\n7 2\\n4 3\\n0 0\\n2\\n2 0 0 0\\n1 4 2 0\", \"4\\n2 1\\n2 2\\n4 5\\n0 0\\n2\\n2 0 0 0\\n1 4 2 1\", \"4\\n2 1\\n4 1\\n5 3\\n2 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n7 2\\n4 4\\n1 3\\n2\\n2 1 0 0\\n1 8 0 1\", \"4\\n1 1\\n4 1\\n4 3\\n1 2\\n2\\n2 0 2 4\\n2 4 0 -1\", \"4\\n1 1\\n4 0\\n4 1\\n1 3\\n2\\n2 1 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 2\\n4 6\\n0 3\\n1\\n2 0 2 5\\n0 4 -1 0\", \"4\\n1 -1\\n7 2\\n4 3\\n0 0\\n2\\n2 0 0 0\\n1 4 2 0\", \"4\\n2 1\\n2 2\\n4 5\\n0 0\\n2\\n2 0 0 1\\n1 4 2 1\", \"4\\n2 1\\n4 1\\n0 3\\n2 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n7 1\\n4 4\\n1 3\\n2\\n2 1 0 0\\n1 8 0 1\", \"4\\n1 1\\n4 0\\n4 1\\n1 3\\n2\\n4 1 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 2\\n4 6\\n0 3\\n1\\n2 0 0 5\\n0 4 -1 0\", \"4\\n1 -1\\n7 2\\n4 3\\n0 0\\n2\\n2 0 0 0\\n1 4 4 0\", \"4\\n2 1\\n7 1\\n0 3\\n2 3\\n2\\n2 0 0 0\\n1 8 2 1\", \"4\\n1 0\\n4 0\\n4 1\\n1 3\\n2\\n4 1 2 5\\n1 4 2 0\", \"4\\n1 -1\\n7 2\\n4 3\\n0 0\\n2\\n2 0 0 0\\n1 5 4 0\", \"4\\n2 1\\n7 1\\n0 3\\n2 3\\n2\\n0 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n7 1\\n4 4\\n1 3\\n2\\n1 1 0 0\\n1 8 0 2\", \"4\\n1 0\\n4 0\\n4 1\\n1 1\\n2\\n4 1 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 2\\n4 6\\n0 3\\n1\\n1 0 0 5\\n0 4 -2 0\", \"4\\n1 -1\\n7 2\\n4 3\\n0 0\\n2\\n2 -1 0 0\\n1 5 4 0\", \"4\\n2 1\\n7 1\\n-1 3\\n2 3\\n2\\n0 0 0 0\\n1 8 2 1\", \"4\\n2 1\\n7 1\\n4 4\\n1 3\\n2\\n1 1 -1 0\\n1 8 0 2\", \"4\\n1 -1\\n7 2\\n4 3\\n0 0\\n2\\n2 -1 0 1\\n1 5 4 0\", \"4\\n1 0\\n3 0\\n4 1\\n1 1\\n2\\n4 2 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 1\\n4 9\\n0 3\\n1\\n1 0 0 5\\n0 4 -2 0\", \"4\\n1 -1\\n7 2\\n4 3\\n0 0\\n2\\n2 -1 0 1\\n1 5 4 1\", \"4\\n1 0\\n5 0\\n4 1\\n1 1\\n2\\n4 2 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 1\\n4 9\\n0 3\\n1\\n1 0 1 5\\n0 4 -2 0\", \"4\\n1 -1\\n7 2\\n4 5\\n0 0\\n2\\n2 -1 0 1\\n1 5 4 1\", \"4\\n1 0\\n5 0\\n4 1\\n2 1\\n2\\n4 2 2 5\\n1 4 2 0\", \"4\\n1 -1\\n7 2\\n4 1\\n0 0\\n2\\n2 -1 0 1\\n1 5 4 1\", \"4\\n1 0\\n6 0\\n4 1\\n2 1\\n2\\n4 2 2 5\\n1 4 2 0\", \"4\\n1 1\\n4 1\\n3 9\\n0 3\\n1\\n1 0 1 5\\n0 4 -2 -1\", \"4\\n1 0\\n7 2\\n4 1\\n0 0\\n2\\n2 -1 0 1\\n1 5 4 1\", \"4\\n1 0\\n6 0\\n4 1\\n3 1\\n2\\n4 2 2 5\\n1 4 2 0\", \"4\\n1 0\\n7 2\\n4 1\\n0 0\\n2\\n2 -1 0 0\\n1 5 4 1\", \"4\\n1 0\\n6 0\\n4 1\\n3 2\\n2\\n4 2 2 5\\n1 4 2 0\", \"4\\n1 0\\n7 2\\n4 1\\n-1 0\\n2\\n2 -1 0 0\\n1 5 4 1\", \"4\\n1 0\\n6 0\\n4 1\\n3 2\\n2\\n4 2 2 5\\n2 4 2 0\", \"4\\n1 0\\n6 0\\n3 1\\n3 2\\n2\\n4 2 2 5\\n2 4 2 0\", \"4\\n1 1\\n4 1\\n3 9\\n1 3\\n1\\n1 0 1 9\\n0 4 -1 -2\", \"4\\n1 0\\n6 0\\n3 1\\n3 2\\n2\\n4 0 2 5\\n2 4 2 0\", \"4\\n1 0\\n6 0\\n3 1\\n3 2\\n2\\n4 -1 2 5\\n2 4 2 0\", \"4\\n1 0\\n11 0\\n3 1\\n3 2\\n2\\n4 -1 2 5\\n2 4 2 0\", \"4\\n0 1\\n6 1\\n3 5\\n1 3\\n1\\n1 0 1 9\\n-1 4 -1 -2\", \"4\\n0 1\\n6 1\\n2 5\\n0 3\\n1\\n1 0 1 9\\n-1 8 -1 0\", \"4\\n-1 1\\n6 1\\n2 5\\n0 3\\n1\\n1 1 1 9\\n0 15 -1 0\", \"4\\n-1 1\\n9 1\\n2 5\\n0 3\\n2\\n1 1 1 9\\n0 15 -1 0\", \"4\\n-1 1\\n9 1\\n2 5\\n0 3\\n2\\n1 1 1 9\\n0 15 -1 1\", \"4\\n-2 1\\n9 1\\n2 5\\n0 3\\n2\\n1 1 1 9\\n0 15 -1 1\", \"4\\n-2 1\\n9 1\\n3 5\\n0 3\\n2\\n1 1 1 9\\n0 15 -1 1\", \"4\\n-1 1\\n9 1\\n3 5\\n0 3\\n2\\n1 1 1 9\\n0 15 -1 1\", \"4\\n-1 1\\n9 1\\n3 5\\n0 1\\n2\\n1 1 1 9\\n0 15 -1 1\", \"4\\n-2 1\\n9 2\\n3 5\\n0 1\\n2\\n1 1 1 9\\n0 15 -1 1\", \"4\\n-2 1\\n9 2\\n3 5\\n0 1\\n2\\n1 1 1 9\\n0 15 -1 0\", \"4\\n-2 1\\n9 2\\n3 5\\n0 1\\n2\\n1 1 1 9\\n-1 15 -1 0\", \"4\\n1 1\\n4 1\\n4 3\\n1 6\\n2\\n2 0 2 4\\n2 4 2 0\", \"4\\n1 1\\n4 1\\n1 3\\n1 3\\n2\\n2 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n8 1\\n4 3\\n0 3\\n2\\n2 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n1\\n2 0 2 5\\n2 4 2 0\", \"4\\n1 1\\n0 2\\n4 3\\n0 3\\n2\\n2 0 2 5\\n0 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n0 2 2 0\", \"4\\n1 1\\n4 2\\n4 2\\n0 3\\n2\\n2 0 0 0\\n1 4 2 0\", \"4\\n1 1\\n4 2\\n4 3\\n0 3\\n2\\n2 0 0 0\\n2 4 2 1\", \"4\\n2 1\\n4 1\\n4 3\\n0 3\\n2\\n2 0 0 0\\n1 4 2 1\"], \"outputs\": [\"2.00000000\\n4.00000000\", \"2.000000000\\n4.000000000\\n\", \"3.000000000\\n4.000000000\\n\", \"2.833333333\\n2.666666667\\n\", \"2.833333333\\n4.535714286\\n\", \"5.500000000\\n4.535714286\\n\", \"0.000000000\\n4.535714286\\n\", \"0.000000000\\n3.586538462\\n\", \"0.000000000\\n3.316666667\\n\", \"0.000000000\\n3.666666667\\n\", \"0.000000000\\n3.285714286\\n\", \"1.166666667\\n3.333333333\\n\", \"2.000000000\\n5.000000000\\n\", \"1.400000000\\n4.000000000\\n\", \"1.792857143\\n2.666666667\\n\", \"2.833333333\\n5.500000000\\n\", \"9.500000000\\n8.516666667\\n\", \"0.000000000\\n5.383333333\\n\", \"0.000000000\\n1.198380567\\n\", \"0.000000000\\n7.285714286\\n\", \"0.000000000\\n2.285714286\\n\", \"0.000000000\\n4.285714286\\n\", \"2.400000000\\n6.285714286\\n\", \"1.166666667\\n2.528846154\\n\", \"1.666666667\\n2.025000000\\n\", \"1.000000000\\n4.000000000\\n\", \"1.775000000\\n0.000000000\\n\", \"0.000000000\\n2.022556391\\n\", \"0.000000000\\n4.000000000\\n\", \"2.400000000\\n7.000000000\\n\", \"0.000000000\\n2.202380952\\n\", \"1.166666667\\n2.693750000\\n\", \"0.983333333\\n2.666666667\\n\", \"4.333333333\\n11.500000000\\n\", \"0.000000000\\n6.390688259\\n\", \"0.000000000\\n0.764705882\\n\", \"0.000000000\\n5.000000000\\n\", \"2.785714286\\n10.000000000\\n\", \"1.166666667\\n4.442307692\\n\", \"1.833333333\\n3.422727273\\n\", \"4.333333333\\n\", \"1.500000000\\n8.459064327\\n\", \"0.214285714\\n0.764705882\\n\", \"0.000000000\\n0.791208791\\n\", \"4.166666667\\n11.000000000\\n\", \"4.500000000\\n3.422727273\\n\", \"1.531674208\\n\", \"1.500000000\\n5.841818182\\n\", \"0.000000000\\n3.437689970\\n\", \"6.000000000\\n4.150000000\\n\", \"1.500000000\\n5.554376658\\n\", \"3.000000000\\n3.437689970\\n\", \"8.666666667\\n11.000000000\\n\", \"3.000000000\\n2.125000000\\n\", \"0.318840580\\n\", \"0.375000000\\n5.554376658\\n\", \"2.000000000\\n2.955026455\\n\", \"5.800000000\\n11.000000000\\n\", \"1.047619048\\n5.554376658\\n\", \"2.500000000\\n1.625000000\\n\", \"0.358974359\\n\", \"1.047619048\\n4.641818182\\n\", \"3.500000000\\n2.625000000\\n\", \"1.750000000\\n\", \"1.111111111\\n9.778592375\\n\", \"3.000000000\\n2.600000000\\n\", \"0.933333333\\n0.681818182\\n\", \"3.333333333\\n3.100000000\\n\", \"2.000000000\\n\", \"0.100000000\\n0.000000000\\n\", \"2.833333333\\n2.777777778\\n\", \"0.000000000\\n0.000000000\\n\", \"4.333333333\\n4.100000000\\n\", \"0.071428571\\n0.000000000\\n\", \"4.333333333\\n4.000000000\\n\", \"3.404761905\\n3.000000000\\n\", \"0.000000000\\n\", \"2.730769231\\n3.000000000\\n\", \"2.479166667\\n3.000000000\\n\", \"2.492753623\\n5.500000000\\n\", \"1.000000000\\n\", \"2.500000000\\n\", \"3.500000000\\n\", \"3.500000000\\n20.994871795\\n\", \"3.500000000\\n21.000000000\\n\", \"4.500000000\\n21.461538462\\n\", \"4.333333333\\n22.461538462\\n\", \"3.333333333\\n22.000000000\\n\", \"0.666666667\\n18.000000000\\n\", \"0.257575758\\n15.545751634\\n\", \"0.257575758\\n15.552032520\\n\", \"0.257575758\\n15.545454545\\n\", \"4.500000000\\n6.000000000\\n\", \"1.666666667\\n1.333333333\\n\", \"3.000000000\\n8.000000000\\n\", \"2.833333333\\n\", \"1.000000000\\n1.361111111\\n\", \"0.000000000\\n5.500000000\\n\", \"0.000000000\\n1.794871795\\n\", \"0.000000000\\n2.666666667\\n\", \"0.000000000\\n4.666666667\\n\"]}", "source": "primeintellect"}
|
<image>
As shown in the figure above, cut a convex polygon g by a line p1p2 and print the area of the cut polygon which is on the left-hand side of the line.
g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n−1) are sides of the convex polygon. The line segment connecting pn and p1 is also a side of the polygon.
Constraints
* 3 ≤ n ≤ 100
* 1 ≤ q ≤ 100
* -10000 ≤ xi, yi ≤ 10000
* -10000 ≤ p1x,p1y,p2x,p2y ≤ 10000
* No point in g will occur more than once.
* p1 ≠ p2
Input
The input is given in the following format:
g (the sequence of the points of the polygon)
q (the number of queries = the number of target lines)
1st query
2nd query
:
qth query
g is given as a sequence of points p1,..., pn in the following format:
n
x1 y1
x2 y2
:
xn yn
The first integer n is the number of points. The coordinate of the i-th point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Note that all interior angles of given convex polygons are less than or equal to 180.
For each query, a line represented by two points p1 and p2 is given. The coordinates of the points are given by four integers p1x, p1y, p2x and p2y.
Output
For each query, print the area of the cut polygon. The output values should be in a decimal fraction with an error less than 0.00001.
Example
Input
4
1 1
4 1
4 3
1 3
2
2 0 2 4
2 4 2 0
Output
2.00000000
4.00000000
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n3 2\\n4 0\\n2 1\", \"3\\n3 2\\n0 0\\n2 1\", \"3\\n3 2\\n0 0\\n3 1\", \"3\\n3 2\\n0 0\\n6 1\", \"3\\n3 4\\n1 -1\\n6 1\", \"3\\n1 4\\n1 -1\\n6 1\", \"3\\n1 4\\n1 -1\\n7 1\", \"3\\n1 4\\n0 -1\\n7 1\", \"3\\n1 2\\n0 -1\\n7 2\", \"3\\n1 6\\n0 -1\\n11 2\", \"3\\n1 6\\n0 -1\\n11 0\", \"3\\n0 6\\n0 -1\\n11 1\", \"3\\n0 8\\n-1 -1\\n1 1\", \"3\\n0 14\\n-1 -1\\n2 1\", \"3\\n0 14\\n0 -1\\n2 1\", \"3\\n1 4\\n0 -1\\n-1 2\", \"3\\n2 4\\n0 0\\n-1 2\", \"3\\n2 2\\n0 -2\\n0 2\", \"3\\n2 4\\n-1 -2\\n1 6\", \"3\\n2 2\\n-1 -2\\n2 7\", \"3\\n0 3\\n-1 -4\\n-1 7\", \"3\\n-1 0\\n0 -3\\n-3 10\", \"3\\n-2 1\\n0 -6\\n-3 6\", \"3\\n-2 0\\n0 -6\\n-5 6\", \"3\\n-1 0\\n0 -4\\n-9 6\", \"3\\n-1 0\\n1 -4\\n-9 6\", \"3\\n0 0\\n1 -2\\n-11 6\", \"3\\n0 0\\n1 -2\\n-14 6\", \"3\\n-1 1\\n1 -2\\n-14 5\", \"3\\n0 1\\n1 -1\\n-9 1\", \"3\\n0 1\\n1 -1\\n-14 1\", \"3\\n0 1\\n0 -1\\n-14 2\", \"3\\n0 1\\n0 -1\\n-14 1\", \"3\\n0 0\\n2 -1\\n-28 1\", \"3\\n2 -1\\n8 -2\\n-28 0\", \"3\\n3 2\\n4 0\\n1 1\", \"3\\n3 2\\n0 0\\n3 2\", \"3\\n3 2\\n0 0\\n10 1\", \"3\\n3 4\\n0 -1\\n5 1\", \"3\\n2 2\\n0 -1\\n7 2\", \"3\\n0 6\\n1 -1\\n11 1\", \"3\\n-1 8\\n0 -1\\n1 1\", \"3\\n0 2\\n0 -1\\n4 1\", \"3\\n-1 2\\n-1 -1\\n0 1\", \"3\\n3 4\\n0 -1\\n-1 2\", \"3\\n2 4\\n0 -2\\n2 6\", \"3\\n-1 0\\n0 -3\\n-4 10\", \"3\\n-2 0\\n1 -5\\n-5 6\", \"3\\n-2 1\\n0 -4\\n-5 6\", \"3\\n-1 0\\n0 -4\\n-15 6\", \"3\\n-1 0\\n1 -4\\n-15 6\", \"3\\n0 0\\n1 -2\\n-22 6\", \"3\\n-1 1\\n1 -2\\n-27 5\", \"3\\n-1 1\\n1 -1\\n-17 5\", \"3\\n0 1\\n1 -1\\n-16 2\", \"3\\n0 1\\n1 -1\\n-6 1\", \"3\\n1 0\\n2 -1\\n-39 1\", \"3\\n2 -2\\n8 -2\\n-26 1\", \"3\\n5 2\\n0 0\\n10 1\", \"3\\n3 4\\n1 -1\\n3 1\", \"3\\n3 4\\n1 -2\\n6 2\", \"3\\n1 2\\n0 -1\\n4 4\", \"3\\n-1 8\\n0 -1\\n2 1\", \"3\\n-1 -1\\n-1 -4\\n-5 6\", \"3\\n0 0\\n1 -2\\n-38 6\", \"3\\n-1 0\\n1 -2\\n-27 5\", \"3\\n0 1\\n1 0\\n-16 2\", \"3\\n0 1\\n1 -1\\n-5 1\", \"3\\n2 1\\n4 -2\\n-28 1\", \"3\\n2 -1\\n8 -2\\n-1 1\", \"3\\n0 -2\\n8 -2\\n-26 1\", \"3\\n0 2\\n0 0\\n10 1\", \"3\\n3 4\\n1 -1\\n2 1\", \"3\\n5 8\\n0 -1\\n5 1\", \"3\\n2 0\\n0 -1\\n3 2\", \"3\\n1 0\\n0 -1\\n8 3\", \"3\\n0 6\\n0 -1\\n22 1\", \"3\\n3 4\\n0 0\\n-1 -1\", \"3\\n-1 2\\n0 -2\\n-1 4\", \"3\\n4 1\\n-1 0\\n2 7\", \"3\\n-3 1\\n0 0\\n-5 6\", \"3\\n-1 -1\\n2 -4\\n-15 6\", \"3\\n-2 -1\\n1 -4\\n-9 2\", \"3\\n-1 0\\n1 0\\n-27 5\", \"3\\n0 1\\n1 -1\\n-17 6\", \"3\\n-1 1\\n0 -2\\n-14 4\", \"3\\n0 1\\n0 -1\\n-5 1\", \"3\\n1 1\\n1 0\\n-8 1\", \"3\\n1 0\\n1 -1\\n-50 1\", \"3\\n1 0\\n0 -1\\n-28 1\", \"3\\n3 0\\n8 -2\\n-44 1\", \"3\\n3 1\\n1 0\\n2 2\", \"3\\n5 8\\n0 -1\\n8 1\", \"3\\n1 4\\n3 -1\\n3 1\", \"3\\n2 0\\n0 -1\\n6 2\", \"3\\n1 6\\n0 -1\\n9 7\", \"3\\n-1 0\\n1 -1\\n11 2\", \"3\\n-1 0\\n1 -1\\n19 1\", \"3\\n-2 8\\n1 -1\\n2 1\", \"3\\n-3 2\\n0 -1\\n0 1\", \"3\\n6 5\\n-1 -4\\n1 7\"], \"outputs\": [\"4\\n0\\n1\", \"4\\n0\\n1\\n\", \"4\\n0\\n3\\n\", \"4\\n0\\n50\\n\", \"4\\n50\\n\", \"0\\n50\\n\", \"0\\n126\\n\", \"0\\n0\\n126\\n\", \"0\\n0\\n428\\n\", \"0\\n0\\n58785\\n\", \"0\\n0\\n0\\n\", \"0\\n0\\n5797\\n\", \"0\\n0\\n\", \"0\\n1\\n\", \"0\\n0\\n1\\n\", \"0\\n0\\n100000000000006\\n\", \"1\\n0\\n100000000000006\\n\", \"1\\n0\\n0\\n\", \"1\\n0\\n\", \"1\\n1\\n\", \"0\\n100000000000006\\n\", \"0\\n0\\n31739708996393\\n\", \"100000000000006\\n0\\n31739708996393\\n\", \"0\\n0\\n60535183122834\\n\", \"0\\n0\\n22492834549729\\n\", \"0\\n22492834549729\\n\", \"0\\n35991216060990\\n\", \"0\\n23645636961410\\n\", \"100000000000006\\n23645636961410\\n\", \"0\\n7869639175555\\n\", \"0\\n26646713544777\\n\", \"0\\n0\\n23645636961410\\n\", \"0\\n0\\n26646713544777\\n\", \"0\\n38969432871695\\n\", \"0\\n\", \"4\\n0\\n0\\n\", \"4\\n0\\n4\\n\", \"4\\n0\\n2187\\n\", \"4\\n0\\n20\\n\", \"1\\n0\\n428\\n\", \"0\\n5797\\n\", \"100000000000006\\n0\\n0\\n\", \"0\\n0\\n8\\n\", \"100000000000006\\n0\\n\", \"4\\n0\\n100000000000006\\n\", \"1\\n0\\n1\\n\", \"0\\n0\\n42224403014399\\n\", \"0\\n60535183122834\\n\", \"100000000000006\\n0\\n60535183122834\\n\", \"0\\n0\\n67214163844076\\n\", \"0\\n67214163844076\\n\", \"0\\n12830370078943\\n\", \"100000000000006\\n4613242031906\\n\", \"100000000000006\\n29327661606567\\n\", \"0\\n45413963478059\\n\", \"0\\n54905114360842\\n\", \"0\\n96525555042631\\n\", \"65452610710273\\n\", \"41\\n0\\n2187\\n\", \"4\\n3\\n\", \"4\\n131\\n\", \"0\\n0\\n13\\n\", \"100000000000006\\n0\\n1\\n\", \"60535183122834\\n\", \"0\\n23759055115768\\n\", \"0\\n4613242031906\\n\", \"0\\n0\\n45413963478059\\n\", \"0\\n54694256176155\\n\", \"1\\n38969432871695\\n\", \"100000000000006\\n\", \"0\\n65452610710273\\n\", \"0\\n0\\n2187\\n\", \"4\\n1\\n\", \"41\\n0\\n20\\n\", \"0\\n0\\n4\\n\", \"0\\n0\\n1429\\n\", \"0\\n0\\n400763222\\n\", \"4\\n0\\n\", \"100000000000006\\n0\\n100000000000006\\n\", \"8\\n0\\n1\\n\", \"60746630828984\\n0\\n60535183122834\\n\", \"67214163844076\\n\", \"22492834549729\\n\", \"0\\n0\\n4613242031906\\n\", \"0\\n29327661606567\\n\", \"100000000000006\\n0\\n23645636961410\\n\", \"0\\n0\\n54694256176155\\n\", \"0\\n0\\n93394946172402\\n\", \"0\\n8880686130582\\n\", \"0\\n0\\n38969432871695\\n\", \"0\\n99247046282461\\n\", \"3\\n0\\n1\\n\", \"41\\n0\\n322\\n\", \"0\\n3\\n\", \"0\\n0\\n131\\n\", \"0\\n0\\n4861\\n\", \"0\\n58785\\n\", \"0\\n18199283\\n\", \"100000000000006\\n1\\n\", \"31739708996393\\n0\\n0\\n\", \"131\\n0\\n\"]}", "source": "primeintellect"}
|
Tug of war is a sport that directly puts two teams against each other in a test of strength.
During school days, both Chef Shifu and Chef Po were champions of tug of war.
On behalf of restaurant's anniversary, Chef Shifu and Chef Po have decided to conduct
a tug of war game for their customers.
Master Chef Oogway has decided the following rules for the game.
Let N be the number of players participating in the game. All of these
players would stand in a circle in clock wise direction.
There are an infinite number of long ropes available.
When a rope is held by exactly two players, it is termed as bonding.
At least one bonding is necessary to conduct a game.
A player can play against multiple people simultaneously i.e he can have more than one bonding at
the same time.
Both members of a pair of players that have a bonding must have the same number of total
bondings. That is, if the player A makes bonding with the player B,
then the number of total bondings of the player A must be the same as
that of the player B.
Bondings should be created in such a fashion that ropes must not intersect each other.
The number of bondings of every player must be no more than K.
Now Master Chef Oogway asked Chef Shifu and Chef Po to find out the number of possible games.
Your task is to help them find this number. As this number might become huge,
you've to find it modulo (10^14+7). Two games are different iff there is some
bonding that is present in only of them.
Input
First line contains T, the number of test cases.
Each of T lines contain 2 positive integers N and K separated by a space.
Output
For each test case, output the number of ways to conduct the game modulo 100000000000007 (10^14+7) in one line.
Example
Input:
3
3 2
4 0
2 1
Output:
4
0
1
Explanation:
For the 1st case, there are 3 players. Let's call them p1, p2, p3.
Different games possible are:
Game 1: p1-p2 (numbers of bondings of p1, p2 are 1 ≤ K = 2)
Game 2: p1-p3 (numbers of bondings of p1, p3 are 1 ≤ K = 2)
Game 3: p2-p3 (numbers of bondings of p2, p3 are 1 ≤ K = 2)
Game 4: p1-p2, p1-p3, p2-p3 (numbers of bondings of p1, p2, p3 are 2 ≤ K
= 2)
For the 2nd test case, we cannot form the game, because K = 0 and hence no
player is allowed to make any bonding. As any game must have atleast one
bonding, no game is possible here.
For the 3rd case, only possible game is:
Game 1: p1-p2 (number of bondings in p1, p2 are 1)
Constraints
1 ≤ T ≤ 10000
0 ≤ N ≤ 10000
0 ≤ K ≤ N
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 5\\n.*...\\n****.\\n.****\\n..**.\\n.....\\n\", \"6 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n....*...\\n........\\n\", \"3 3\\n*.*\\n.*.\\n*.*\\n\", \"5 5\\n.*...\\n***..\\n.*...\\n.*...\\n.....\\n\", \"3 3\\n.*.\\n***\\n**.\\n\", \"3 3\\n**.\\n***\\n.*.\\n\", \"3 3\\n.*.\\n***\\n.*.\\n\", \"3 3\\n...\\n...\\n...\\n\", \"100 3\\n.*.\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n**.\\n\", \"100 3\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n*..\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n.*.\\n***\\n.*.\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n...\\n\", \"100 3\\n.*.\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n***\\n.*.\\n\", \"6 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n....*...\\n........\\n\", \"3 3\\n*.*\\n***\\n.*.\\n\", \"6 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n...*....\\n........\\n\", \"3 3\\n*.*\\n*..\\n*.*\\n\", \"5 5\\n.*...\\n***..\\n...*.\\n.*...\\n.....\\n\", \"3 3\\n*.*\\n..*\\n*.*\\n\", \"5 5\\n.*...\\n***..\\n...*.\\n...*.\\n.....\\n\", \"2 3\\n*.*\\n.*.\\n*.*\\n\", \"3 3\\n.**\\n***\\n.*.\\n\", \"2 3\\n*.*\\n..*\\n*.*\\n\", \"5 5\\n.*...\\n*.*.*\\n...*.\\n...*.\\n.....\\n\", \"2 3\\n*.*\\n*..\\n*.*\\n\", \"3 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n....*...\\n........\\n\", \"6 8\\n....*...\\n...**...\\n.*****..\\n...**...\\n...*....\\n........\\n\", \"2 3\\n*.*\\n..*\\n*.)\\n\", \"2 3\\n*.*\\n..*\\n+.*\\n\", \"5 5\\n.*...\\n.**.*\\n...*.\\n...*.\\n.....\\n\", \"3 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n...*....\\n........\\n\", \"2 3\\n*.*\\n*..\\n*.)\\n\", \"5 5\\n.*...\\n.**.*\\n...*.\\n.*...\\n.....\\n\", \"5 5\\n...*.\\n.**.*\\n...*.\\n.*...\\n.....\\n\", \"3 3\\n.*.\\n***\\n*..\\n\", \"5 5\\n.*...\\n.****\\n.****\\n..**.\\n.....\\n\", \"6 8\\n....*...\\n...**...\\n..*****.\\n...*..*.\\n....*...\\n........\\n\", \"5 5\\n...*.\\n***..\\n...*.\\n.*...\\n.....\\n\", \"2 3\\n*.*\\n..*\\n*.+\\n\", \"3 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n../.*...\\n........\\n\", \"3 8\\n....*...\\n...**...\\n.*****..\\n...**...\\n...*....\\n........\\n\", \"2 3\\n*.*\\n..*\\n).)\\n\", \"3 8\\n....*...\\n...**...\\n..*****.\\n...**...\\n....*...\\n......./\\n\", \"2 3\\n*.*\\n.*.\\n*.)\\n\", \"1 3\\n.*.\\n***\\n*..\\n\", \"1 5\\n.*...\\n.****\\n.****\\n..**.\\n.....\\n\", \"3 8\\n....*...\\n...*...*\\n..*****.\\n...**...\\n../.*...\\n........\\n\", \"2 3\\n**.\\n.*.\\n*.)\\n\", \"1 3\\n.*.\\n***\\n*./\\n\", \"1 5\\n.*...\\n****.\\n.****\\n..**.\\n.....\\n\", \"3 8\\n....*...\\n...*...*\\n..*****.\\n...**...\\n...*./..\\n........\\n\", \"1 3\\n..*\\n***\\n*./\\n\", \"1 5\\n.*...\\n****.\\n.****\\n..**.\\n....-\\n\", \"3 8\\n....*...\\n...*...*\\n..*****.\\n../**...\\n...*./..\\n........\\n\", \"1 3\\n..*\\n***\\n*//\\n\", \"3 8\\n.......*\\n...*...*\\n..*****.\\n../**...\\n...*./..\\n........\\n\"], \"outputs\": [\"3\\n2 2 1\\n3 3 1\\n3 4 1\\n\", \"2\\n3 4 1\\n3 5 2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"1\\n2 2 1\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"98\\n2 2 1\\n3 2 1\\n4 2 1\\n5 2 1\\n6 2 1\\n7 2 1\\n8 2 1\\n9 2 1\\n10 2 1\\n11 2 1\\n12 2 1\\n13 2 1\\n14 2 1\\n15 2 1\\n16 2 1\\n17 2 1\\n18 2 1\\n19 2 1\\n20 2 1\\n21 2 1\\n22 2 1\\n23 2 1\\n24 2 1\\n25 2 1\\n26 2 1\\n27 2 1\\n28 2 1\\n29 2 1\\n30 2 1\\n31 2 1\\n32 2 1\\n33 2 1\\n34 2 1\\n35 2 1\\n36 2 1\\n37 2 1\\n38 2 1\\n39 2 1\\n40 2 1\\n41 2 1\\n42 2 1\\n43 2 1\\n44 2 1\\n45 2 1\\n46 2 1\\n47 2 1\\n48 2 1\\n49 2 1\\n50 2 1\\n51 2 1\\n52 2 1\\n53 2 1\\n54 2 1\\n55 2 1\\n56 2 1\\n57 2 1\\n58 2 1\\n59 2 1\\n60 2 1\\n61 2 1\\n62 2 1\\n63 2 1\\n64 2 1\\n65 2 1\\n66 2 1\\n67 2 1\\n68 2 1\\n69 2 1\\n70 2 1\\n71 2 1\\n72 2 1\\n73 2 1\\n74 2 1\\n75 2 1\\n76 2 1\\n77 2 1\\n78 2 1\\n79 2 1\\n80 2 1\\n81 2 1\\n82 2 1\\n83 2 1\\n84 2 1\\n85 2 1\\n86 2 1\\n87 2 1\\n88 2 1\\n89 2 1\\n90 2 1\\n91 2 1\\n92 2 1\\n93 2 1\\n94 2 1\\n95 2 1\\n96 2 1\\n97 2 1\\n98 2 1\\n99 2 1\\n\", \"2\\n3 4 1\\n3 5 2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\"]}", "source": "primeintellect"}
|
A star is a figure of the following type: an asterisk character '*' in the center of the figure and four rays (to the left, right, top, bottom) of the same positive length. The size of a star is the length of its rays. The size of a star must be a positive number (i.e. rays of length 0 are not allowed).
Let's consider empty cells are denoted by '.', then the following figures are stars:
<image> The leftmost figure is a star of size 1, the middle figure is a star of size 2 and the rightmost figure is a star of size 3.
You are given a rectangular grid of size n × m consisting only of asterisks '*' and periods (dots) '.'. Rows are numbered from 1 to n, columns are numbered from 1 to m. Your task is to draw this grid using any number of stars or find out that it is impossible. Stars can intersect, overlap or even coincide with each other. The number of stars in the output can't exceed n ⋅ m. Each star should be completely inside the grid. You can use stars of same and arbitrary sizes.
In this problem, you do not need to minimize the number of stars. Just find any way to draw the given grid with at most n ⋅ m stars.
Input
The first line of the input contains two integers n and m (3 ≤ n, m ≤ 1000) — the sizes of the given grid.
The next n lines contains m characters each, the i-th line describes the i-th row of the grid. It is guaranteed that grid consists of characters '*' and '.' only.
Output
If it is impossible to draw the given grid using stars only, print "-1".
Otherwise in the first line print one integer k (0 ≤ k ≤ n ⋅ m) — the number of stars needed to draw the given grid. The next k lines should contain three integers each — x_j, y_j and s_j, where x_j is the row index of the central star character, y_j is the column index of the central star character and s_j is the size of the star. Each star should be completely inside the grid.
Examples
Input
6 8
....*...
...**...
..*****.
...**...
....*...
........
Output
3
3 4 1
3 5 2
3 5 1
Input
5 5
.*...
****.
.****
..**.
.....
Output
3
2 2 1
3 3 1
3 4 1
Input
5 5
.*...
***..
.*...
.*...
.....
Output
-1
Input
3 3
*.*
.*.
*.*
Output
-1
Note
In the first example the output
2
3 4 1
3 5 2
is also correct.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
{"tests": "{\"inputs\": [\"2 1 2 1\\n\", \"2 2 1 2\\n\", \"1 1 1 1\\n\", \"24 25 16 38\\n\", \"1000000 1000000 1000000 1000000\\n\", \"100000000 100000000 99999999 100000000\\n\", \"1000000 1000000 999999 1000000\\n\", \"23 1 12 2\\n\", \"1000000 1 1000000 1\\n\", \"100000000 1 100000000 1\\n\", \"18 3 8 15\\n\", \"50 50 50 50\\n\", \"672810 797124 51792 404095\\n\", \"19661988 30021918 8795449 27534575\\n\", \"1 50 1 50\\n\", \"47 40 42 49\\n\", \"960051 866743 887923 926936\\n\", \"100000000 100000000 100000000 100000000\\n\", \"1000 1000 700 20000\\n\", \"6 4 2 7\\n\", \"49 45 49 46\\n\", \"98948781 84140283 95485812 84557929\\n\", \"2 1 1 1\\n\", \"1000000 1000010 1000000 1000000\\n\", \"100000000 100001000 99999999 100000000\\n\", \"1000000 1000000 962711 1000000\\n\", \"34 1 12 2\\n\", \"100000001 1 100000000 1\\n\", \"29 3 8 15\\n\", \"50 50 50 48\\n\", \"672810 797124 89236 404095\\n\", \"31865344 30021918 8795449 27534575\\n\", \"1 64 1 50\\n\", \"47 40 42 66\\n\", \"960051 1669438 887923 926936\\n\", \"1000 1000 700 632\\n\", \"6 4 2 2\\n\", \"49 69 49 46\\n\", \"98948781 84140283 74937405 84557929\\n\", \"3 1 1 1\\n\", \"1000000 1000010 1000000 1000100\\n\", \"100000000 100001000 99999999 100100000\\n\", \"1000100 1000000 962711 1000000\\n\", \"100100001 1 100000000 1\\n\", \"29 3 8 30\\n\", \"672810 797124 89236 738045\\n\", \"31865344 30021918 8795449 4120545\\n\", \"1 64 1 43\\n\", \"47 40 42 132\\n\", \"1000 0000 700 632\\n\", \"3 4 2 2\\n\", \"98948781 84140283 74937405 107051347\\n\", \"1100000 1000010 1000000 1000100\\n\", \"100000000 100101000 99999999 100100000\\n\", \"1000100 1000000 962711 1010000\\n\", \"29 3 8 59\\n\", \"672810 586626 89236 738045\\n\", \"31865344 30021918 8795449 4250910\\n\", \"47 40 42 213\\n\", \"1000 0000 700 897\\n\", \"3 4 2 0\\n\", \"98948781 84140283 74937405 86258391\\n\", \"2 1 -1 0\\n\", \"100000000 000101000 99999999 100100000\\n\", \"1000100 1000001 962711 1010000\\n\", \"34 1 2 1\\n\", \"100100001 2 100100000 1\\n\", \"672810 202965 89236 738045\\n\", \"31865344 39210913 8795449 4250910\\n\", \"1 64 0 75\\n\", \"47 40 42 298\\n\", \"1000 0000 700 1533\\n\", \"6 4 2 0\\n\", \"98948781 84140283 74937405 104036139\\n\", \"100000000 000101000 99999999 100100010\\n\", \"34 1 2 0\\n\", \"33 3 10 59\\n\", \"672810 284821 89236 738045\\n\", \"31865344 39210913 8795449 7755017\\n\", \"2 64 0 75\\n\", \"47 40 42 287\\n\", \"1100 0000 700 1533\\n\", \"6 0 2 0\\n\", \"98948781 84140283 74937405 26252466\\n\", \"2 1 0 1\\n\", \"34 1 2 2\\n\", \"2 1 -1 1\\n\", \"3 0 1 1\\n\", \"34 1 1 2\\n\", \"100100001 1 100100000 1\\n\", \"1 64 0 43\\n\", \"6 0 1 1\\n\", \"1100000 1000010 1001000 1000100\\n\", \"29 3 10 59\\n\", \"3 1 -1 0\\n\", \"8 0 1 1\\n\", \"1100000 1000010 1011000 1000100\\n\", \"3 1 0 0\\n\", \"8 0 2 1\\n\"], \"outputs\": [\"12\\n\", \"16\\n\", \"10\\n\", \"178\\n\", \"6000004\\n\", \"600000004\\n\", \"6000004\\n\", \"56\\n\", \"2000008\\n\", \"200000008\\n\", \"76\\n\", \"304\\n\", \"3748062\\n\", \"154436966\\n\", \"206\\n\", \"276\\n\", \"5507464\\n\", \"600000004\\n\", \"44004\\n\", \"38\\n\", \"284\\n\", \"535293990\\n\", \"12\\n\", \"6000024\\n\", \"600002004\\n\", \"6000004\\n\", \"78\\n\", \"200000010\\n\", \"98\\n\", \"300\\n\", \"3748062\\n\", \"178843678\\n\", \"234\\n\", \"310\\n\", \"7112854\\n\", \"5268\\n\", \"28\\n\", \"332\\n\", \"535293990\\n\", \"14\\n\", \"6000224\\n\", \"600202004\\n\", \"6000204\\n\", \"200200010\\n\", \"128\\n\", \"4415962\\n\", \"132015618\\n\", \"220\\n\", \"442\\n\", \"3268\\n\", \"22\\n\", \"580280826\\n\", \"6200224\\n\", \"600402004\\n\", \"6020204\\n\", \"186\\n\", \"3994966\\n\", \"132276348\\n\", \"604\\n\", \"3798\\n\", \"18\\n\", \"538694914\\n\", \"10\\n\", \"400402004\\n\", \"6020206\\n\", \"76\\n\", \"200200012\\n\", \"3227644\\n\", \"150654338\\n\", \"284\\n\", \"774\\n\", \"5070\\n\", \"24\\n\", \"574250410\\n\", \"400402024\\n\", \"74\\n\", \"194\\n\", \"3391356\\n\", \"157662552\\n\", \"286\\n\", \"752\\n\", \"5270\\n\", \"16\\n\", \"418683064\\n\", \"12\\n\", \"78\\n\", \"12\\n\", \"12\\n\", \"78\\n\", \"200200010\\n\", \"220\\n\", \"18\\n\", \"6200224\\n\", \"186\\n\", \"12\\n\", \"22\\n\", \"6200224\\n\", \"12\\n\", \"22\\n\"]}", "source": "primeintellect"}
|
In order to make the "Sea Battle" game more interesting, Boris decided to add a new ship type to it. The ship consists of two rectangles. The first rectangle has a width of w_1 and a height of h_1, while the second rectangle has a width of w_2 and a height of h_2, where w_1 ≥ w_2. In this game, exactly one ship is used, made up of two rectangles. There are no other ships on the field.
The rectangles are placed on field in the following way:
* the second rectangle is on top the first rectangle;
* they are aligned to the left, i.e. their left sides are on the same line;
* the rectangles are adjacent to each other without a gap.
See the pictures in the notes: the first rectangle is colored red, the second rectangle is colored blue.
Formally, let's introduce a coordinate system. Then, the leftmost bottom cell of the first rectangle has coordinates (1, 1), the rightmost top cell of the first rectangle has coordinates (w_1, h_1), the leftmost bottom cell of the second rectangle has coordinates (1, h_1 + 1) and the rightmost top cell of the second rectangle has coordinates (w_2, h_1 + h_2).
After the ship is completely destroyed, all cells neighboring by side or a corner with the ship are marked. Of course, only cells, which don't belong to the ship are marked. On the pictures in the notes such cells are colored green.
Find out how many cells should be marked after the ship is destroyed. The field of the game is infinite in any direction.
Input
Four lines contain integers w_1, h_1, w_2 and h_2 (1 ≤ w_1, h_1, w_2, h_2 ≤ 10^8, w_1 ≥ w_2) — the width of the first rectangle, the height of the first rectangle, the width of the second rectangle and the height of the second rectangle. You can't rotate the rectangles.
Output
Print exactly one integer — the number of cells, which should be marked after the ship is destroyed.
Examples
Input
2 1 2 1
Output
12
Input
2 2 1 2
Output
16
Note
In the first example the field looks as follows (the first rectangle is red, the second rectangle is blue, green shows the marked squares):
<image>
In the second example the field looks as:
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 14\\n\", \"1 3\\n\", \"88005553535 99999999999\\n\", \"101 102\\n\", \"707992299833239702 823650821768525121\\n\", \"181925 50919323688216219\\n\", \"31 32\\n\", \"4 938109031727472839\\n\", \"10 10005\\n\", \"83 402908796418729484\\n\", \"527941 442152825894997769\\n\", \"100879890062904086 919413561635743169\\n\", \"695663532 895293500915617175\\n\", \"1 15\\n\", \"23 24\\n\", \"41 49\\n\", \"326567 37935433686691901\\n\", \"368832015800862643 959710835602923836\\n\", \"1 1000000000000000000\\n\", \"388880291 600967254143436109\\n\", \"530374 187390675797908550\\n\", \"40 40\\n\", \"646642585834105117 769289603843435752\\n\", \"266032540 775808641238027030\\n\", \"344719938937955218 881301645881541177\\n\", \"26485417666693938 897520336114069539\\n\", \"5395748081576952 729478239858216626\\n\", \"32 32\\n\", \"721835 480390263313130557\\n\", \"89 401221084162832590\\n\", \"618006176 999508457373565393\\n\", \"110132820763723554 347999721032847655\\n\", \"89 573300466228828028\\n\", \"1 1\\n\", \"100 101\\n\", \"7 515369014347518317\\n\", \"576700324 851922153058604707\\n\", \"635978584340918932 834420611888682362\\n\", \"33 37\\n\", \"25 31\\n\", \"96271473323594764 177985918874532496\\n\", \"77 35400606000902437\\n\", \"15 19\\n\", \"153492417505670053 969968962188753713\\n\", \"1000000000000000000 1000000000000000000\\n\", \"1001 10000\\n\", \"148123 50919323688216219\\n\", \"24 32\\n\", \"3 938109031727472839\\n\", \"10 16207\\n\", \"44 402908796418729484\\n\", \"1025824 442152825894997769\\n\", \"183398036177115834 919413561635743169\\n\", \"900040402 895293500915617175\\n\", \"1 28\\n\", \"23 22\\n\", \"12 49\\n\", \"326567 10329551310440485\\n\", \"368832015800862643 982051966877342250\\n\", \"1 1000000001000000000\\n\", \"388880291 568195393812573480\\n\", \"794273 187390675797908550\\n\", \"113676491284177131 769289603843435752\\n\", \"395254310 775808641238027030\\n\", \"245941685969845594 881301645881541177\\n\", \"42142231503528288 897520336114069539\\n\", \"5395748081576952 777853455745509154\\n\", \"32 45\\n\", \"396811 480390263313130557\\n\", \"89 339734296068762197\\n\", \"618006176 80076710989508420\\n\", \"183047604200249078 347999721032847655\\n\", \"89 780094064352311191\\n\", \"100 111\\n\", \"1 515369014347518317\\n\", \"210551342 851922153058604707\\n\", \"25 56\\n\", \"96271473323594764 312557383081357355\\n\", \"77 1858741141352751\\n\", \"12 19\\n\", \"153492417505670053 606711098097846107\\n\", \"1000000000000000000 1000000000010000000\\n\", \"0001 10000\\n\", \"5 26\\n\", \"148123 48118609298346200\\n\", \"10 31840\\n\", \"84 402908796418729484\\n\", \"1856064 442152825894997769\\n\", \"139298995909844908 919413561635743169\\n\", \"828228377 895293500915617175\\n\", \"1 36\\n\", \"23 38\\n\", \"12 27\\n\", \"326567 8693869880514308\\n\", \"416536557455107605 982051966877342250\\n\", \"1 1000000011000000000\\n\", \"167510548 568195393812573480\\n\", \"812785 187390675797908550\\n\", \"754738754 775808641238027030\\n\", \"354034076087041320 881301645881541177\\n\", \"42142231503528288 299170350717614296\\n\", \"1892016064771857 777853455745509154\\n\", \"32 38\\n\", \"622437 480390263313130557\\n\", \"8 339734296068762197\\n\", \"661882332 80076710989508420\\n\", \"280686787435210148 347999721032847655\\n\", \"127 780094064352311191\\n\", \"1 201785000506186665\\n\", \"319470402 851922153058604707\\n\", \"41 56\\n\", \"115829172805618423 312557383081357355\\n\", \"21 1858741141352751\\n\", \"0001 10001\\n\", \"7 26\\n\", \"5860 48118609298346200\\n\", \"13 402908796418729484\\n\", \"567427 442152825894997769\\n\", \"314207215 895293500915617175\\n\", \"1 37\\n\", \"22 27\\n\", \"58228 8693869880514308\\n\", \"1 1000000011000001000\\n\", \"167510548 915246793361672690\\n\", \"1088657 187390675797908550\\n\", \"754738754 1131163303774424516\\n\", \"354034076087041320 850834562585709769\\n\", \"42142231503528288 247943927429255082\\n\", \"3571802507850232 777853455745509154\\n\", \"32 57\\n\", \"259129 480390263313130557\\n\", \"6 339734296068762197\\n\", \"672207327 80076710989508420\\n\", \"280686787435210148 326969496972669644\\n\", \"20 19\\n\"], \"outputs\": [\"105\\n\", \"7\\n\", \"761141116\\n\", \"236\\n\", \"69962460\\n\", \"792029406\\n\", \"63\\n\", \"220366485\\n\", \"50474956\\n\", \"94558013\\n\", \"805109416\\n\", \"824441806\\n\", \"523981139\\n\", \"135\\n\", \"52\\n\", \"432\\n\", \"886000420\\n\", \"380949759\\n\", \"724824772\\n\", \"344155484\\n\", \"537179299\\n\", \"38\\n\", \"930095792\\n\", \"34396457\\n\", \"901594724\\n\", \"684062123\\n\", \"604591615\\n\", \"22\\n\", \"319808831\\n\", \"240772492\\n\", \"358521726\\n\", \"416849587\\n\", \"136047880\\n\", \"1\\n\", \"232\\n\", \"207784181\\n\", \"615581490\\n\", \"481130628\\n\", \"140\\n\", \"245\\n\", \"357444025\\n\", \"144605114\\n\", \"76\\n\", \"867480243\\n\", \"975735772\\n\", \"49878360\\n\", \"40972934\\n\", \"294\\n\", \"220366489\\n\", \"145309738\\n\", \"94560472\\n\", \"257541929\\n\", \"688660460\\n\", \"491424953\\n\", \"434\\n\", \"0\\n\", \"1186\\n\", \"479381625\\n\", \"858652671\\n\", \"894674459\\n\", \"306119811\\n\", \"443021650\\n\", \"34720459\\n\", \"601088682\\n\", \"775613983\\n\", \"900255208\\n\", \"996626737\\n\", \"490\\n\", \"254651269\\n\", \"692753429\\n\", \"408175347\\n\", \"79354776\\n\", \"294197040\\n\", \"1512\\n\", \"207784203\\n\", \"13070622\\n\", \"1395\\n\", \"205150923\\n\", \"345788919\\n\", \"124\\n\", \"149507\\n\", \"636734266\\n\", \"50429581\\n\", \"356\\n\", \"757122198\\n\", \"556863685\\n\", \"94557932\\n\", \"454253673\\n\", \"898637686\\n\", \"917061343\\n\", \"681\\n\", \"493\\n\", \"332\\n\", \"187944458\\n\", \"967837783\\n\", \"593176705\\n\", \"386594985\\n\", \"633996185\\n\", \"219631117\\n\", \"96106938\\n\", \"686500655\\n\", \"311287773\\n\", \"196\\n\", \"453485341\\n\", \"692757320\\n\", \"605459531\\n\", \"947026545\\n\", \"294192100\\n\", \"336093976\\n\", \"493837910\\n\", \"880\\n\", \"398131335\\n\", \"345791671\\n\", \"50438661\\n\", \"344\\n\", \"64844826\\n\", \"94561338\\n\", \"156136459\\n\", \"433440268\\n\", \"713\\n\", \"168\\n\", \"973439592\\n\", \"329788873\\n\", \"736219850\\n\", \"946651492\\n\", \"862043150\\n\", \"773655646\\n\", \"761258495\\n\", \"628363364\\n\", \"1222\\n\", \"969253768\\n\", \"692757336\\n\", \"904253261\\n\", \"612646031\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Nazar, a student of the scientific lyceum of the Kingdom of Kremland, is known for his outstanding mathematical abilities. Today a math teacher gave him a very difficult task.
Consider two infinite sets of numbers. The first set consists of odd positive numbers (1, 3, 5, 7, …), and the second set consists of even positive numbers (2, 4, 6, 8, …). At the first stage, the teacher writes the first number on the endless blackboard from the first set, in the second stage — the first two numbers from the second set, on the third stage — the next four numbers from the first set, on the fourth — the next eight numbers from the second set and so on. In other words, at each stage, starting from the second, he writes out two times more numbers than at the previous one, and also changes the set from which these numbers are written out to another.
The ten first written numbers: 1, 2, 4, 3, 5, 7, 9, 6, 8, 10. Let's number the numbers written, starting with one.
The task is to find the sum of numbers with numbers from l to r for given integers l and r. The answer may be big, so you need to find the remainder of the division by 1000000007 (10^9+7).
Nazar thought about this problem for a long time, but didn't come up with a solution. Help him solve this problem.
Input
The first line contains two integers l and r (1 ≤ l ≤ r ≤ 10^{18}) — the range in which you need to find the sum.
Output
Print a single integer — the answer modulo 1000000007 (10^9+7).
Examples
Input
1 3
Output
7
Input
5 14
Output
105
Input
88005553535 99999999999
Output
761141116
Note
In the first example, the answer is the sum of the first three numbers written out (1 + 2 + 4 = 7).
In the second example, the numbers with numbers from 5 to 14: 5, 7, 9, 6, 8, 10, 12, 14, 16, 18. Their sum is 105.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\na\\nzzaaz\\nccff\\ncbddbb\\n\", \"1\\naababbaaamr\\n\", \"1\\naabambaaamr\\n\", \"1\\ndeep\\n\", \"1\\namrb\\n\", \"1\\namraa\\n\", \"1\\nsrijande\\n\", \"1\\nqw\\n\", \"1\\namra\\n\", \"1\\namrdd\\n\", \"1\\nartijakls\\n\", \"1\\namr\\n\", \"1\\nammr\\n\", \"1\\nlksjnksjfksjfksjfksjnfksjfsksjdf\\n\", \"1\\nacvvrfgefgtwbqzlkgitengq\\n\", \"1\\naabambaarmr\\n\", \"1\\naacd\\n\", \"2\\nduyduyduy\\ndduuyyyu\\n\", \"1\\nammsdsdadasdsadssadassadsadasdsadsadr\\n\", \"1\\nammsdsdadasdsadsadassadsadasdsadsadr\\n\", \"1\\ndpee\\n\", \"1\\nbmrb\\n\", \"1\\namrab\\n\", \"1\\nsqijande\\n\", \"1\\npw\\n\", \"1\\ndmrad\\n\", \"1\\nartijakms\\n\", \"1\\nrmma\\n\", \"1\\nfdjsksfjskfnjskfjskfjskfjsknjskl\\n\", \"1\\nacvvrfgeegtwbqzlkgitengq\\n\", \"1\\naace\\n\", \"2\\ndyyduuduy\\ndduuyyyu\\n\", \"1\\nammsdsdadasdsadssadassadsadasdsadsads\\n\", \"1\\ndqee\\n\", \"1\\nbbrm\\n\", \"1\\npx\\n\", \"1\\neaca\\n\", \"2\\ndyydvuduy\\ndduuyyyu\\n\", \"1\\nammsdsdaeasdsadssadassadsadasdsadsads\\n\", \"1\\ndree\\n\", \"1\\nbbsm\\n\", \"1\\nbasma\\n\", \"1\\nearmd\\n\", \"1\\nsmkaiitra\\n\", \"1\\nlksjmksjfksjfksjjksfnfksjfsksjdf\\n\", \"1\\nacvvrfgdegbwtqzlkgitengq\\n\", \"1\\neacb\\n\", \"2\\ndzydvuduy\\ndduuyyyu\\n\", \"1\\ndref\\n\", \"1\\nbcrm\\n\", \"1\\naaram\\n\", \"1\\ndenajips\\n\", \"1\\nqx\\n\", \"1\\nearld\\n\", \"1\\nsmkbiitra\\n\", \"1\\nllsjmksjfksjfksjjksfnfksjfsksjdf\\n\", \"1\\nacvvrfgdegbvtqzlkgitengq\\n\", \"1\\naaqam\\n\", \"1\\ndenajios\\n\", \"1\\nearle\\n\", \"1\\neere\\n\", \"1\\naaqbm\\n\", \"1\\nwq\\n\", \"1\\nsmibtkira\\n\", \"2\\ndzydvuduy\\nuyyyvddu\\n\", \"1\\nedre\\n\", \"1\\nbcrl\\n\", \"1\\naaqbl\\n\", \"1\\nelsae\\n\", \"1\\nmlsjmksjfksjfkrjjksfnfksjfsksjdf\\n\", \"1\\nqgmdtigklzqtvbgedgfrvvca\\n\", \"1\\nvp\\n\", \"1\\nbqcl\\n\", \"1\\nkbqaa\\n\", \"1\\nvo\\n\", \"1\\nbarma\\n\", \"1\\nednajiqs\\n\", \"1\\ndarmd\\n\", \"1\\nsmkajitra\\n\", \"1\\nlksjnksjfksjfksjjksfnfksjfsksjdf\\n\", \"1\\nacvvrfgeegbwtqzlkgitengq\\n\", \"1\\ndenajiqs\\n\", \"1\\nxp\\n\", \"1\\nsmmsdsdaeasdsadssadaasadsadasdsadsads\\n\", \"1\\nbcae\\n\", \"2\\ndzydvuduy\\nudduyyyu\\n\", \"1\\nsdasdasdsadasdasaadassdasdsaeadsdsmms\\n\", \"1\\neerd\\n\", \"1\\nccrm\\n\", \"1\\nxq\\n\", \"1\\nsmkbtiira\\n\", \"1\\nfdjsksfjskfnfskjjskfjskfjskmjsll\\n\", \"1\\nacvvrfgdegbvtqzlkgitdngq\\n\", \"2\\ndzydvuduy\\nuyyyuddu\\n\", \"1\\nmrcc\\n\", \"1\\nienajdos\\n\", \"1\\nelrae\\n\", \"1\\nmlsjmksjfksjfksjjksfnfksjfsksjdf\\n\", \"1\\nqgndtigklzqtvbgedgfrvvca\\n\", \"1\\nwp\\n\", \"1\\nsmibtairk\\n\", \"2\\nyuduvdyzd\\nuyyyvddu\\n\", \"1\\nddre\\n\", \"1\\nbrcl\\n\", \"1\\nlbqaa\\n\", \"1\\neleas\\n\", \"1\\nskibtairm\\n\", \"1\\nfdjsksfjskfnfskjjrkfjskfjskmjslm\\n\", \"1\\nacvvrfgdegbvtqzlkgitdmgq\\n\", \"2\\nzuduvdyzd\\nuyyyvddu\\n\", \"1\\nerdd\\n\", \"1\\nsaele\\n\"], \"outputs\": [\"a\\nz\\n\\nbc\\n\", \"abmr\\n\", \"abmr\\n\", \"dp\\n\", \"abmr\\n\", \"amr\\n\", \"adeijnrs\\n\", \"qw\\n\", \"amr\\n\", \"amr\\n\", \"aijklrst\\n\", \"amr\\n\", \"ar\\n\", \"dfjklns\\n\", \"abcefgiklnqrtwz\\n\", \"abmr\\n\", \"cd\\n\", \"duy\\nuy\\n\", \"adrs\\n\", \"adrs\\n\", \"dp\\n\", \"bmr\\n\", \"abmr\\n\", \"adeijnqs\\n\", \"pw\\n\", \"admr\\n\", \"aijkmrst\\n\", \"ar\\n\", \"dfjklns\\n\", \"abcefgiklnqrtwz\\n\", \"ce\\n\", \"duy\\nuy\\n\", \"ads\\n\", \"dq\\n\", \"mr\\n\", \"px\\n\", \"ace\\n\", \"duvy\\nuy\\n\", \"ades\\n\", \"dr\\n\", \"ms\\n\", \"abms\\n\", \"ademr\\n\", \"akmrst\\n\", \"dfjklmns\\n\", \"abcdefgiklnqrtwz\\n\", \"abce\\n\", \"duvyz\\nuy\\n\", \"defr\\n\", \"bcmr\\n\", \"amr\\n\", \"adeijnps\\n\", \"qx\\n\", \"adelr\\n\", \"abkmrst\\n\", \"dfjkmns\\n\", \"abcdefgiklnqrtvz\\n\", \"amq\\n\", \"adeijnos\\n\", \"aelr\\n\", \"er\\n\", \"bmq\\n\", \"qw\\n\", \"abikmrst\\n\", \"duvyz\\nuvy\\n\", \"der\\n\", \"bclr\\n\", \"blq\\n\", \"aels\\n\", \"dfjklmnrs\\n\", \"abcdefgiklmqrtvz\\n\", \"pv\\n\", \"bclq\\n\", \"bkq\\n\", \"ov\\n\", \"abmr\\n\", \"adeijnqs\\n\", \"admr\\n\", \"aijkmrst\\n\", \"dfjklns\\n\", \"abcefgiklnqrtwz\\n\", \"adeijnqs\\n\", \"px\\n\", \"ades\\n\", \"abce\\n\", \"duvyz\\nuy\\n\", \"ades\\n\", \"dr\\n\", \"mr\\n\", \"qx\\n\", \"abkmrst\\n\", \"dfjkmns\\n\", \"abcdefgiklnqrtvz\\n\", \"duvyz\\nuy\\n\", \"mr\\n\", \"adeijnos\\n\", \"aelr\\n\", \"dfjklmns\\n\", \"abcdefgiklnqrtvz\\n\", \"pw\\n\", \"abikmrst\\n\", \"duvyz\\nuvy\\n\", \"er\\n\", \"bclr\\n\", \"blq\\n\", \"aels\\n\", \"abikmrst\\n\", \"dfjklmnrs\\n\", \"abcdefgiklmqrtvz\\n\", \"duvyz\\nuvy\\n\", \"er\\n\", \"aels\\n\"]}", "source": "primeintellect"}
|
Recently Polycarp noticed that some of the buttons of his keyboard are malfunctioning. For simplicity, we assume that Polycarp's keyboard contains 26 buttons (one for each letter of the Latin alphabet). Each button is either working fine or malfunctioning.
To check which buttons need replacement, Polycarp pressed some buttons in sequence, and a string s appeared on the screen. When Polycarp presses a button with character c, one of the following events happened:
* if the button was working correctly, a character c appeared at the end of the string Polycarp was typing;
* if the button was malfunctioning, two characters c appeared at the end of the string.
For example, suppose the buttons corresponding to characters a and c are working correctly, and the button corresponding to b is malfunctioning. If Polycarp presses the buttons in the order a, b, a, c, a, b, a, then the string he is typing changes as follows: a → abb → abba → abbac → abbaca → abbacabb → abbacabba.
You are given a string s which appeared on the screen after Polycarp pressed some buttons. Help Polycarp to determine which buttons are working correctly for sure (that is, this string could not appear on the screen if any of these buttons was malfunctioning).
You may assume that the buttons don't start malfunctioning when Polycarp types the string: each button either works correctly throughout the whole process, or malfunctions throughout the whole process.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases in the input.
Then the test cases follow. Each test case is represented by one line containing a string s consisting of no less than 1 and no more than 500 lowercase Latin letters.
Output
For each test case, print one line containing a string res. The string res should contain all characters which correspond to buttons that work correctly in alphabetical order, without any separators or repetitions. If all buttons may malfunction, res should be empty.
Example
Input
4
a
zzaaz
ccff
cbddbb
Output
a
z
bc
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 4\\nazaza\\nzazaz\\nazaz\\n\", \"6 5\\naabbaa\\nbaaaab\\naaaaa\\n\", \"9 12\\nabcabcabc\\nxyzxyzxyz\\nabcabcayzxyz\\n\", \"50 100\\nejdbvpkfoymumiujhtplntndyfkkujqvkgipbrbycmwzawcely\\nyomcgzecbzkvaeziqmbkoknfavurydjupmsfnsthvdgookxfdx\\nejdbvpkfoymumiujhtplntndyfkkujqvkgipbrbycmwzawcelyyomcgzecbzkvaeziqmbkoknfavurydjupmsfnsthvdgookxfdx\\n\", \"20 10\\naaaaaaaaaamaaaaaaaax\\nfaaaaaaaaaaaaaaaaaaa\\naaaaaaaaaa\\n\", \"100 10\\nedcfynedcfynedcfynedcfynedcfynegcfynedcfynedcfynedcfynedcfynedcfwnedcfynedcfynedcfynedcfynedcfynedcf\\nnedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcdynedc\\nfynedcfyne\\n\", \"100 100\\nxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxb\\nxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxb\\nxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxbxb\\n\", \"20 17\\nkpooixkpooixkpokpowi\\noixtpooixkpooixoixkp\\npooixkpoixkpooixk\\n\", \"19 13\\nfafaffafaffaffafaff\\nafafaafafaafaafafaa\\nfafafafafaafa\\n\", \"100 89\\nshpashpaypayshayshpyshpashpayhpaysayshpyshpashpayhpayspayshshpayhpayspayshayshpyshpahpayspayshayshpy\\nayspayshyshpashpayhpayspayshayshpshpayhpayspayshayshpyshpahpayspayshayshpyshpashpayayshpyshpashpayhp\\npayshayshpyshpashpayhpayspayshayshpyshpashpaypayshayshpyshpashpayhpaysayshpyshpashpayhpay\\n\", \"99 105\\nanhrqanhrqanhranhrqanhrqanhranhrqanhranhrqanhrqanhranhrqanhrqanhranhaqanhranhrqanhrqanhranhrqanhran\\nqanhrqanhrqqanhrqanhrqqanhrqqanhrqanhrqqanhraanhrqqanhrqqanhrqanhrqqanhrqqanhrqanhrqqanhrqanhrqqanh\\nanhranhrqanhrqanhranhrqanhranhrqanhrqanhranhrqanhrqanhrqanhrqqanhrqqanhrqanhrqqanhrqanhrqqanhrqqanhrqanhr\\n\", \"20 2\\nrrrrrrrrrrrrrrrrrrrr\\nrrrrrrrrrrrrrrrrrrrr\\nrr\\n\", \"100 9\\nunujjnunujujnjnunujujnnujujnjnuujnjnunujnujujnjnuujnjnunujjnunujujnujnjnunujjnunujujnnujujnjnunujujn\\nnunujnujujnjnuujnjnunujjnunujujnujnjnunujjnunujujnnujujnjnujnunujujnnujujnjnuujnpnunujnujujnjnuujnjn\\njjnunujuj\\n\", \"20 40\\nypqwnaiotllzrsoaqvau\\nzjveavedxiqzzusesven\\nypqwnaiotllzrsoaqvauzjveavedxiqzzusesven\\n\", \"100 200\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsg\\nazrxzoqaombkfdlqocjgufzhtogekkfqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsgazrxzoqaombkfdlqocjgufzhtogekkzqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\n\", \"100 133\\nsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfds\\ndsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfd\\nfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsf\\n\", \"100 24\\nzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmzvahgmahgmzvahgmahgmzvahgmzvahgm\\nzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgm\\ngmahgmzvahgmahgmzvahgmzv\\n\", \"20 40\\ngvgvgvgvgvgvgvgvgvgv\\ngvgvgvgvgvgvgvgvgvgv\\ngvgvgvgvgvgvgvgvgvgvgvgvgvgvgvgvgvgvgvgv\\n\", \"20 11\\nlmmflflmlmflmfmflflm\\nmlmfmfllmfaflflmflml\\nlmlmfmfllmf\\n\", \"20 27\\nmmmmmmmmmmmmmmmmmmmm\\nmmmmmmmmmmmmmmmmmmmm\\nmmmmmmmmmmmmmmmmmmmmmmmmmmm\\n\", \"20 10\\ndctctdtdcctdtdcdcttd\\ntdcdctdctctdtdcctdtd\\ncdctctddct\\n\", \"100 33\\ncqcqqccqqcqccqqccqcqqcqccqcqqccqqcqccqcqqcqccqqccqcqqcqccqcqqccqqcqccqqccqcqqccqqcqccqcqqcqccqqccqcq\\ncqccqqccqcqqcqccqcqqccqqcqccqqccqcqqccqqcqccqcqqcqccqqccqcqqcqccqcqqccqqcqccqcqqcqccqqccqcqqccqqcqcc\\nqcqqccqqcqccqcqqcqccqqccqcqqcqccq\\n\", \"1 2\\nj\\nj\\njj\\n\", \"20 40\\nxxxxxxxxxxxxxxxxxxxx\\nxxxxxxxxxxxxxxxxxxxx\\nxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\\n\", \"20 6\\ndqgdqgdqydqgdqgqqgdq\\ndqtdqgdqgdqgdqgdfgdq\\ndqgdqg\\n\", \"20 25\\nzvozvozvozvozvozvozv\\nozvozvozvozvozvozvoz\\nzvozvozvozvozvozvozvozvoz\\n\", \"20 15\\nwwawaawwaawawwaawwaw\\nawawwawaawhaawcwwawa\\nwwawaawwaawawwa\\n\", \"100 200\\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\\n\", \"20 23\\nzizizzizizzizzizizzi\\niziziizizpiziiziziiz\\nzizizzizzizizziiziziizi\\n\", \"50 100\\nclentmsedhhrdafyrzkgnzugyvncohjkrknsmljsnhuycjdczg\\nchkzmprhkklrijxswxbscgxoobsmfduyscbxnmsnabrddkritf\\nclentmsedhhrdafyrzkgnzugyvncohjkrknsmljsnhuycjdczgchkzmprhkklrijxswxbscgxoobnmfduyscbxnmsnabrddkritf\\n\", \"100 200\\noqbywigblumgeyvlesocpdrevxgyjgjjwzjldwjqeodthpjvygateqslhidczhwlaafovdjsdmzfyfiqoojsyszqjbrzlnqboets\\nxkxlxbmdzvtgplzpcepazuuuumwjmrftrlxbnawbeejiagywxssitkixdjdjfwthldtovkfzciaugahqexdwjnlummvtgbpawxbs\\noqbywigblumgeyvlesocpdrevxgyjgjjwzjldwjqeodthpjvygateqslhidczhwlaafovdjsdmzfyfiqoojsyszqjbrzlnqboetsxkxlxbmdzvtgplzpcepazuuuumwjmrftrlxbnawbeejiagywxssitkixdjdjfwthldtovkfzciaugahqexdwjnlummvtgbpawxbs\\n\", \"20 8\\nurrndundurdurnurndnd\\nurndrnduurndrndundur\\nrndundur\\n\", \"100 94\\nmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmm\\nkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkk\\nkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmk\\n\", \"100 33\\nuuuluyguuuuuuuouuwuuumuuuuuuuuluuuvuuuuzfuuuuusuuuuuuuuuuuuuuuuuuuuuuuuduunuuuuuuhuuuuuuuueuuumuuumu\\nuueuuuuuuuuuuuuuzuuuuuuuuuuuuuuuuuuuduuuuuuuuuuuuuuouuuuuueuuuuaujuuruuuuuguuuuuuuuuuuuuuuuuuuuuuuuw\\nuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu\\n\", \"20 22\\nxsxxsxssxsxxssxxsxss\\nxssxsxxssxxsxssxxssx\\nxxsxssxsxxssxxsxssxsxx\\n\", \"100 2\\ntttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt\\ntttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt\\ntt\\n\", \"20 31\\npspsppspsppsppspspps\\nspspsspspsspsspspssp\\npspsppsppspsppspsspspsspsspspss\\n\", \"20 40\\nxdjlcpeaimrjukhizoan\\nobkcqzkcrvxxfbrvzoco\\nxdrlcpeaimrjukhizoanobkcqzkcrvxxfbrvzoco\\n\", \"20 35\\ncyvvqscyvvqscyvvqscy\\nscyvvqscyvvqscyvvqsc\\nvqscyvvqscyvvqscyvvqscyvvqscyvvqscy\\n\", \"100 20\\nrrrrrrprrjrrrhrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrerrwrrrrrrrrrrrrlrrrrrr\\nrrrrrrrrrrrrlrrrrkrrrrrrrrrrrrrrrrrrrrrrrrrqrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrcrrrrrrrr\\nrrrrrrrrrrrrrrrrrrrr\\n\", \"100 100\\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\\n\", \"1 2\\nt\\nt\\ntt\\n\", \"100 136\\ncunhfnhfncunhfnhfncunhfncunhfnhfncunhfnhfncunhfncunhfnhfncunhfncunhfnhfncunhfnhfncunhfncunhfnhfncunh\\nhfncuncunhfncuncunhfncunhfncuncunhfncuncunhfncunhfncuncunhfncunhfncuncunhfncuncunhfncunhfncuncunhfnc\\nhfncunhfnhfncunhfnhfncunhfncunhfnhfncunhfncunhfnhfncunhfnhfncunhfncunhfnhfnhfncuncunhfncunhfncuncunhfncunhfncuncunhfncuncunhfncunhfncunc\\n\", \"20 10\\nxaaaaaaaamaaaaaaaaaa\\nfaaaaaaaaaaaaaaaaaaa\\naaaaaaaaaa\\n\", \"100 10\\nedcfynedcfynedcfynedcfynedcfynegcfynedcfynedcfynedcfynedcfynedcfwnedbfynedcfynedcfynedcfynedcfynedcf\\nnedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcdynedc\\nfynedcfyne\\n\", \"19 13\\nfafaffafaffaffafaff\\nafafaafafaafaafafaa\\nafaafafafafaf\\n\", \"100 24\\nzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmzvahgmahgmzvahgmbhgmzvahgmzvahgm\\nzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgm\\ngmahgmzvahgmahgmzvahgmzv\\n\", \"20 27\\nmmmmmmmmmmmmmmmmnmmm\\nmmmmmmmmmmmmmmmmmmmm\\nmmmmmmmmmmmmmmmmmmmmmmmmmmm\\n\", \"20 6\\ndqgdqgdqydqgdqgqqgdq\\nqdgfdgqdgqdgqdgqdtqd\\ndqgdqg\\n\", \"20 25\\nzvozvozvozvozvozvozv\\nozvozvozvozvzzvoovoz\\nzvozvozvozvozvozvozvozvoz\\n\", \"100 94\\nmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmm\\nkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmk\\nkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmk\\n\", \"100 2\\ntttttttttttttttttttttttttttttttutttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt\\ntttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt\\ntt\\n\", \"20 15\\nwawwaawwawaawwaawaww\\nawawwawaawhaawcwwawa\\nawwawaawwaawaww\\n\", \"100 89\\nshpashpaypayshayshpyshpashpayhpaysayshpyshpashpayhpayspayshshpayhpayspayshayshpyshpahpayspayshayshpy\\nayspayshyshpashpayhpayspayshayshpshpayhpayspayshayshpyshpahpayspayshayshpyshpashpayayshpyshpashpayhp\\npayshayshpyshpashpayhpayspayshayshpyshpashpaypayshayshppshpashyayhpaysayshpyshpashpayhpay\\n\", \"99 105\\nnarhnaqrhnarhnaqrhnaqrhnarhnaqahnarhnaqrhnaqrhnarhnaqrhnaqrhnarhnaqrhnarhnaqrhnaqrhnarhnaqrhnaqrhna\\nqanhrqanhrqqanhrqanhrqqanhrqqanhrqanhrqqanhraanhrqqanhrqqanhrqanhrqqanhrqqanhrqanhrqqanhrqanhrqqanh\\nanhranhrqanhrqanhranhrqanhranhrqanhrqanhranhrqanhrqanhrqanhrqqanhrqqanhrqanhrqqanhrqanhrqqanhrqqanhrqanhr\\n\", \"100 200\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsg\\nazrxzoqaombkfdlqocjgufzhtogekkfqqtkndjydeiulljvowvtvyszrlnvumwbflyyhlqrnthiqmguskrhzfktwcxdzidbyoqtn\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsgazrxzoqaombkfdlqocjgufzhtogekkzqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\n\", \"100 133\\nsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfds\\ndsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfd\\nfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsedsfdsfdsfdsfdsf\\n\", \"20 11\\nlmmflflmlmflmfmflflm\\nmlmfmfllmfaflflmflml\\nlmlmfmfklmf\\n\", \"20 15\\nwwawaawwaawawwaawwaw\\nawawwawaawhaawcwwawa\\nawwawaawwaawaww\\n\", \"20 23\\nzizizzizizzizzizizzi\\nziiziziizipziziizizi\\nzizizzizzizizziiziziizi\\n\", \"100 200\\noqbywigblumgeyvlesocpdrevxgyjgjjwzjldwjqeodthpjvygateqslhidczhwlaafovdjsdmzfyfiqoojsyszqjbrzlnqboets\\nxkxlxbmdzvtgplzpcepazuuuumwjmrqtrlxbnawbeejiagywxssitkixdjdjfwthldtovkfzciaugahfexdwjnlummvtgbpawxbs\\noqbywigblumgeyvlesocpdrevxgyjgjjwzjldwjqeodthpjvygateqslhidczhwlaafovdjsdmzfyfiqoojsyszqjbrzlnqboetsxkxlxbmdzvtgplzpcepazuuuumwjmrftrlxbnawbeejiagywxssitkixdjdjfwthldtovkfzciaugahqexdwjnlummvtgbpawxbs\\n\", \"20 22\\nxsxxsxssxsxxssxxsxss\\nxssxsxxrsxxsxssxxssx\\nxxsxssxsxxssxxsxssxsxx\\n\", \"20 31\\npspsppspsppsppspspps\\nspspsspspsspsspspssp\\npsptppsppspsppspsspspsspsspspss\\n\", \"20 40\\nxdjmcpeaimrjukhizoan\\nobkcqzkcrvxxfbrvzoco\\nxdrlcpeaimrjukhizoanobkcqzkcrvxxfbrvzoco\\n\", \"20 35\\ncyvvqscyvvqscyvvqscy\\nscyvvqsvyvvqscyvcqsc\\nvqscyvvqscyvvqscyvvqscyvvqscyvvqscy\\n\", \"100 20\\nrrrrrrprrjrrrhrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrerrwrrrrrrrrrrrrlrrrrrr\\nrrrrrrrrrrrrlrrrrkrrrrrrrrrrrrrrrrrrrrrrrrrqrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrcrrrrrrrr\\nqrrrrrrrrrrrrrrrrrrr\\n\", \"100 10\\nedcfynedcfynedcfynedcfynedcfynegcfynedcfynedcfynedcfynedcfynedcfwnedbfynedcfynedcfynedcfynedcfynedcf\\nnedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcfynedcdynedc\\nenyfcdenyf\\n\", \"100 89\\nshpashpaypayshayshpyshpashpayhpaysayshpyshpashpayhpayspayshshpayhpayspayshayshpyshpahpayspayshayshpy\\nayspayshyshpashpayhpayspayshayshpshpayhpayspayshayshpyshpahpayspayshayshpyshpashpayayshpyshpashpayhp\\nyaphyaphsaphsyphsyasyaphyayhsaphspphsyahsyapyaphsaphsyphsyahsyapsyaphyaphsaphsyphsyahsyap\\n\", \"99 105\\nnarhnaqrhnarhnaqrhnaqrhnarhnaqahnarhnaqrhnaqrhnarhnaqrhnaqrhnarhnaqrhnarhnaqrhnaqrhnarhnaqrhnaqrhna\\nqanhrqanhrqqanhrqanhhqqanhrqqanhrqanhrqqanhraanhrqqanhrqqanhrqanhrqqanhrqqanhrqanhrqqanhrqanrrqqanh\\nanhranhrqanhrqanhranhrqanhranhrqanhrqanhranhrqanhrqanhrqanhrqqanhrqqanhrqanhrqqanhrqanhrqqanhrqqanhrqanhr\\n\", \"100 200\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsg\\nazrxzoqaombkfdlqocjgufzhtogekkfqqtkndjydeiulljvowvtvyszrlnvumwbflyyhlqrnthiqmguskrhzfktwcxdzidbyoqtn\\nboxjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsgazrxzoqaombkfdlqocjgufzhtogekkzqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\n\", \"100 133\\nsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfds\\ndsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfd\\nfdsfdsfdsfdsfdsfdsfdsfssfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfddfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsedsfdsfdsfdsfdsf\\n\", \"100 24\\nzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmzvahgmahgmzvahgmbhgmzvahgmzvahgm\\nzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgm\\ngmahgmzvahgmahgmzvahgmyv\\n\", \"20 23\\nzizizzizizzizzizizzi\\nziizizhizipziziizizi\\nzizizzizzizizziiziziizi\\n\", \"100 200\\noqbywigblumgeyvlesocpdrevxgyjgjjwzjldwjqeodthpjvygateqslhidczhwlaafovdjsdmzfyfiqoojsyszqjbrzlnqboets\\nxkxlxbmdzvtgplzpcepazuuuumwjmrqtrlxbnawbeejiagywxssitkixdjdjfwthlctovkfzciaugahfexdwjnlummvtgbpawxbs\\noqbywigblumgeyvlesocpdrevxgyjgjjwzjldwjqeodthpjvygateqslhidczhwlaafovdjsdmzfyfiqoojsyszqjbrzlnqboetsxkxlxbmdzvtgplzpcepazuuuumwjmrftrlxbnawbeejiagywxssitkixdjdjfwthldtovkfzciaugahqexdwjnlummvtgbpawxbs\\n\", \"100 94\\nmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmknmkmmkmkmmkmmkmkmmkmkmm\\nkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmk\\nkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmk\\n\", \"20 31\\npspsppspsppsppspspps\\nspppsssspsspsspspssp\\npsptppsppspsppspsspspsspsspspss\\n\", \"100 20\\nrrrrrrprrjrrrhrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrerrwrrrrrrrrrrrrlrrrrrr\\nrrrrrrrrcrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrqrrrrrrrrrrrrrrrrrrrrrrrrrkrrrrlrrrrrrrrrrrr\\nqrrrrrrrrrrrrrrrrrrr\\n\", \"100 200\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsg\\nazrxzoqaombkfdlqocjgufzhtogekkfqqtkndjydeiulljvowvtvyszrlnvumwbflyyhlqrnthiqmguskrhzfktwcxdzidbyoqtn\\nboxjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwettaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsgazrxzoqaombkfdlqocjgufzhtogekkzqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\n\", \"100 133\\nsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfds\\ndsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfd\\nfdsfdsfdsfdsgdsfdsfdsfssfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfddfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsedsfdsfdsfdsfdsf\\n\", \"100 24\\nzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmahgmzvahgmzvahgmahgmzvahgmzvahgmahgmzvahgmbhgmzvahgmzvahgm\\nzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgmzvzvahgmzvahgmzvzvahgmzvzvahgmzvahgnzvzvahgmzvzvahgm\\ngmahgmzvahgmahgmzvahgmyv\\n\", \"20 15\\nwawwaawwawaawwaawaww\\nawawwawaawhaawcwwawa\\nbwwawaawwaawaww\\n\", \"20 23\\nizzizizzizzizizziziz\\nziizizhizipziziizizi\\nzizizzizzizizziiziziizi\\n\", \"100 94\\nmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmknmkmmkmkmmkmmkmkmmkmkmm\\nkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmjmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmk\\nkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmk\\n\", \"100 200\\nboyjrjoeozwqgxexhcuioymcmnkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsg\\nazrxzoqaombkfdlqocjgufzhtogekkfqqtkndjydeiulljvowvtvyszrlnvumwbflyyhlqrnthiqmguskrhzfktwcxdzidbyoqtn\\nboxjrjoeozwqgxexhcuioymcmnjvctbmnmsycolzhooftwndexqtwbttuwwettaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsgazrxzoqaombkfdlqocjgufzhtogekkzqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\n\", \"100 133\\nsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdrfdsfdsfdsfdsfdsfdsfdsfds\\ndsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfd\\nfdsfdsfdsfdsgdsfdsfdsfssfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfddfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsfdsedsfdsfdsfdsfdsf\\n\", \"20 15\\nwawwaawwawaawwaawaww\\nawawwawaawhaawcwwawa\\nbwwawaawxaawaww\\n\", \"100 94\\nmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmknmkmmkmkmmkmmkmkmmkmkmm\\nkkmkmkkmkmkkmkkmjmkkmkkmkmkkmkmkkmkkmkmkkmkkmjmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmk\\nkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmk\\n\", \"100 200\\nboyjrjoeozwqgxexhcuioymcmmkvctbmnmsycolzhooftwndexqtwbttuwwfttaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsg\\nazrxzoqaombkfdlqocjgufzhtogekkfqqtkndjydeiulljvowvtvyszrlnvumwbflyyhlqrnthiqmguskrhzfktwcxdzidbyoqtn\\nboxjrjoeozwqgxexhcuioymcmnjvctbmnmsycolzhooftwndexqtwbttuwwettaxymqsjiihgsdjasaxycgoznjiorzfiwabmhsgazrxzoqaombkfdlqocjgufzhtogekkzqqtkndjydeiulljvuwvtvyszrlnvumwbflyyhlqrnthiqmgoskrhzfktwcxdzidbyoqtn\\n\", \"20 15\\nwwawaawwaawawwaawwaw\\nawawwawaawhaawcwwawa\\nbwwawaawxaawaww\\n\", \"100 94\\nmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmknmkmmkmkmmkmmkmkmmkmkmm\\nkkmkmkkmkmkkmkkmjmkkmkkmkmkkmkmkkmkkmkmkkmkkmjmkkmkmkkmkkmkmkkmkmkjmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkmk\\nkmkmmkmkmmkmmkmkmmkmkmmkmmkmkmmkmmkmkmmkmkkmkmkkmkmkkmkkmkmkkmkmkkmkkmkmkkmkkmkmkkmkmkkmkkmkmk\\n\"], \"outputs\": [\"11\", \"4\", \"2\", \"1\", \"561\", \"120\", \"45276\", \"0\", \"3\", \"0\", \"0\", \"20\", \"23\", \"1\", \"0\", \"6072\", \"98\", \"1\", \"10\", \"560\", \"0\", \"112\", \"1\", \"1\", \"13\", \"126\", \"14\", \"1\", \"1\", \"0\", \"1\", \"4\", \"10\", \"40\", \"4\", \"100\", \"3\", \"0\", \"0\", \"14414\", \"176451\", \"1\", \"2\", \"570\\n\", \"120\\n\", \"0\\n\", \"66\\n\", \"220\\n\", \"3\\n\", \"18\\n\", \"4\\n\", \"99\\n\", \"7\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Vasya had three strings a, b and s, which consist of lowercase English letters. The lengths of strings a and b are equal to n, the length of the string s is equal to m.
Vasya decided to choose a substring of the string a, then choose a substring of the string b and concatenate them. Formally, he chooses a segment [l_1, r_1] (1 ≤ l_1 ≤ r_1 ≤ n) and a segment [l_2, r_2] (1 ≤ l_2 ≤ r_2 ≤ n), and after concatenation he obtains a string a[l_1, r_1] + b[l_2, r_2] = a_{l_1} a_{l_1 + 1} … a_{r_1} b_{l_2} b_{l_2 + 1} … b_{r_2}.
Now, Vasya is interested in counting number of ways to choose those segments adhering to the following conditions:
* segments [l_1, r_1] and [l_2, r_2] have non-empty intersection, i.e. there exists at least one integer x, such that l_1 ≤ x ≤ r_1 and l_2 ≤ x ≤ r_2;
* the string a[l_1, r_1] + b[l_2, r_2] is equal to the string s.
Input
The first line contains integers n and m (1 ≤ n ≤ 500 000, 2 ≤ m ≤ 2 ⋅ n) — the length of strings a and b and the length of the string s.
The next three lines contain strings a, b and s, respectively. The length of the strings a and b is n, while the length of the string s is m.
All strings consist of lowercase English letters.
Output
Print one integer — the number of ways to choose a pair of segments, which satisfy Vasya's conditions.
Examples
Input
6 5
aabbaa
baaaab
aaaaa
Output
4
Input
5 4
azaza
zazaz
azaz
Output
11
Input
9 12
abcabcabc
xyzxyzxyz
abcabcayzxyz
Output
2
Note
Let's list all the pairs of segments that Vasya could choose in the first example:
1. [2, 2] and [2, 5];
2. [1, 2] and [2, 4];
3. [5, 5] and [2, 5];
4. [5, 6] and [3, 5];
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"defineintlonglong\\nsignedmain\\n\", \"rotator\\nrotator\\n\", \"cacdcdbbbb\\nbdcaccdbbb\\n\", \"abab\\nba\\n\", \"eternalalexandersookeustzeouuanisafqaqautomaton\\nnoiol\\n\", \"acacdddadaddcbbbbdacb\\nbabbbcadddacacdaddbdc\\n\", \"yz\\nzy\\n\", \"tqlrrtidhfpgevosrsya\\nysrsvgphitrrqtldfeoa\\n\", \"babbaaababbbbabbaaaababbbaabababbaabbaababbaaabaabbabaabbaababababbaabaaabaaaaababbaabaaaaabaabbabaaababbbb\\nbbaabbbbabbbbaaaaaababbbabaaabbbbabababbbaabbbbbabaababbaabaaabaabbababababaaaaabaabbabaaabaaaaaaaaaaaaabbb\\n\", \"dadebcabefcbaffce\\ncffbfcaddebabecae\\n\", \"ebkkiajfffiiifcgheijbcdafkcdckgdakhicebfgkeiffjbkdbgjeb\\nebffigfbciadcdfdbiehgciiifakbekijfffjcakckgkhekejbkdgjb\\n\", \"baabbaaaaa\\nababa\\n\", \"cbaabccadacadbaacbadddcdabcacdbbabccbbcbbcbbaadcabadcbdcadddccbbbbdacdbcbaddacaadbcddadbabbdbbacabdd\\ncccdacdabbacbbcacdca\\n\", \"d\\nd\\n\", \"f\\np\\n\", \"eternalalexandersookeustzeouuanisafqaqautomaton\\nnojol\\n\", \"baabaaaaba\\nbaaba\\n\", \"e\\ne\\n\", \"baabaa`aba\\nbaaba\\n\", \"baabaa`aba\\nbabba\\n\", \"acacdddadaddcbbbbdacb\\nbabbbcadddacacdaddbdd\\n\", \"zz\\nzy\\n\", \"tqlrrtidhfpgevosrsya\\nysrsvgehitrrqtldfpoa\\n\", \"bbbbabaaababbaabaaaaabaabbabaaaaabaaabaabbabababaabbaababbaabaaabbabaabbaabbababaabbbabaaaabbabbbbabaaabbab\\nbbaabbbbabbbbaaaaaababbbabaaabbbbabababbbaabbbbbabaababbaabaaabaabbababababaaaaabaabbabaaabaaaaaaaaaaaaabbb\\n\", \"dadebcacefcbaffce\\ncffbfcaddebabecae\\n\", \"ebkkiaifffiiifcghejjbcdafkcdckgdakhicebfgkeiffjbkdbgjeb\\nebffigfbciadcdfdbiehgciiifakbekijfffjcakckgkhekejbkdgjb\\n\", \"baabbaaaaa\\nbaaba\\n\", \"cbaabccadacadbaacbadddcdabcacdbbabccbbcbbcbbaadcabadcbdcadddccbbbbdacdbcbaddacaadbcddadbabbdbbacabdd\\ncccdaceabbacbbcacdca\\n\", \"d\\ne\\n\", \"g\\np\\n\", \"defineinulonglong\\nsignedmain\\n\", \"rotator\\nrntator\\n\", \"c`cdcdbbbb\\nbdcaccdbbb\\n\", \"eternalalexandersookeustzeouuanisafqaqautomaton\\nnojnl\\n\", \"acacdddadaddcbbbbdacb\\nb`bbbcadddacacdaddbdd\\n\", \"{z\\nzy\\n\", \"tplrrtidhfqgevosrsya\\nysrsvgehitrrqtldfpoa\\n\", \"bbbbabaaabbbbaabaaaaabaabbabaaaaabaaabaabbabababaabbaababbaabaaabbabaabbaabbababaabbbabaaaabbabbbbabaaabbab\\nbbaabbbbabbbbaaaaaababbbabaaabbbbabababbbaabbbbbabaababbaabaaabaabbababababaaaaabaabbabaaabaaaaaaaaaaaaabbb\\n\", \"dadebcacefcbaffce\\ncffbfcaddebabebae\\n\", \"ebkkiaifffiiifcghejjbcdafkcdckgdakhicebfgkeiffjbkdbgjeb\\nebffigfdciadcbfdbiehgciiifakbekijfffjcakckgkhekejbkdgjb\\n\", \"cbaabccadacadbaacbadddcdabcacdbbabccbbcbbcbbaadcabadcbdcadddccbbbbdacdbcbaddacaadbcddadbabbdbbacabdd\\ncccdaceacbacbbcacdca\\n\", \"g\\nq\\n\", \"gnolgnolunienifed\\nsignedmain\\n\", \"rotator\\nrotatnr\\n\", \"c`cdcdbbbb\\nbdcadccbbb\\n\", \"eternalalexandersookeustzeouuanisafqaqautomaton\\nnojnk\\n\", \"acacdddad`ddcbbbbdacb\\nb`bbbcadddacacdaddbdd\\n\", \"{z\\nyz\\n\", \"tplrrtidhfqgrvosesya\\nysrsvgehitrrqtldfpoa\\n\", \"bbbbabaaabbbbaabaaaaabaabbabaaaaabaaabaabbabababaabbaababbaabaaabbabaabbaabbababaabbbabaaaabbabbbbabaaabbab\\nbbbaaaaaaaaaaaaabaaababbaabaaaaabababababbaabaaabaabbabaababbbbbaabbbabababbbbaaababbbabaaaaaabbbbabbbbaabb\\n\", \"ecffabcfecacbedad\\ncffbfcaddebabebae\\n\", \"ebkkiaifffiiifcghejjbcdafkcdckgdakhicebfgkeiffjbkdbgjeb\\nebffigfdciadcbfdbiehgciiifakbekijfffjcakckglhekejbkdgjb\\n\", \"cbaabccadacadbaacbadddcdabcacdbbabccbbcbbcbbaadcabadcbdcadddccbbbbdacdbcbaddacaadbcddadbabbdbbacabdd\\ncccdadeacbacbbcaccca\\n\", \"f\\ne\\n\", \"f\\nq\\n\", \"gnolgnolunneiifed\\nsignedmain\\n\", \"rotator\\nnotatrr\\n\", \"c`cccdbbbb\\nbdcadccbbb\\n\", \"eternalalexandersookeustzeouuanisafqaqautomaton\\nnoknk\\n\", \"acacdddad`ddcbbbcdacb\\nb`bbbcadddacacdaddbdd\\n\", \"zz\\nyz\\n\", \"tpmrrtidhfqgrvosesya\\nysrsvgehitrrqtldfpoa\\n\", \"babbaaababbbbabbaaaababbbaabababbaabbaababbaaabaabbabaabbaababababbaabaaabaaaaababbaabaaaaabaabbbbaaababbbb\\nbbbaaaaaaaaaaaaabaaababbaabaaaaabababababbaabaaabaabbabaababbbbbaabbbabababbbbaaababbbabaaaaaabbbbabbbbaabb\\n\", \"ecffabcfecacbedad\\ncgfbfcaddebabebae\\n\", \"ebkkiaifffiiifcghejjbcdafkcdckgdakhicebfgkeiffjbkdbgjeb\\nbjgdkbjekehlgkckacjfffjikebkafiiicgheibdfbcdaicdfgiffbe\\n\", \"cbaabccadacadbaacbadddcdabcacdbbabccbbcbbcbbaadcabadcbdcadddccbbbbdacdbcbaddacaadbcddadbabbdbcacabdd\\ncccdadeacbacbbcaccca\\n\", \"g\\ne\\n\", \"f\\no\\n\", \"gnolgnolunneiifed\\nniamdengis\\n\", \"rotator\\nnotbtrr\\n\", \"c`cccdbbbb\\nbdcadccbcb\\n\", \"eternalalexandersookeustzeouvanisafqaqautomaton\\nnoknk\\n\", \"acacdddad`ddcbbbcdacb\\nddbddadcacadddacbbb`b\\n\", \"yz\\nyz\\n\", \"tpmrrtidhfqgrvosesyb\\nysrsvgehitrrqtldfpoa\\n\", \"babbaaababbbbabbaaaababbbaabababbaabbaababbaaabaabbabaabbaababababbaab`aabaaaaababbaabaaaaabaabbbbaaababbbb\\nbbbaaaaaaaaaaaaabaaababbaabaaaaabababababbaabaaabaabbabaababbbbbaabbbabababbbbaaababbbabaaaaaabbbbabbbbaabb\\n\", \"dadebcacefcbaffce\\ncgfbfcaddebabebae\\n\", \"ebkkiaifffiiifcghejjbcdafkcdcjgdakhicebfgkeiffjbkdbgjeb\\nebffigfdciadcbfdbiehgciiifakbekijfffjcakckglhekejbkdgjb\\n\", \"baabaa`aba\\ncabba\\n\", \"cbaabccbdacadbaacbadddcdabcacdbbabccbbcbbcbbaadcabadcbdcadddccbbbbdacdbcbaddacaadbcddadbabbdbcacabdd\\ncccdadeacbacbbcaccca\\n\", \"g\\nf\\n\", \"f\\nn\\n\", \"fnolgnolunneiifed\\nniamdengis\\n\", \"rotatnr\\nnotbtrr\\n\", \"bbbbdccc`c\\nbdcadccbcb\\n\", \"eternalalexandersookeustzfouvanisafqaqautomaton\\nnoknk\\n\", \"acacdddad`ddcbbbcdacb\\nddbddadcacaddd`cbbb`b\\n\", \"yz\\n{y\\n\"], \"outputs\": [\"0\", \"4\", \"24\", \"12\", \"1920\", \"64\", \"2\", \"2\", \"284471294\", \"2\", \"12\", \"120\", \"773806867\", \"2\", \"0\", \"0\\n\", \"152\\n\", \"2\\n\", \"96\\n\", \"12\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Kaavi, the mysterious fortune teller, deeply believes that one's fate is inevitable and unavoidable. Of course, she makes her living by predicting others' future. While doing divination, Kaavi believes that magic spells can provide great power for her to see the future.
<image>
Kaavi has a string T of length m and all the strings with the prefix T are magic spells. Kaavi also has a string S of length n and an empty string A.
During the divination, Kaavi needs to perform a sequence of operations. There are two different operations:
* Delete the first character of S and add it at the front of A.
* Delete the first character of S and add it at the back of A.
Kaavi can perform no more than n operations. To finish the divination, she wants to know the number of different operation sequences to make A a magic spell (i.e. with the prefix T). As her assistant, can you help her? The answer might be huge, so Kaavi only needs to know the answer modulo 998 244 353.
Two operation sequences are considered different if they are different in length or there exists an i that their i-th operation is different.
A substring is a contiguous sequence of characters within a string. A prefix of a string S is a substring of S that occurs at the beginning of S.
Input
The first line contains a string S of length n (1 ≤ n ≤ 3000).
The second line contains a string T of length m (1 ≤ m ≤ n).
Both strings contain only lowercase Latin letters.
Output
The output contains only one integer — the answer modulo 998 244 353.
Examples
Input
abab
ba
Output
12
Input
defineintlonglong
signedmain
Output
0
Input
rotator
rotator
Output
4
Input
cacdcdbbbb
bdcaccdbbb
Output
24
Note
The first test:
<image>
The red ones are the magic spells. In the first operation, Kaavi can either add the first character "a" at the front or the back of A, although the results are the same, they are considered as different operations. So the answer is 6×2=12.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 3\\n2 1\\n2 3\\n4 3\\n\", \"4 4\\n1 2\\n2 3\\n3 4\\n4 1\\n\", \"50 49\\n1 3\\n6 46\\n47 25\\n11 49\\n47 10\\n26 10\\n12 38\\n45 38\\n24 39\\n34 22\\n36 3\\n21 16\\n43 44\\n45 23\\n2 31\\n26 13\\n28 42\\n43 30\\n12 27\\n32 44\\n24 25\\n28 20\\n15 19\\n6 48\\n41 7\\n15 17\\n8 9\\n2 48\\n33 5\\n33 23\\n4 19\\n40 31\\n11 9\\n40 39\\n35 27\\n14 37\\n32 50\\n41 20\\n21 13\\n14 42\\n18 30\\n35 22\\n36 5\\n18 7\\n4 49\\n29 16\\n29 17\\n8 37\\n34 46\\n\", \"2 1\\n2 1\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n4 5\\n5 6\\n6 7\\n7 3\\n8 3\\n8 9\\n10 9\\n10 11\\n12 11\\n12 13\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n3 1\\n6 4\\n3 6\\n2 9\\n5 2\\n3 9\\n6 8\\n8 7\\n10 4\\n7 4\\n8 5\\n3 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"10 9\\n8 5\\n3 5\\n3 7\\n10 6\\n4 6\\n8 1\\n9 2\\n4 2\\n9 7\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n4 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 9\\n10 11\\n12 11\\n12 13\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n3 1\\n6 4\\n3 6\\n2 9\\n5 2\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n8 5\\n3 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"4 4\\n1 2\\n2 1\\n3 4\\n4 1\\n\", \"13 13\\n2 1\\n2 2\\n1 4\\n4 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 7\\n10 11\\n12 11\\n12 13\\n\", \"4 4\\n2 2\\n2 1\\n3 4\\n3 1\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n4 5\\n5 6\\n6 7\\n7 3\\n12 3\\n8 9\\n10 9\\n10 11\\n12 11\\n12 13\\n\", \"13 13\\n2 1\\n2 2\\n1 4\\n4 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 9\\n10 11\\n12 8\\n12 13\\n\", \"4 3\\n1 2\\n3 2\\n3 4\\n4 2\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n4 5\\n5 6\\n2 7\\n2 3\\n8 3\\n8 9\\n10 7\\n10 11\\n12 11\\n12 13\\n\", \"13 13\\n2 1\\n2 2\\n1 4\\n4 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 9\\n10 11\\n12 11\\n12 13\\n\", \"4 4\\n1 2\\n2 1\\n3 4\\n4 2\\n\", \"4 4\\n1 2\\n2 2\\n3 4\\n4 2\\n\", \"4 4\\n1 2\\n2 3\\n3 3\\n4 1\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n3 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 9\\n10 11\\n12 11\\n12 13\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n3 1\\n6 4\\n3 6\\n2 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n8 5\\n3 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"4 4\\n2 2\\n2 1\\n3 4\\n4 1\\n\", \"4 4\\n1 2\\n3 1\\n3 4\\n4 2\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n4 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 7\\n10 11\\n12 11\\n12 13\\n\", \"4 4\\n1 2\\n2 3\\n3 2\\n4 1\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n3 1\\n6 4\\n3 6\\n2 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n8 5\\n6 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"4 3\\n1 2\\n3 1\\n3 4\\n4 2\\n\", \"4 4\\n1 2\\n2 3\\n3 2\\n4 2\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n5 1\\n6 4\\n3 6\\n2 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n8 5\\n6 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n5 1\\n6 4\\n3 6\\n2 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n8 5\\n6 4\\n6 7\\n2 6\\n2 6\\n3 8\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n5 1\\n6 4\\n3 6\\n3 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n8 5\\n6 4\\n6 7\\n2 6\\n2 6\\n3 8\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n5 1\\n6 4\\n3 6\\n3 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n2 5\\n6 4\\n6 7\\n2 6\\n2 6\\n3 8\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n5 1\\n6 4\\n6 6\\n3 9\\n5 4\\n3 9\\n6 8\\n8 7\\n10 4\\n8 4\\n2 5\\n6 4\\n6 7\\n2 6\\n2 6\\n3 8\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n3 1\\n6 4\\n3 6\\n2 9\\n5 2\\n3 9\\n6 8\\n8 7\\n10 4\\n7 8\\n8 5\\n3 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"10 9\\n8 5\\n3 5\\n3 7\\n10 6\\n4 6\\n10 1\\n9 2\\n4 2\\n9 7\\n\", \"4 4\\n1 2\\n4 3\\n3 4\\n4 1\\n\", \"13 13\\n2 1\\n2 3\\n1 4\\n2 5\\n5 6\\n6 7\\n2 3\\n8 3\\n8 9\\n10 9\\n10 11\\n12 11\\n12 13\\n\", \"10 20\\n2 1\\n7 9\\n10 2\\n4 9\\n3 1\\n6 4\\n3 6\\n2 9\\n5 2\\n3 9\\n6 3\\n8 7\\n10 4\\n8 4\\n8 5\\n3 4\\n6 7\\n2 6\\n10 6\\n3 8\\n\", \"4 4\\n1 2\\n2 1\\n3 2\\n4 1\\n\", \"4 4\\n2 2\\n2 1\\n3 4\\n3 2\\n\"], \"outputs\": [\"10\\n\", \"2\\n\", \"16495294\\n\", \"2\\n\", \"74\\n\", \"3\\n\", \"520\\n\", \"263\\n\", \"3\\n\", \"2\\n\", \"23\\n\", \"5\\n\", \"10\\n\", \"20\\n\", \"6\\n\", \"69\\n\", \"263\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"263\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"23\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"263\\n\", \"3\\n\", \"2\\n\", \"6\\n\"]}", "source": "primeintellect"}
|
You are given a directed graph of n vertices and m edges. Vertices are numbered from 1 to n. There is a token in vertex 1.
The following actions are allowed:
* Token movement. To move the token from vertex u to vertex v if there is an edge u → v in the graph. This action takes 1 second.
* Graph transposition. To transpose all the edges in the graph: replace each edge u → v by an edge v → u. This action takes increasingly more time: k-th transposition takes 2^{k-1} seconds, i.e. the first transposition takes 1 second, the second one takes 2 seconds, the third one takes 4 seconds, and so on.
The goal is to move the token from vertex 1 to vertex n in the shortest possible time. Print this time modulo 998 244 353.
Input
The first line of input contains two integers n, m (1 ≤ n, m ≤ 200 000).
The next m lines contain two integers each: u, v (1 ≤ u, v ≤ n; u ≠ v), which represent the edges of the graph. It is guaranteed that all ordered pairs (u, v) are distinct.
It is guaranteed that it is possible to move the token from vertex 1 to vertex n using the actions above.
Output
Print one integer: the minimum required time modulo 998 244 353.
Examples
Input
4 4
1 2
2 3
3 4
4 1
Output
2
Input
4 3
2 1
2 3
4 3
Output
10
Note
The first example can be solved by transposing the graph and moving the token to vertex 4, taking 2 seconds.
The best way to solve the second example is the following: transpose the graph, move the token to vertex 2, transpose the graph again, move the token to vertex 3, transpose the graph once more and move the token to vertex 4.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.5
|
{"tests": "{\"inputs\": [\"4\\n1 2 3 4\\n5 5 5 5\\n3 1 4 1\\n100 20 20 100\\n\", \"4\\n1 0 3 4\\n5 5 5 5\\n3 1 4 1\\n100 20 20 100\\n\", \"4\\n1 1 3 4\\n5 5 5 5\\n3 1 4 1\\n100 20 20 100\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n3 1 4 1\\n100 20 20 100\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n1 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n1 1 4 1\\n101 20 20 101\\n\", \"4\\n1 1 3 4\\n2 5 3 5\\n1 1 4 1\\n101 20 20 101\\n\", \"4\\n1 1 3 4\\n2 5 3 5\\n2 1 4 1\\n101 20 20 101\\n\", \"4\\n1 1 3 4\\n2 5 3 5\\n2 1 4 1\\n101 29 37 101\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 21 54 111\\n\", \"4\\n1 1 3 4\\n4 8 5 5\\n2 1 4 1\\n101 21 54 111\\n\", \"4\\n1 1 3 4\\n4 8 5 4\\n2 1 4 1\\n100 21 54 111\\n\", \"4\\n1 1 3 4\\n4 16 5 4\\n2 0 4 1\\n100 21 55 111\\n\", \"4\\n1 1 3 4\\n4 16 5 4\\n2 0 4 1\\n100 21 55 011\\n\", \"4\\n1 1 1 4\\n4 16 5 4\\n2 0 4 1\\n100 21 55 011\\n\", \"4\\n1 1 1 4\\n4 16 5 4\\n2 0 4 1\\n100 21 47 011\\n\", \"4\\n1 2 1 4\\n4 16 5 4\\n2 0 4 1\\n100 21 47 011\\n\", \"4\\n0 2 1 4\\n4 16 5 4\\n2 0 4 1\\n100 21 47 011\\n\", \"4\\n0 2 1 4\\n6 16 5 4\\n2 0 4 1\\n100 21 47 011\\n\", \"4\\n0 4 1 4\\n6 14 5 6\\n1 0 2 1\\n100 21 47 011\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n1 0 3 1\\n101 40 47 011\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n1 0 3 1\\n101 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n1 1 3 1\\n101 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n1 1 3 1\\n001 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 2 6\\n1 1 3 1\\n001 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n1 5 2 4\\n6 23 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n1 5 2 7\\n6 23 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 7\\n6 23 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n6 23 2 2\\n1 1 0 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n7 23 2 2\\n1 1 1 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n7 23 2 2\\n1 1 1 1\\n011 40 47 000\\n\", \"4\\n1 2 3 4\\n5 4 5 5\\n3 1 4 1\\n100 20 20 100\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n4 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 5 4\\n5 5 3 5\\n1 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n2 5 1 5\\n2 1 4 1\\n101 20 20 101\\n\", \"4\\n1 1 1 4\\n2 5 3 5\\n2 1 4 1\\n101 20 37 101\\n\", \"4\\n1 1 3 4\\n2 5 4 5\\n2 1 4 1\\n101 58 37 101\\n\", \"4\\n1 1 3 4\\n2 5 5 5\\n4 1 4 1\\n101 29 37 101\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 29 54 100\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 29 54 011\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 21 0 111\\n\", \"4\\n1 1 3 4\\n4 8 5 6\\n2 1 4 1\\n101 21 54 111\\n\", \"4\\n1 1 3 4\\n1 8 5 4\\n2 1 4 1\\n101 21 54 111\\n\", \"4\\n1 1 3 4\\n4 8 5 4\\n2 1 4 1\\n100 11 54 111\\n\", \"4\\n1 0 3 4\\n4 16 5 4\\n2 1 4 1\\n100 21 54 111\\n\", \"4\\n1 1 2 4\\n4 16 5 4\\n2 0 4 1\\n100 21 55 011\\n\", \"4\\n1 1 1 4\\n4 1 5 4\\n2 0 4 1\\n100 21 55 011\\n\", \"4\\n1 2 1 4\\n4 16 3 4\\n2 0 4 1\\n100 21 47 011\\n\", \"4\\n0 2 1 4\\n6 16 5 4\\n2 0 4 1\\n100 21 47 001\\n\", \"4\\n0 2 1 4\\n6 14 5 4\\n2 0 4 1\\n100 21 60 011\\n\", \"4\\n0 4 1 4\\n6 14 5 4\\n2 0 2 1\\n100 21 17 011\\n\", \"4\\n0 4 1 4\\n6 14 5 8\\n1 0 2 1\\n100 21 47 011\\n\", \"4\\n0 4 2 4\\n6 14 5 6\\n1 0 2 1\\n101 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n1 1 3 2\\n101 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 2 6\\n0 1 3 1\\n001 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 2 6\\n2 1 3 1\\n011 40 47 010\\n\", \"4\\n1 5 4 7\\n6 23 2 0\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n6 23 0 2\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n5 23 2 2\\n1 1 0 1\\n011 40 47 010\\n\", \"4\\n2 5 4 1\\n7 23 2 2\\n1 1 1 1\\n011 66 47 000\\n\", \"4\\n1 1 3 6\\n5 5 3 5\\n3 1 4 0\\n100 20 20 100\\n\", \"4\\n1 1 5 4\\n0 5 3 5\\n1 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n1 1 4 2\\n101 34 20 101\\n\", \"4\\n1 1 3 4\\n2 5 4 5\\n2 1 4 1\\n001 58 37 101\\n\", \"4\\n0 1 3 4\\n2 5 5 5\\n4 1 4 1\\n101 29 37 101\\n\", \"4\\n1 1 3 4\\n2 5 5 5\\n2 0 4 1\\n101 29 49 101\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 29 27 100\\n\", \"4\\n1 1 3 4\\n1 8 5 5\\n2 1 4 1\\n101 29 54 011\\n\", \"4\\n1 1 3 4\\n4 8 5 6\\n2 1 4 1\\n101 21 54 011\\n\", \"4\\n1 1 3 4\\n1 8 10 4\\n2 1 4 1\\n101 21 54 111\\n\", \"4\\n1 0 3 4\\n4 8 5 4\\n2 1 4 1\\n100 11 54 111\\n\", \"4\\n1 1 3 5\\n4 16 5 7\\n2 0 4 1\\n100 21 55 111\\n\", \"4\\n1 1 2 4\\n8 16 5 4\\n2 0 4 1\\n100 21 55 011\\n\", \"4\\n1 1 1 4\\n4 1 5 4\\n2 0 4 1\\n100 21 55 010\\n\", \"4\\n1 1 1 4\\n4 16 8 4\\n1 0 4 1\\n100 21 47 011\\n\", \"4\\n0 2 1 4\\n6 16 5 3\\n2 0 4 1\\n100 21 47 001\\n\", \"4\\n0 4 1 4\\n6 14 5 4\\n2 0 2 1\\n100 21 17 010\\n\", \"4\\n0 4 1 4\\n6 14 5 6\\n1 0 2 0\\n100 21 75 011\\n\", \"4\\n0 5 0 4\\n6 14 5 6\\n1 0 3 1\\n101 40 30 011\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n1 1 1 1\\n000 40 47 010\\n\", \"4\\n1 5 2 7\\n6 23 2 5\\n0 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n5 23 2 2\\n1 1 0 1\\n011 40 47 110\\n\", \"4\\n2 5 4 0\\n7 23 2 2\\n1 1 1 2\\n011 40 47 100\\n\", \"4\\n2 5 4 1\\n7 23 2 2\\n1 1 1 1\\n011 66 47 010\\n\", \"4\\n1 2 3 4\\n5 4 5 5\\n3 1 3 1\\n100 20 17 100\\n\", \"4\\n1 1 3 2\\n5 5 3 5\\n3 1 4 0\\n100 20 20 100\\n\", \"4\\n1 1 3 3\\n5 5 3 5\\n4 1 4 1\\n100 20 19 101\\n\", \"4\\n1 1 5 3\\n0 5 3 5\\n1 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n1 1 4 2\\n101 34 22 101\\n\", \"4\\n1 1 3 4\\n2 5 1 5\\n3 1 4 1\\n101 21 20 101\\n\", \"4\\n1 1 1 1\\n2 5 3 5\\n2 1 4 1\\n101 20 37 001\\n\", \"4\\n0 1 3 4\\n3 5 5 5\\n4 1 4 1\\n101 29 37 101\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 1 1\\n101 29 27 100\\n\", \"4\\n1 1 3 4\\n1 8 5 5\\n2 1 4 1\\n101 4 54 011\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n4 1 4 1\\n101 21 0 011\\n\", \"4\\n1 1 5 4\\n4 16 5 4\\n2 1 4 1\\n100 21 54 111\\n\", \"4\\n1 1 1 5\\n4 16 5 7\\n2 0 4 1\\n100 21 55 111\\n\", \"4\\n1 1 2 4\\n8 16 5 4\\n2 0 4 1\\n100 3 55 011\\n\", \"4\\n1 2 1 4\\n4 1 5 4\\n2 0 4 1\\n100 21 55 010\\n\", \"4\\n1 0 1 4\\n4 16 8 4\\n1 0 4 1\\n100 21 47 011\\n\", \"4\\n0 2 1 4\\n6 16 5 3\\n2 0 4 1\\n100 21 55 001\\n\", \"4\\n0 2 1 4\\n6 14 5 4\\n1 0 4 1\\n100 21 60 111\\n\", \"4\\n0 4 2 4\\n8 14 5 6\\n1 0 0 1\\n101 40 47 010\\n\", \"4\\n0 5 2 4\\n6 14 10 6\\n0 1 3 2\\n101 40 47 000\\n\", \"4\\n0 5 2 4\\n3 14 10 6\\n1 1 1 1\\n000 40 47 010\\n\", \"4\\n0 1 2 4\\n6 14 2 6\\n2 1 3 1\\n011 40 32 010\\n\", \"4\\n2 5 4 7\\n6 23 2 0\\n1 1 3 1\\n010 40 47 010\\n\", \"4\\n0 8 4 0\\n6 23 2 6\\n1 1 3 1\\n011 62 47 010\\n\", \"4\\n2 5 4 0\\n12 23 2 2\\n1 1 1 2\\n011 40 47 100\\n\", \"4\\n2 3 4 0\\n7 23 2 4\\n1 1 1 1\\n011 66 18 100\\n\", \"4\\n1 2 3 4\\n5 4 3 5\\n3 1 3 1\\n100 20 17 100\\n\", \"4\\n1 1 3 4\\n5 5 1 3\\n3 1 4 2\\n100 20 20 110\\n\", \"4\\n1 1 3 2\\n5 5 3 5\\n3 1 4 0\\n000 20 20 100\\n\", \"4\\n1 1 3 3\\n5 5 3 5\\n4 1 4 1\\n100 20 19 001\\n\", \"4\\n1 1 3 4\\n2 5 2 5\\n0 1 4 2\\n101 20 20 101\\n\", \"4\\n0 1 3 4\\n2 5 1 5\\n3 1 4 1\\n101 21 20 101\\n\", \"4\\n1 1 1 1\\n2 5 3 5\\n2 1 4 1\\n101 20 37 000\\n\", \"4\\n1 1 3 4\\n2 7 5 5\\n2 1 4 1\\n111 29 4 101\\n\", \"4\\n1 1 3 4\\n1 5 5 5\\n1 0 4 1\\n101 29 49 101\\n\", \"4\\n1 1 3 4\\n2 8 5 6\\n2 1 1 1\\n101 29 27 100\\n\", \"4\\n1 1 3 8\\n4 5 5 6\\n2 1 4 1\\n101 21 54 011\\n\", \"4\\n1 1 3 4\\n0 8 10 4\\n2 1 6 1\\n101 21 54 111\\n\", \"4\\n1 1 5 4\\n4 16 10 4\\n2 1 4 1\\n100 21 54 111\\n\", \"4\\n1 1 4 4\\n4 16 5 4\\n2 1 0 1\\n100 21 55 111\\n\", \"4\\n1 1 1 5\\n4 16 0 7\\n2 0 4 1\\n100 21 55 111\\n\", \"4\\n1 1 2 4\\n8 16 5 4\\n2 0 4 1\\n000 3 55 011\\n\", \"4\\n1 2 1 4\\n4 1 5 4\\n2 0 4 1\\n100 21 69 010\\n\", \"4\\n0 4 1 0\\n6 14 5 4\\n2 0 2 1\\n100 21 32 010\\n\", \"4\\n0 4 1 4\\n6 14 5 6\\n0 0 2 0\\n100 21 75 001\\n\", \"4\\n0 5 2 4\\n6 14 10 3\\n2 0 5 1\\n101 40 47 111\\n\", \"4\\n1 5 2 4\\n6 24 10 6\\n1 0 3 1\\n100 11 47 010\\n\", \"4\\n0 5 2 4\\n3 14 10 6\\n1 1 1 1\\n100 40 47 010\\n\", \"4\\n1 8 3 7\\n6 23 2 5\\n0 1 3 1\\n011 40 47 010\\n\", \"4\\n2 3 4 0\\n7 23 0 2\\n1 1 0 1\\n011 40 47 010\\n\", \"4\\n2 9 4 0\\n5 23 2 2\\n1 1 0 1\\n011 40 60 110\\n\", \"4\\n0 5 4 0\\n6 23 2 2\\n1 1 1 1\\n110 40 83 010\\n\", \"4\\n2 5 4 1\\n7 23 2 3\\n1 1 0 1\\n011 66 47 010\\n\", \"4\\n2 3 4 0\\n7 23 2 4\\n1 1 1 1\\n011 83 18 100\\n\", \"4\\n1 1 3 4\\n5 5 1 3\\n3 1 4 2\\n100 18 20 110\\n\", \"4\\n2 1 5 5\\n0 5 3 5\\n1 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n1 1 4 2\\n111 34 22 111\\n\", \"4\\n0 1 3 4\\n2 5 1 5\\n3 1 4 1\\n101 8 20 101\\n\", \"4\\n1 1 3 4\\n2 7 5 5\\n2 0 4 1\\n111 29 4 101\\n\", \"4\\n1 1 3 4\\n2 8 4 5\\n2 1 4 1\\n001 95 6 101\\n\", \"4\\n1 1 3 4\\n1 5 5 5\\n1 0 4 1\\n101 29 49 100\\n\", \"4\\n2 1 3 4\\n1 8 5 5\\n2 1 4 1\\n101 4 20 011\\n\", \"4\\n1 1 5 8\\n4 16 10 4\\n2 1 4 1\\n100 21 54 111\\n\", \"4\\n1 2 1 4\\n4 1 5 4\\n2 0 4 1\\n100 21 69 011\\n\", \"4\\n0 2 1 2\\n4 16 12 4\\n4 0 4 1\\n100 21 47 011\\n\", \"4\\n0 4 1 4\\n6 14 5 11\\n0 0 2 0\\n100 21 75 001\\n\", \"4\\n0 5 2 4\\n3 20 10 6\\n0 1 3 2\\n101 40 47 000\\n\", \"4\\n2 5 4 0\\n12 19 2 2\\n1 1 1 2\\n011 40 25 100\\n\", \"4\\n2 5 4 1\\n1 23 2 3\\n1 1 0 1\\n011 66 47 010\\n\", \"4\\n2 3 4 0\\n7 23 2 4\\n1 1 1 1\\n111 83 18 100\\n\", \"4\\n1 0 3 4\\n5 5 1 3\\n3 1 4 2\\n100 18 20 110\\n\", \"4\\n1 1 3 2\\n5 5 3 5\\n3 1 0 0\\n010 20 20 100\\n\", \"4\\n2 1 5 5\\n0 5 3 5\\n2 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n1 1 4 2\\n111 34 30 111\\n\", \"4\\n2 1 3 4\\n2 5 2 5\\n0 1 4 2\\n100 20 20 101\\n\", \"4\\n0 1 3 4\\n2 5 1 5\\n3 1 4 1\\n101 8 20 001\\n\", \"4\\n1 1 1 4\\n2 7 5 5\\n2 0 4 1\\n111 29 4 101\\n\", \"4\\n2 1 3 4\\n1 8 5 5\\n2 1 4 1\\n101 4 22 011\\n\", \"4\\n1 1 3 4\\n2 4 5 5\\n4 0 4 1\\n101 21 0 111\\n\", \"4\\n1 1 3 8\\n4 5 5 8\\n2 0 4 1\\n101 21 54 011\\n\", \"4\\n1 1 3 6\\n0 8 10 4\\n2 1 6 1\\n101 25 54 111\\n\", \"4\\n1 1 4 4\\n4 16 5 0\\n2 1 0 1\\n100 21 55 101\\n\", \"4\\n1 1 1 6\\n4 16 0 7\\n2 0 4 1\\n100 21 55 011\\n\", \"4\\n1 2 1 4\\n4 1 5 4\\n2 0 4 1\\n100 21 102 011\\n\", \"4\\n0 2 1 4\\n4 31 3 4\\n1 0 4 1\\n101 21 47 011\\n\", \"4\\n0 2 0 7\\n9 16 5 3\\n2 0 4 1\\n100 21 55 001\\n\", \"4\\n1 2 1 6\\n6 14 5 4\\n1 0 4 1\\n100 21 60 110\\n\", \"4\\n1 7 2 4\\n2 24 10 6\\n1 0 3 1\\n100 11 47 010\\n\", \"4\\n4 5 4 7\\n10 23 2 0\\n1 1 3 1\\n010 40 47 010\\n\", \"4\\n2 3 4 0\\n7 23 0 2\\n0 1 0 1\\n011 40 47 000\\n\", \"4\\n2 9 4 0\\n5 23 2 1\\n1 0 0 1\\n011 40 60 110\\n\", \"4\\n0 5 4 0\\n6 23 2 2\\n2 1 1 1\\n110 40 83 000\\n\", \"4\\n1 1 3 4\\n5 5 3 5\\n3 1 4 1\\n100 20 20 101\\n\", \"4\\n1 1 3 4\\n2 5 3 5\\n2 1 4 1\\n101 20 37 101\\n\", \"4\\n1 1 3 4\\n2 5 4 5\\n2 1 4 1\\n101 29 37 101\\n\", \"4\\n1 1 3 4\\n2 5 5 5\\n2 1 4 1\\n101 29 37 101\\n\", \"4\\n1 1 3 4\\n2 5 5 5\\n2 1 4 1\\n101 29 54 101\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 29 54 101\\n\", \"4\\n1 1 3 4\\n2 8 5 5\\n2 1 4 1\\n101 29 54 111\\n\", \"4\\n1 1 3 4\\n4 8 5 4\\n2 1 4 1\\n101 21 54 111\\n\", \"4\\n1 1 3 4\\n4 16 5 4\\n2 1 4 1\\n100 21 54 111\\n\", \"4\\n1 1 3 4\\n4 16 5 4\\n2 1 4 1\\n100 21 55 111\\n\", \"4\\n0 2 1 4\\n6 14 5 4\\n2 0 4 1\\n100 21 47 011\\n\", \"4\\n0 2 1 4\\n6 14 5 4\\n2 0 2 1\\n100 21 47 011\\n\", \"4\\n0 4 1 4\\n6 14 5 4\\n2 0 2 1\\n100 21 47 011\\n\", \"4\\n0 4 1 4\\n6 14 5 4\\n1 0 2 1\\n100 21 47 011\\n\", \"4\\n0 4 1 4\\n6 14 5 6\\n1 0 2 1\\n101 21 47 011\\n\", \"4\\n0 4 1 4\\n6 14 5 6\\n1 0 2 1\\n101 40 47 011\\n\", \"4\\n0 4 2 4\\n6 14 5 6\\n1 0 2 1\\n101 40 47 011\\n\", \"4\\n0 5 2 4\\n6 14 5 6\\n1 0 2 1\\n101 40 47 011\\n\", \"4\\n0 5 2 4\\n6 14 5 6\\n1 0 3 1\\n101 40 47 011\\n\", \"4\\n0 5 2 4\\n6 23 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n1 5 4 7\\n6 23 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n6 23 2 6\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n6 23 2 2\\n1 1 3 1\\n011 40 47 010\\n\", \"4\\n2 5 4 0\\n6 23 2 2\\n1 1 1 1\\n011 40 47 010\\n\"], \"outputs\": [\"\\n3\\n25\\n3\\n2000\\n\", \"0\\n25\\n3\\n2000\\n\", \"3\\n25\\n3\\n2000\\n\", \"3\\n15\\n3\\n2000\\n\", \"3\\n15\\n1\\n2000\\n\", \"3\\n15\\n1\\n2020\\n\", \"3\\n10\\n1\\n2020\\n\", \"3\\n10\\n2\\n2020\\n\", \"3\\n10\\n2\\n2929\\n\", \"3\\n10\\n2\\n2121\\n\", \"3\\n20\\n2\\n2121\\n\", \"3\\n20\\n2\\n2100\\n\", \"3\\n20\\n0\\n2100\\n\", \"3\\n20\\n0\\n605\\n\", \"1\\n20\\n0\\n605\\n\", \"1\\n20\\n0\\n517\\n\", \"2\\n20\\n0\\n517\\n\", \"0\\n20\\n0\\n517\\n\", \"0\\n24\\n0\\n517\\n\", \"0\\n30\\n0\\n517\\n\", \"0\\n60\\n0\\n517\\n\", \"0\\n60\\n0\\n470\\n\", \"0\\n60\\n1\\n470\\n\", \"0\\n60\\n1\\n40\\n\", \"0\\n12\\n1\\n40\\n\", \"0\\n12\\n1\\n400\\n\", \"4\\n12\\n1\\n400\\n\", \"5\\n12\\n1\\n400\\n\", \"10\\n12\\n1\\n400\\n\", \"0\\n12\\n0\\n400\\n\", \"0\\n14\\n1\\n400\\n\", \"0\\n14\\n1\\n0\\n\", \"3\\n20\\n3\\n2000\\n\", \"3\\n15\\n4\\n2000\\n\", \"4\\n15\\n1\\n2000\\n\", \"3\\n5\\n2\\n2020\\n\", \"1\\n10\\n2\\n2020\\n\", \"3\\n10\\n2\\n3737\\n\", \"3\\n10\\n4\\n2929\\n\", \"3\\n10\\n2\\n2900\\n\", \"3\\n10\\n2\\n594\\n\", \"3\\n10\\n2\\n0\\n\", \"3\\n24\\n2\\n2121\\n\", \"3\\n5\\n2\\n2121\\n\", \"3\\n20\\n2\\n1100\\n\", \"0\\n20\\n2\\n2100\\n\", \"2\\n20\\n0\\n605\\n\", \"1\\n4\\n0\\n605\\n\", \"2\\n12\\n0\\n517\\n\", \"0\\n24\\n0\\n47\\n\", \"0\\n24\\n0\\n660\\n\", \"0\\n24\\n0\\n231\\n\", \"0\\n40\\n0\\n517\\n\", \"0\\n30\\n0\\n470\\n\", \"0\\n60\\n2\\n470\\n\", \"0\\n12\\n0\\n40\\n\", \"0\\n12\\n2\\n400\\n\", \"5\\n0\\n1\\n400\\n\", \"0\\n0\\n1\\n400\\n\", \"0\\n10\\n0\\n400\\n\", \"4\\n14\\n1\\n0\\n\", \"3\\n15\\n0\\n2000\\n\", \"4\\n0\\n1\\n2000\\n\", \"3\\n15\\n2\\n2020\\n\", \"3\\n10\\n2\\n58\\n\", \"0\\n10\\n4\\n2929\\n\", \"3\\n10\\n0\\n2929\\n\", \"3\\n10\\n2\\n2700\\n\", \"3\\n5\\n2\\n594\\n\", \"3\\n24\\n2\\n594\\n\", \"3\\n8\\n2\\n2121\\n\", \"0\\n20\\n2\\n1100\\n\", \"3\\n28\\n0\\n2100\\n\", \"2\\n32\\n0\\n605\\n\", \"1\\n4\\n0\\n550\\n\", \"1\\n32\\n0\\n517\\n\", \"0\\n18\\n0\\n47\\n\", \"0\\n24\\n0\\n210\\n\", \"0\\n30\\n0\\n825\\n\", \"0\\n30\\n0\\n440\\n\", \"0\\n60\\n1\\n0\\n\", \"5\\n12\\n0\\n400\\n\", \"0\\n10\\n0\\n517\\n\", \"0\\n14\\n1\\n517\\n\", \"4\\n14\\n1\\n470\\n\", \"3\\n20\\n3\\n1700\\n\", \"2\\n15\\n0\\n2000\\n\", \"3\\n15\\n4\\n1900\\n\", \"3\\n0\\n1\\n2000\\n\", \"3\\n15\\n2\\n2222\\n\", \"3\\n5\\n3\\n2020\\n\", \"1\\n10\\n2\\n37\\n\", \"0\\n15\\n4\\n2929\\n\", \"3\\n10\\n1\\n2700\\n\", \"3\\n5\\n2\\n216\\n\", \"3\\n10\\n4\\n0\\n\", \"4\\n20\\n2\\n2100\\n\", \"1\\n28\\n0\\n2100\\n\", \"2\\n32\\n0\\n165\\n\", \"2\\n4\\n0\\n550\\n\", \"0\\n32\\n0\\n517\\n\", \"0\\n18\\n0\\n55\\n\", \"0\\n24\\n0\\n2100\\n\", \"0\\n40\\n0\\n470\\n\", \"0\\n60\\n0\\n0\\n\", \"0\\n30\\n1\\n0\\n\", \"0\\n12\\n2\\n320\\n\", \"10\\n0\\n1\\n400\\n\", \"0\\n12\\n1\\n470\\n\", \"0\\n24\\n1\\n517\\n\", \"0\\n14\\n1\\n726\\n\", \"3\\n15\\n3\\n1700\\n\", \"3\\n5\\n3\\n2000\\n\", \"2\\n15\\n0\\n0\\n\", \"3\\n15\\n4\\n20\\n\", \"3\\n10\\n0\\n2020\\n\", \"0\\n5\\n3\\n2020\\n\", \"1\\n10\\n2\\n0\\n\", \"3\\n10\\n2\\n404\\n\", \"3\\n5\\n0\\n2929\\n\", \"3\\n12\\n1\\n2700\\n\", \"3\\n20\\n2\\n594\\n\", \"3\\n0\\n2\\n2121\\n\", \"4\\n40\\n2\\n2100\\n\", \"4\\n20\\n0\\n2100\\n\", \"1\\n0\\n0\\n2100\\n\", \"2\\n32\\n0\\n0\\n\", \"2\\n4\\n0\\n690\\n\", \"0\\n24\\n0\\n320\\n\", \"0\\n30\\n0\\n75\\n\", \"0\\n30\\n0\\n4040\\n\", \"4\\n60\\n0\\n470\\n\", \"0\\n30\\n1\\n470\\n\", \"7\\n12\\n0\\n400\\n\", \"0\\n0\\n0\\n400\\n\", \"0\\n10\\n0\\n660\\n\", \"0\\n12\\n1\\n830\\n\", \"4\\n14\\n0\\n470\\n\", \"0\\n14\\n1\\n913\\n\", \"3\\n5\\n3\\n1800\\n\", \"5\\n0\\n1\\n2000\\n\", \"3\\n15\\n2\\n2442\\n\", \"0\\n5\\n3\\n808\\n\", \"3\\n10\\n0\\n404\\n\", \"3\\n10\\n2\\n95\\n\", \"3\\n5\\n0\\n2900\\n\", \"3\\n5\\n2\\n80\\n\", \"5\\n40\\n2\\n2100\\n\", \"2\\n4\\n0\\n759\\n\", \"0\\n48\\n0\\n517\\n\", \"0\\n55\\n0\\n75\\n\", \"0\\n30\\n0\\n0\\n\", \"0\\n24\\n1\\n440\\n\", \"4\\n3\\n0\\n470\\n\", \"0\\n14\\n1\\n1800\\n\", \"0\\n5\\n3\\n1800\\n\", \"2\\n15\\n0\\n200\\n\", \"5\\n0\\n2\\n2000\\n\", \"3\\n15\\n2\\n3330\\n\", \"3\\n10\\n0\\n2000\\n\", \"0\\n5\\n3\\n20\\n\", \"1\\n10\\n0\\n404\\n\", \"3\\n5\\n2\\n88\\n\", \"3\\n10\\n0\\n0\\n\", \"3\\n20\\n0\\n594\\n\", \"3\\n0\\n2\\n2525\\n\", \"4\\n0\\n0\\n2100\\n\", \"1\\n0\\n0\\n605\\n\", \"2\\n4\\n0\\n1100\\n\", \"0\\n12\\n0\\n517\\n\", \"0\\n27\\n0\\n55\\n\", \"2\\n24\\n0\\n2100\\n\", \"4\\n20\\n0\\n470\\n\", \"20\\n0\\n1\\n400\\n\", \"0\\n0\\n0\\n0\\n\", \"0\\n5\\n0\\n660\\n\", \"0\\n12\\n1\\n0\\n\", \"3\\n15\\n3\\n2000\\n\", \"3\\n10\\n2\\n2020\\n\", \"3\\n10\\n2\\n2929\\n\", \"3\\n10\\n2\\n2929\\n\", \"3\\n10\\n2\\n2929\\n\", \"3\\n10\\n2\\n2929\\n\", \"3\\n10\\n2\\n2929\\n\", \"3\\n20\\n2\\n2121\\n\", \"3\\n20\\n2\\n2100\\n\", \"3\\n20\\n2\\n2100\\n\", \"0\\n24\\n0\\n517\\n\", \"0\\n24\\n0\\n517\\n\", \"0\\n24\\n0\\n517\\n\", \"0\\n24\\n0\\n517\\n\", \"0\\n30\\n0\\n517\\n\", \"0\\n30\\n0\\n517\\n\", \"0\\n30\\n0\\n517\\n\", \"0\\n30\\n0\\n517\\n\", \"0\\n30\\n0\\n517\\n\", \"0\\n12\\n1\\n400\\n\", \"5\\n12\\n1\\n400\\n\", \"0\\n12\\n1\\n400\\n\", \"0\\n12\\n1\\n400\\n\", \"0\\n12\\n1\\n400\\n\"]}", "source": "primeintellect"}
|
Monocarp wants to draw four line segments on a sheet of paper. He wants the i-th segment to have its length equal to a_i (1 ≤ i ≤ 4). These segments can intersect with each other, and each segment should be either horizontal or vertical.
Monocarp wants to draw the segments in such a way that they enclose a rectangular space, and the area of that rectangular space should be maximum possible.
For example, if Monocarp wants to draw four segments with lengths 1, 2, 3 and 4, he can do it the following way:
<image> Here, Monocarp has drawn segments AB (with length 1), CD (with length 2), BC (with length 3) and EF (with length 4). He got a rectangle ABCF with area equal to 3 that is enclosed by the segments.
Calculate the maximum area of a rectangle Monocarp can enclose with four segments.
Input
The first line contains one integer t (1 ≤ t ≤ 3 ⋅ 10^4) — the number of test cases.
Each test case consists of a single line containing four integers a_1, a_2, a_3, a_4 (1 ≤ a_i ≤ 10^4) — the lengths of the segments Monocarp wants to draw.
Output
For each test case, print one integer — the maximum area of a rectangle Monocarp can enclose with four segments (it can be shown that the answer is always an integer).
Example
Input
4
1 2 3 4
5 5 5 5
3 1 4 1
100 20 20 100
Output
3
25
3
2000
Note
The first test case of the example is described in the statement.
For the second test case, Monocarp can draw the segments AB, BC, CD and DA as follows:
<image> Here, Monocarp has drawn segments AB (with length 5), BC (with length 5), CD (with length 5) and DA (with length 5). He got a rectangle ABCD with area equal to 25 that is enclosed by the segments.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"400 234567899\\n\", \"4 100000007\\n\", \"3 100000007\\n\", \"6 100000007\\n\", \"5 999999937\\n\", \"350 999999733\\n\", \"398 999999733\\n\", \"399 999999733\\n\", \"7 100000007\\n\", \"100 999999733\\n\", \"400 999999733\\n\", \"397 999999733\\n\", \"400 100000007\\n\", \"272 100000007\\n\", \"399 725786323\\n\", \"8 100000007\\n\", \"27 100000007\\n\", \"52 100000007\\n\", \"9 100000007\\n\", \"110 999999733\\n\", \"272 134247353\\n\", \"19 100000007\\n\", \"85 100000007\\n\", \"14 100000007\\n\", \"11 100000007\\n\", \"58 999999733\\n\", \"12 100000007\\n\", \"47 100000007\\n\", \"90 100000007\\n\", \"28 100000007\\n\", \"17 100000007\\n\", \"6 181680133\\n\", \"42 100000007\\n\", \"34 100000007\\n\", \"53 100000007\\n\", \"29 100000007\\n\", \"45 100000007\\n\", \"69 134247353\\n\", \"10 100000007\\n\", \"103 100000007\\n\", \"40 100000007\\n\", \"5 221625461\\n\", \"64 999999733\\n\", \"111 999999733\\n\", \"111 100000007\\n\", \"3 181680133\\n\", \"110 100000007\\n\", \"7 181680133\\n\", \"84 100000007\\n\", \"54 100000007\\n\", \"29 43389487\\n\", \"58 134247353\\n\", \"47 999999733\\n\", \"391 100000007\\n\", \"378 725786323\\n\", \"33 100000007\\n\", \"59 999999733\\n\", \"42 44202437\\n\", \"4 221625461\\n\", \"167 100000007\\n\", \"111 482132753\\n\", \"101 100000007\\n\", \"64 100000007\\n\", \"47 43389487\\n\", \"108 134247353\\n\", \"81 999999733\\n\", \"113 999999733\\n\", \"94 100000007\\n\", \"101 482132753\\n\", \"93 43389487\\n\", \"155 134247353\\n\", \"107 999999733\\n\", \"145 43389487\\n\", \"142 999999733\\n\", \"101 999999733\\n\", \"120 999999733\\n\", \"230 999999733\\n\", \"15 100000007\\n\", \"17 181680133\\n\", \"55 100000007\\n\", \"46 100000007\\n\", \"32 100000007\\n\", \"148 100000007\\n\", \"44 999999733\\n\", \"301 725786323\\n\", \"121 100000007\\n\", \"206 134247353\\n\", \"158 999999733\\n\", \"45 999999733\\n\", \"80 100000007\\n\", \"180 43389487\\n\", \"266 999999733\\n\", \"17 61218329\\n\", \"60 100000007\\n\", \"14 999999733\\n\", \"52 999999733\\n\", \"205 100000007\\n\", \"104 43389487\\n\", \"51 999999733\\n\", \"205 52952293\\n\", \"102 999999733\\n\", \"72 999999733\\n\", \"144 999999733\\n\", \"56 725786323\\n\", \"27 76656413\\n\", \"30 100000007\\n\", \"79 100000007\\n\", \"73 100000007\\n\", \"165 100000007\\n\", \"67 134247353\\n\", \"33 999999733\\n\", \"366 725786323\\n\", \"48 100000007\\n\", \"93 999999733\\n\", \"17 44202437\\n\", \"65 100000007\\n\", \"110 482132753\\n\", \"13 43389487\\n\", \"107 134247353\\n\", \"146 999999733\\n\", \"168 100000007\\n\", \"100 482132753\\n\", \"197 134247353\\n\", \"232 999999733\\n\", \"216 999999733\\n\", \"17 61589449\\n\", \"74 100000007\\n\", \"36 100000007\\n\", \"114 100000007\\n\", \"186 43389487\\n\", \"155 999999733\\n\", \"210 52952293\\n\", \"37 999999733\\n\", \"53 76656413\\n\", \"68 100000007\\n\", \"249 100000007\\n\", \"104 134247353\\n\", \"69 100000007\\n\", \"55 134247353\\n\", \"131 999999733\\n\", \"28 61589449\\n\", \"97 100000007\\n\", \"71 100000007\\n\", \"80 43389487\\n\", \"363 52952293\\n\", \"34 999999733\\n\", \"104 261991259\\n\", \"13 44202437\\n\", \"25 61589449\\n\", \"62 100000007\\n\", \"137 261991259\\n\", \"96 100000007\\n\", \"128 261991259\\n\", \"189 100000007\\n\", \"386 100000007\\n\", \"118 725786323\\n\", \"114 134247353\\n\", \"162 100000007\\n\", \"15 181680133\\n\", \"79 999999733\\n\", \"82 100000007\\n\", \"42 179301611\\n\", \"63 100000007\\n\", \"25 100000007\\n\", \"97 134247353\\n\", \"111 35834489\\n\", \"15 999999733\\n\", \"51 100000007\\n\", \"33 34731083\\n\", \"35 100000007\\n\", \"119 100000007\\n\", \"212 134247353\\n\", \"26 43389487\\n\", \"131 134247353\\n\", \"161 999999733\\n\", \"88 100000007\\n\", \"21 999999733\\n\", \"60 999999733\\n\", \"119 725786323\\n\", \"124 100000007\\n\", \"304 999999733\\n\", \"85 999999733\\n\", \"35 999999733\\n\", \"124 43389487\\n\", \"49 76656413\\n\", \"276 100000007\\n\", \"113 134247353\\n\", \"17 999999733\\n\", \"138 134247353\\n\", \"378 999999733\\n\", \"109 100000007\\n\", \"168 43389487\\n\", \"101 52952293\\n\", \"56 999999733\\n\", \"41 134247353\\n\", \"73 261991259\\n\", \"86 100000007\\n\", \"226 261991259\\n\", \"378 100000007\\n\", \"177 725786323\\n\", \"312 100000007\\n\", \"13 100000007\\n\", \"101 35834489\\n\", \"91 100000007\\n\", \"66 34731083\\n\", \"92 100000007\\n\", \"38 43389487\\n\", \"75 134247353\\n\", \"129 999999733\\n\", \"13 51195379\\n\", \"119 786718193\\n\", \"47 13692311\\n\", \"72 134247353\\n\"], \"outputs\": [\"\\n20914007\\n\", \"\\n20\\n\", \"\\n6\\n\", \"344\\n\", \"78\\n\", \"255248393\\n\", \"875462745\\n\", \"530105147\\n\", \"1680\\n\", \"499246611\\n\", \"564062758\\n\", \"239189389\\n\", \"29181726\\n\", \"73904574\\n\", \"9715904\\n\", \"8960\\n\", \"62452100\\n\", \"35333050\\n\", \"51768\\n\", \"919976194\\n\", \"37037601\\n\", \"55293185\\n\", \"12650209\\n\", \"9152321\\n\", \"2145360\\n\", \"428007698\\n\", \"15220640\\n\", \"60836281\\n\", \"19202885\\n\", \"80966827\\n\", \"68008509\\n\", \"344\\n\", \"95721439\\n\", \"1497642\\n\", \"35180339\\n\", \"71952613\\n\", \"39262980\\n\", \"27954112\\n\", \"322064\\n\", \"62810055\\n\", \"20172847\\n\", \"78\\n\", \"345325701\\n\", \"554292800\\n\", \"15073611\\n\", \"6\\n\", \"56320783\\n\", \"1680\\n\", \"41594426\\n\", \"48478466\\n\", \"39910831\\n\", \"6532896\\n\", \"664576113\\n\", \"82580591\\n\", \"556732360\\n\", \"34449187\\n\", \"379387125\\n\", \"26574784\\n\", \"20\\n\", \"47246578\\n\", \"451663604\\n\", \"90786404\\n\", \"75904930\\n\", \"36433377\\n\", \"44188121\\n\", \"619624501\\n\", \"656494817\\n\", \"83313241\\n\", \"107422565\\n\", \"5257554\\n\", \"54134394\\n\", \"567447715\\n\", \"13502521\\n\", \"826718193\\n\", \"638002633\\n\", \"369795752\\n\", \"357829536\\n\", \"98810355\\n\", \"51043517\\n\", \"36394071\\n\", \"78021629\\n\", \"8337008\\n\", \"3080273\\n\", \"839550516\\n\", \"413097025\\n\", \"87663736\\n\", \"66960583\\n\", \"613559016\\n\", \"409387281\\n\", \"74122434\\n\", \"13263378\\n\", \"973615875\\n\", \"13289631\\n\", \"24620459\\n\", \"909152384\\n\", \"705063244\\n\", \"63668382\\n\", \"32918642\\n\", \"714466118\\n\", \"47567781\\n\", \"239682482\\n\", \"582070211\\n\", \"156228299\\n\", \"660820532\\n\", \"53058401\\n\", \"91346436\\n\", \"45857073\\n\", \"66478630\\n\", \"19676706\\n\", \"117945347\\n\", \"590284248\\n\", \"180215193\\n\", \"73521092\\n\", \"6965158\\n\", \"6323248\\n\", \"7970465\\n\", \"244660769\\n\", \"27697234\\n\", \"16380630\\n\", \"847144736\\n\", \"83954748\\n\", \"29978800\\n\", \"43610022\\n\", \"577735650\\n\", \"196379360\\n\", \"54411\\n\", \"52797613\\n\", \"69418781\\n\", \"58293590\\n\", \"16191824\\n\", \"814946780\\n\", \"23720348\\n\", \"485799469\\n\", \"65179177\\n\", \"83836730\\n\", \"30479946\\n\", \"25173523\\n\", \"25466373\\n\", \"47254760\\n\", \"663900687\\n\", \"17006067\\n\", \"56202808\\n\", \"51841314\\n\", \"41459126\\n\", \"21145332\\n\", \"917063630\\n\", \"141886493\\n\", \"26071334\\n\", \"13494983\\n\", \"43399829\\n\", \"259573809\\n\", \"20473085\\n\", \"164133369\\n\", \"65751944\\n\", \"47959858\\n\", \"223338383\\n\", \"129932953\\n\", \"30624479\\n\", \"149925427\\n\", \"983469599\\n\", \"95817795\\n\", \"120307114\\n\", \"49709767\\n\", \"25920438\\n\", \"9291945\\n\", \"9680624\\n\", \"598812749\\n\", \"30803733\\n\", \"22631045\\n\", \"55679379\\n\", \"81317863\\n\", \"55548429\\n\", \"21623\\n\", \"80118928\\n\", \"237909944\\n\", \"36896240\\n\", \"675450040\\n\", \"827583949\\n\", \"395842459\\n\", \"61670354\\n\", \"912619264\\n\", \"847515686\\n\", \"102958663\\n\", \"5140487\\n\", \"65168612\\n\", \"7779343\\n\", \"116621456\\n\", \"768214465\\n\", \"123955143\\n\", \"389524319\\n\", \"50713603\\n\", \"35740025\\n\", \"23628570\\n\", \"754627912\\n\", \"3594797\\n\", \"76698436\\n\", \"52531640\\n\", \"188750940\\n\", \"81890382\\n\", \"587150771\\n\", \"63633849\\n\", \"14476201\\n\", \"32428933\\n\", \"60061576\\n\", \"3754313\\n\", \"49956329\\n\", \"34582271\\n\", \"10315073\\n\", \"998743528\\n\", \"12085450\\n\", \"397442128\\n\", \"10315856\\n\", \"20051165\\n\"]}", "source": "primeintellect"}
|
There are n computers in a row, all originally off, and Phoenix wants to turn all of them on. He will manually turn on computers one at a time. At any point, if computer i-1 and computer i+1 are both on, computer i (2 ≤ i ≤ n-1) will turn on automatically if it is not already on. Note that Phoenix cannot manually turn on a computer that already turned on automatically.
If we only consider the sequence of computers that Phoenix turns on manually, how many ways can he turn on all the computers? Two sequences are distinct if either the set of computers turned on manually is distinct, or the order of computers turned on manually is distinct. Since this number may be large, please print it modulo M.
Input
The first line contains two integers n and M (3 ≤ n ≤ 400; 10^8 ≤ M ≤ 10^9) — the number of computers and the modulo. It is guaranteed that M is prime.
Output
Print one integer — the number of ways to turn on the computers modulo M.
Examples
Input
3 100000007
Output
6
Input
4 100000007
Output
20
Input
400 234567899
Output
20914007
Note
In the first example, these are the 6 orders in which Phoenix can turn on all computers:
* [1,3]. Turn on computer 1, then 3. Note that computer 2 turns on automatically after computer 3 is turned on manually, but we only consider the sequence of computers that are turned on manually.
* [3,1]. Turn on computer 3, then 1.
* [1,2,3]. Turn on computer 1, 2, then 3.
* [2,1,3]
* [2,3,1]
* [3,2,1]
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"15\\n+ 2432543\\n-\\n+ 4567886\\n+ 65638788\\n-\\n+ 578943\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 998244352\\n-\\n-\\n\", \"4\\n-\\n+ 1\\n+ 2\\n-\\n\", \"3\\n+ 489111368\\n+ 489111368\\n+ 489111368\\n\", \"3\\n+ 202794029\\n+ 810021800\\n+ 810021800\\n\", \"2\\n+ 717107178\\n+ 717107178\\n\", \"4\\n+ 68335221\\n+ 68335221\\n+ 68335221\\n-\\n\", \"3\\n-\\n-\\n-\\n\", \"4\\n+ 637139306\\n-\\n+ 637139306\\n-\\n\", \"3\\n+ 59671102\\n+ 59671102\\n-\\n\", \"2\\n-\\n+ 470437382\\n\", \"3\\n+ 84007770\\n+ 132687880\\n+ 132687880\\n\", \"4\\n-\\n-\\n+ 929119327\\n-\\n\", \"4\\n+ 208445053\\n-\\n-\\n+ 208445053\\n\", \"1\\n-\\n\", \"3\\n-\\n+ 351651123\\n-\\n\", \"4\\n+ 774599552\\n+ 774599552\\n+ 774599552\\n+ 774599552\\n\", \"4\\n+ 97265632\\n+ 267294833\\n+ 267294833\\n+ 97265632\\n\", \"4\\n+ 418176064\\n+ 148508573\\n+ 148508573\\n+ 148508573\\n\", \"4\\n+ 525931171\\n+ 710156085\\n+ 710156085\\n-\\n\", \"4\\n-\\n-\\n-\\n-\\n\", \"4\\n-\\n+ 389245653\\n+ 389245653\\n+ 225287031\\n\", \"3\\n+ 462776116\\n-\\n+ 380581534\\n\", \"2\\n-\\n-\\n\", \"2\\n+ 480447249\\n+ 480447249\\n\", \"1\\n+ 194959066\\n\", \"4\\n+ 646243272\\n+ 646243272\\n+ 646243272\\n+ 147162825\\n\", \"3\\n+ 143999655\\n+ 810021800\\n+ 810021800\\n\", \"2\\n+ 827106334\\n+ 717107178\\n\", \"4\\n+ 68335221\\n+ 68335221\\n+ 116056179\\n-\\n\", \"2\\n-\\n+ 356110597\\n\", \"4\\n+ 1476911953\\n+ 774599552\\n+ 774599552\\n+ 774599552\\n\", \"4\\n+ 97265632\\n+ 123075838\\n+ 267294833\\n+ 97265632\\n\", \"4\\n+ 418176064\\n+ 148508573\\n+ 52650170\\n+ 148508573\\n\", \"4\\n+ 525931171\\n+ 178798906\\n+ 710156085\\n-\\n\", \"3\\n+ 462776116\\n-\\n+ 519458975\\n\", \"2\\n+ 480447249\\n+ 160039419\\n\", \"15\\n+ 2101039\\n-\\n+ 4567886\\n+ 65638788\\n-\\n+ 578943\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 998244352\\n-\\n-\\n\", \"3\\n+ 143999655\\n+ 810021800\\n+ 148973576\\n\", \"4\\n+ 68335221\\n+ 57874311\\n+ 116056179\\n-\\n\", \"4\\n+ 97265632\\n+ 38370193\\n+ 267294833\\n+ 97265632\\n\", \"4\\n+ 294084271\\n+ 148508573\\n+ 52650170\\n+ 148508573\\n\", \"3\\n+ 462776116\\n-\\n+ 39800150\\n\", \"2\\n+ 631637691\\n+ 160039419\\n\", \"15\\n+ 2101039\\n-\\n+ 4567886\\n+ 65638788\\n-\\n+ 578943\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 797735011\\n-\\n-\\n\", \"3\\n+ 178057586\\n+ 810021800\\n+ 148973576\\n\", \"4\\n+ 34735408\\n+ 38370193\\n+ 267294833\\n+ 97265632\\n\", \"15\\n+ 2101039\\n-\\n+ 4567886\\n+ 113371486\\n-\\n+ 578943\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 797735011\\n-\\n-\\n\", \"4\\n+ 34735408\\n+ 38370193\\n+ 377974807\\n+ 97265632\\n\", \"15\\n+ 2168539\\n-\\n+ 4567886\\n+ 113371486\\n-\\n+ 578943\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 797735011\\n-\\n-\\n\", \"4\\n+ 59830128\\n+ 38370193\\n+ 377974807\\n+ 97265632\\n\", \"15\\n+ 2168539\\n-\\n+ 4567886\\n+ 113371486\\n-\\n+ 549801\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 797735011\\n-\\n-\\n\", \"3\\n+ 489111368\\n+ 489111368\\n+ 64959148\\n\", \"3\\n+ 59671102\\n+ 31099716\\n-\\n\", \"4\\n+ 403305450\\n-\\n-\\n+ 208445053\\n\", \"3\\n-\\n+ 297028140\\n-\\n\", \"4\\n+ 774599552\\n+ 774599552\\n+ 774599552\\n+ 966934840\\n\", \"4\\n+ 97265632\\n+ 92176432\\n+ 267294833\\n+ 97265632\\n\", \"4\\n+ 418176064\\n+ 148508573\\n+ 148508573\\n+ 123454617\\n\", \"3\\n+ 403013898\\n-\\n+ 380581534\\n\", \"1\\n+ 93464739\\n\", \"3\\n+ 143999655\\n+ 810021800\\n+ 576458357\\n\", \"2\\n+ 612941747\\n+ 717107178\\n\", \"4\\n+ 92130491\\n+ 68335221\\n+ 116056179\\n-\\n\", \"2\\n-\\n+ 6643512\\n\", \"4\\n+ 97265632\\n+ 123075838\\n+ 388192683\\n+ 97265632\\n\", \"4\\n+ 418176064\\n+ 148508573\\n+ 70396545\\n+ 148508573\\n\", \"4\\n+ 525931171\\n+ 178798906\\n+ 419824913\\n-\\n\", \"3\\n+ 152256965\\n-\\n+ 519458975\\n\", \"15\\n+ 2101039\\n-\\n+ 4567886\\n+ 65638788\\n-\\n+ 691209\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 998244352\\n-\\n-\\n\", \"3\\n+ 129293759\\n+ 810021800\\n+ 148973576\\n\", \"4\\n+ 68335221\\n+ 57874311\\n+ 97941762\\n-\\n\", \"4\\n+ 97265632\\n+ 38370193\\n+ 267294833\\n+ 135921860\\n\", \"4\\n+ 377812415\\n+ 148508573\\n+ 52650170\\n+ 148508573\\n\", \"3\\n+ 462776116\\n-\\n+ 78368875\\n\", \"2\\n+ 765531546\\n+ 160039419\\n\", \"15\\n+ 2101039\\n-\\n+ 979217\\n+ 65638788\\n-\\n+ 578943\\n-\\n-\\n+ 62356680\\n-\\n+ 711111\\n-\\n+ 797735011\\n-\\n-\\n\", \"3\\n+ 197641906\\n+ 489111368\\n+ 64959148\\n\", \"3\\n+ 59671102\\n+ 58831837\\n-\\n\", \"4\\n+ 774599552\\n+ 774599552\\n+ 340120965\\n+ 966934840\\n\", \"3\\n+ 763334808\\n-\\n+ 380581534\\n\", \"1\\n+ 7127255\\n\", \"2\\n+ 865445572\\n+ 717107178\\n\", \"4\\n+ 92130491\\n+ 42002272\\n+ 116056179\\n-\\n\", \"4\\n+ 97265632\\n+ 26153880\\n+ 388192683\\n+ 97265632\\n\", \"4\\n+ 418176064\\n+ 148508573\\n+ 70020664\\n+ 148508573\\n\", \"4\\n+ 456016453\\n+ 178798906\\n+ 419824913\\n-\\n\", \"3\\n+ 78719912\\n+ 810021800\\n+ 148973576\\n\", \"4\\n+ 377812415\\n+ 148508573\\n+ 56953752\\n+ 148508573\\n\", \"2\\n+ 432008778\\n+ 160039419\\n\", \"3\\n+ 197641906\\n+ 568123374\\n+ 64959148\\n\", \"4\\n+ 1397411850\\n+ 774599552\\n+ 340120965\\n+ 966934840\\n\", \"3\\n+ 763334808\\n-\\n+ 759883533\\n\", \"1\\n+ 13952371\\n\", \"2\\n+ 244291162\\n+ 717107178\\n\", \"4\\n+ 97265632\\n+ 30914506\\n+ 388192683\\n+ 97265632\\n\", \"4\\n+ 562729094\\n+ 148508573\\n+ 70020664\\n+ 148508573\\n\", \"4\\n+ 456016453\\n+ 163378298\\n+ 419824913\\n-\\n\", \"3\\n+ 78719912\\n+ 698718992\\n+ 148973576\\n\", \"4\\n+ 377812415\\n+ 79638617\\n+ 56953752\\n+ 148508573\\n\", \"3\\n+ 197641906\\n+ 568123374\\n+ 22481886\\n\", \"1\\n+ 25100199\\n\", \"2\\n+ 244291162\\n+ 210098575\\n\", \"4\\n+ 562729094\\n+ 148508573\\n+ 70020664\\n+ 52221375\\n\", \"4\\n+ 220147102\\n+ 79638617\\n+ 56953752\\n+ 148508573\\n\", \"3\\n+ 334961902\\n+ 568123374\\n+ 22481886\\n\", \"1\\n+ 31045113\\n\", \"2\\n+ 244291162\\n+ 168088875\\n\", \"4\\n+ 562729094\\n+ 148508573\\n+ 120492503\\n+ 52221375\\n\", \"3\\n+ 334961902\\n+ 626970064\\n+ 22481886\\n\", \"1\\n+ 2018800\\n\", \"2\\n+ 142210582\\n+ 168088875\\n\", \"4\\n+ 562729094\\n+ 65591651\\n+ 120492503\\n+ 52221375\\n\", \"3\\n+ 331697717\\n+ 626970064\\n+ 22481886\\n\", \"2\\n+ 236744084\\n+ 168088875\\n\", \"4\\n+ 562729094\\n+ 65591651\\n+ 120492503\\n+ 68921237\\n\", \"2\\n+ 144284847\\n+ 168088875\\n\", \"4\\n+ 562729094\\n+ 65591651\\n+ 149289241\\n+ 68921237\\n\", \"2\\n+ 144284847\\n+ 968045\\n\", \"4\\n+ 562729094\\n+ 65591651\\n+ 62245966\\n+ 68921237\\n\", \"2\\n+ 936239707\\n+ 717107178\\n\", \"4\\n+ 68335221\\n+ 19524164\\n+ 68335221\\n-\\n\", \"3\\n+ 59671102\\n+ 37041301\\n-\\n\", \"2\\n-\\n+ 61414946\\n\", \"4\\n-\\n-\\n+ 906775121\\n-\\n\", \"4\\n+ 97265632\\n+ 267294833\\n+ 267294833\\n+ 91555805\\n\", \"4\\n+ 418176064\\n+ 291969474\\n+ 148508573\\n+ 148508573\\n\"], \"outputs\": [\"750759115\\n\", \"16\\n\", \"878114651\\n\", \"303640045\\n\", \"871940006\\n\", \"163454404\\n\", \"0\\n\", \"466997730\\n\", \"298355510\\n\", \"940874764\\n\", \"399289767\\n\", \"721744249\\n\", \"87961824\\n\", \"0\\n\", \"703302246\\n\", \"829321192\\n\", \"841745675\\n\", \"920148146\\n\", \"355065906\\n\", \"0\\n\", \"44271872\\n\", \"451389662\\n\", \"0\\n\", \"923544643\\n\", \"194959066\\n\", \"715231480\\n\", \"68462549\\n\", \"93693965\\n\", \"497501110\\n\", \"712221194\\n\", \"458354282\\n\", \"686238068\\n\", \"153280922\\n\", \"855920421\\n\", \"8655073\\n\", \"282728983\\n\", \"586333131\\n\", \"419002712\\n\", \"455657470\\n\", \"8592908\\n\", \"158790931\\n\", \"86508479\\n\", \"585109867\\n\", \"76843958\\n\", \"555234436\\n\", \"506595469\\n\", \"431927902\\n\", \"393790908\\n\", \"465407902\\n\", \"594548668\\n\", \"457947550\\n\", \"179750124\\n\", \"241212738\\n\", \"477682618\\n\", \"594056280\\n\", \"371514790\\n\", \"439042820\\n\", \"719716498\\n\", \"331865226\\n\", \"93464739\\n\", \"132453130\\n\", \"663609144\\n\", \"640272730\\n\", \"13287024\\n\", \"655176515\\n\", \"295251922\\n\", \"926197181\\n\", \"385861124\\n\", \"615073227\\n\", \"360179128\\n\", \"328856551\\n\", \"317842732\\n\", \"828616083\\n\", \"240783379\\n\", \"852897577\\n\", \"749955364\\n\", \"12116629\\n\", \"296676980\\n\", \"888663506\\n\", \"54262693\\n\", \"7127255\\n\", \"170372441\\n\", \"534940934\\n\", \"878045204\\n\", \"292244874\\n\", \"436794155\\n\", \"157883740\\n\", \"863044739\\n\", \"185852041\\n\", \"328164653\\n\", \"879940125\\n\", \"573226336\\n\", \"13952371\\n\", \"924552327\\n\", \"916130212\\n\", \"450424761\\n\", \"375111723\\n\", \"710916861\\n\", \"312085091\\n\", \"158255605\\n\", \"25100199\\n\", \"908779474\\n\", \"678371530\\n\", \"49006940\\n\", \"707535589\\n\", \"31045113\\n\", \"824760074\\n\", \"83901889\\n\", \"942922349\\n\", \"2018800\\n\", \"620598914\\n\", \"418810866\\n\", \"929865609\\n\", \"809665918\\n\", \"552409762\\n\", \"624747444\\n\", \"782783666\\n\", \"290505784\\n\", \"86437466\\n\", \"311960711\\n\", \"966454529\\n\", \"253095908\\n\", \"122829892\\n\", \"632367425\\n\", \"796067059\\n\", \"71346648\\n\"]}", "source": "primeintellect"}
|
You are given a sequence A, where its elements are either in the form + x or -, where x is an integer.
For such a sequence S where its elements are either in the form + x or -, define f(S) as follows:
* iterate through S's elements from the first one to the last one, and maintain a multiset T as you iterate through it.
* for each element, if it's in the form + x, add x to T; otherwise, erase the smallest element from T (if T is empty, do nothing).
* after iterating through all S's elements, compute the sum of all elements in T. f(S) is defined as the sum.
The sequence b is a subsequence of the sequence a if b can be derived from a by removing zero or more elements without changing the order of the remaining elements. For all A's subsequences B, compute the sum of f(B), modulo 998 244 353.
Input
The first line contains an integer n (1≤ n≤ 500) — the length of A.
Each of the next n lines begins with an operator + or -. If the operator is +, then it's followed by an integer x (1≤ x<998 244 353). The i-th line of those n lines describes the i-th element in A.
Output
Print one integer, which is the answer to the problem, modulo 998 244 353.
Examples
Input
4
-
+ 1
+ 2
-
Output
16
Input
15
+ 2432543
-
+ 4567886
+ 65638788
-
+ 578943
-
-
+ 62356680
-
+ 711111
-
+ 998244352
-
-
Output
750759115
Note
In the first example, the following are all possible pairs of B and f(B):
* B= {}, f(B)=0.
* B= {-}, f(B)=0.
* B= {+ 1, -}, f(B)=0.
* B= {-, + 1, -}, f(B)=0.
* B= {+ 2, -}, f(B)=0.
* B= {-, + 2, -}, f(B)=0.
* B= {-}, f(B)=0.
* B= {-, -}, f(B)=0.
* B= {+ 1, + 2}, f(B)=3.
* B= {+ 1, + 2, -}, f(B)=2.
* B= {-, + 1, + 2}, f(B)=3.
* B= {-, + 1, + 2, -}, f(B)=2.
* B= {-, + 1}, f(B)=1.
* B= {+ 1}, f(B)=1.
* B= {-, + 2}, f(B)=2.
* B= {+ 2}, f(B)=2.
The sum of these values is 16.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"0 0 1\\n6 0 3\\n\", \"-10 10 3\\n10 -10 3\\n\", \"41 17 3\\n71 -86 10\\n\", \"826 4417 2901\\n833 -2286 3802\\n\", \"0 3278 2382\\n2312 1 1111\\n\", \"659 -674 277\\n-345 -556 127\\n\", \"2587 4850 3327\\n3278 -204 1774\\n\", \"-6 3 8\\n7 2 1\\n\", \"4763 2945 956\\n3591 9812 180\\n\", \"0 1 3\\n1 -1 1\\n\", \"83 -64 85\\n27 80 89\\n\", \"4 0 2\\n6 -1 10\\n\", \"10000 10000 1\\n-10000 -10000 1\\n\", \"2 1 3\\n8 9 5\\n\", \"-2 0 1\\n3 -2 1\\n\", \"1055 -5271 60\\n-2992 8832 38\\n\", \"-5051 -7339 9\\n-9030 755 8\\n\", \"103 104 5\\n97 96 5\\n\", \"-171 762 304\\n-428 -85 523\\n\", \"192 -295 1386\\n-54 -78 1\\n\", \"1003 -5005 3399\\n-6036 -1729 4365\\n\", \"-5134 -9860 5513\\n6291 -855 9034\\n\", \"-7 -10 1\\n-4 3 1\\n\", \"6370 7728 933\\n4595 3736 2748\\n\", \"-10000 42 10000\\n10000 43 10000\\n\", \"0 0 1\\n-10 -10 9\\n\", \"-655 -750 68\\n905 -161 68\\n\", \"10000 -9268 1\\n-9898 9000 10\\n\", \"6651 8200 610\\n-9228 9387 10000\\n\", \"-74 27 535\\n18 84 1\\n\", \"123 21 50\\n10 100 1000\\n\", \"3 4 5\\n5 12 13\\n\", \"28 -63 2382\\n43 -83 1364\\n\", \"-9577 9051 5276\\n-4315 -1295 8453\\n\", \"0 -1 1\\n1 -1 1\\n\", \"-34 -5 836\\n52 -39 706\\n\", \"0 5 2\\n8 -4 94\\n\", \"761 641 6\\n506 -293 5\\n\", \"3 -7 5749\\n1 -6 9750\\n\", \"-454 -721 72\\n-33 279 911\\n\", \"315 -532 7813\\n407 -157 2121\\n\", \"4 0 201\\n-6 4 279\\n\", \"-2 7 5\\n4 0 6\\n\", \"41 17 3\\n71 -137 10\\n\", \"826 4417 2901\\n833 -2286 4272\\n\", \"0 3278 2382\\n3552 1 1111\\n\", \"659 -674 249\\n-345 -556 127\\n\", \"4566 4850 3327\\n3278 -204 1774\\n\", \"-5 3 8\\n7 2 1\\n\", \"4763 2945 164\\n3591 9812 180\\n\", \"0 0 3\\n1 -1 1\\n\", \"10000 10010 1\\n-10000 -10000 1\\n\", \"2 1 3\\n7 9 5\\n\", \"-2 0 1\\n0 -2 1\\n\", \"1055 -5271 60\\n-2992 16522 38\\n\", \"-5051 -7339 9\\n-911 755 8\\n\", \"-171 762 304\\n-400 -85 523\\n\", \"192 -295 1386\\n-100 -78 1\\n\", \"1003 -5005 3399\\n-10705 -1729 4365\\n\", \"-9445 -9860 5513\\n6291 -855 9034\\n\", \"-7 -10 1\\n-4 0 1\\n\", \"11049 7728 933\\n4595 3736 2748\\n\", \"-10000 42 10000\\n10100 43 10000\\n\", \"0 0 2\\n-10 -10 9\\n\", \"-655 -728 68\\n905 -161 68\\n\", \"10000 -9268 1\\n-9898 5228 10\\n\", \"6651 7750 610\\n-9228 9387 10000\\n\", \"-74 27 535\\n10 84 1\\n\", \"123 21 50\\n11 100 1000\\n\", \"28 -63 2382\\n40 -83 1364\\n\", \"-9577 9051 5276\\n-4315 -1295 3517\\n\", \"-34 -5 836\\n28 -39 706\\n\", \"0 5 2\\n7 -4 94\\n\", \"761 641 6\\n506 -293 6\\n\", \"3 -7 5749\\n1 -3 9750\\n\", \"-454 -721 1\\n-33 279 911\\n\", \"479 -532 7813\\n407 -157 2121\\n\", \"0 0 201\\n-6 4 279\\n\", \"0 0 1\\n5 0 3\\n\", \"-10 10 3\\n10 -10 2\\n\", \"41 17 6\\n71 -137 10\\n\", \"0 3278 2382\\n3552 2 1111\\n\", \"659 -674 29\\n-345 -556 127\\n\", \"4566 305 3327\\n3278 -204 1774\\n\", \"4763 2945 164\\n3591 18438 180\\n\", \"10000 10010 1\\n-10000 -8097 1\\n\", \"2 1 3\\n7 9 4\\n\", \"-2 0 1\\n1 -2 1\\n\", \"1055 -5271 45\\n-2992 16522 38\\n\", \"-2425 -7339 9\\n-911 755 8\\n\", \"103 104 5\\n108 116 5\\n\", \"-71 762 304\\n-400 -85 523\\n\", \"192 -295 1386\\n-100 -103 1\\n\", \"1003 -5005 3399\\n-17447 -1729 4365\\n\", \"-9445 -9860 3526\\n6291 -855 9034\\n\", \"-7 -10 1\\n-3 0 1\\n\", \"11049 7728 1114\\n4595 3736 2748\\n\", \"0 0 2\\n-10 -16 9\\n\", \"-655 -728 19\\n905 -161 68\\n\", \"10000 -14278 1\\n-9898 5228 10\\n\", \"-74 42 535\\n10 84 1\\n\", \"166 21 50\\n10 100 1000\\n\", \"27 -63 2382\\n40 -83 1364\\n\", \"-9577 9051 5276\\n-4315 -1295 854\\n\", \"0 -2 1\\n1 0 1\\n\", \"-34 -1 836\\n28 -39 706\\n\", \"0 5 2\\n12 -4 94\\n\", \"761 641 11\\n506 -293 6\\n\", \"3 -7 5749\\n1 -3 5621\\n\", \"-454 -721 1\\n-33 299 911\\n\", \"479 -532 11899\\n407 -157 2121\\n\", \"0 0 201\\n-6 4 371\\n\", \"-10 15 3\\n10 -10 2\\n\", \"41 17 6\\n71 -170 10\\n\", \"83 -64 85\\n27 71 89\\n\", \"4 0 2\\n6 -1 2\\n\", \"103 104 5\\n108 96 5\\n\", \"3 4 5\\n2 12 13\\n\", \"0 -1 1\\n1 0 1\\n\", \"-2 3 5\\n4 0 6\\n\", \"826 4417 2901\\n1367 -2286 4272\\n\", \"-1 0 3\\n1 -1 1\\n\", \"83 -64 85\\n40 71 89\\n\", \"4 0 2\\n7 -1 2\\n\", \"-10000 42 11000\\n10100 43 10000\\n\", \"666 7750 610\\n-9228 9387 10000\\n\", \"3 4 5\\n0 12 13\\n\", \"-2 2 5\\n4 0 6\\n\", \"1 0 1\\n5 0 3\\n\"], \"outputs\": [\"1.0000000000\\n\", \"11.1421356237\\n\", \"47.1400037286\\n\", \"0.0018275394\\n\", \"258.7476779690\\n\", \"303.4552403527\\n\", \"0.0096059415\\n\", \"2.0192024052\\n\", \"2915.1477502397\\n\", \"0.0000000\\n\", \"0.0000000\\n\", \"2.8819660113\\n\", \"14141.1356237310\\n\", \"1.0000000000\\n\", \"1.6925824036\\n\", \"7287.0891829366\\n\", \"4501.0808286358\\n\", \"0.0000000000\\n\", \"29.0658143147\\n\", \"528.4839946834\\n\", \"0.0000321999\\n\", \"0.0935066513\\n\", \"5.6708320321\\n\", \"343.9157685752\\n\", \"0.0000125000\\n\", \"2.0710678119\\n\", \"765.7447151257\\n\", \"13500.5192877102\\n\", \"2656.6519956602\\n\", \"212.8866929490\\n\", \"406.0616217191\\n\", \"0.0000000\\n\", \"496.5000000000\\n\", \"0.0000000\\n\", \"0.0000000\\n\", \"18.7614879132\\n\", \"39.9792027106\\n\", \"478.5921916330\\n\", \"1999.3819660113\\n\", \"51.0036866234\\n\", \"2652.9397762355\\n\", \"33.6148351929\\n\", \"0.0000000\\n\", \"71.94743462982075\\n\", \"0.0\\n\", \"669.8729534159252\\n\", \"317.4552403526943\\n\", \"57.27012023682801\\n\", \"1.5207972893961479\\n\", \"3311.1477502397165\\n\", \"0.2928932188134524\\n\", \"14144.671599468156\\n\", \"0.7169905660283016\\n\", \"0.41421356237309515\\n\", \"11033.79136770155\\n\", \"4537.169257656126\\n\", \"25.205482071970494\\n\", \"510.5982408001506\\n\", \"2196.845285084989\\n\", \"1791.7043689042112\\n\", \"4.220153254455275\\n\", \"1953.9097037615747\\n\", \"50.000012437811165\\n\", \"1.5710678118654755\\n\", \"761.923038600568\\n\", \"12303.687828609976\\n\", \"2676.5789478022452\\n\", \"216.24322705293412\\n\", \"406.47080913946235\\n\", \"497.33809621030946\\n\", \"1407.1273140166404\\n\", \"29.644660940672622\\n\", \"40.29912287450431\\n\", \"478.09219163295745\\n\", \"1998.2639320224998\\n\", \"86.50368662341828\\n\", \"2655.075276614054\\n\", \"35.394448724536005\\n\", \"0.5\\n\", \"11.642135623730951\\n\", \"70.44743462982075\\n\", \"669.533940158954\\n\", \"427.4552403526943\\n\", \"84.0361020240839\\n\", \"7596.632971765367\\n\", \"13488.472274703707\\n\", \"1.2169905660283016\\n\", \"0.8027756377319946\\n\", \"11041.29136770155\\n\", \"4108.690546962819\\n\", \"1.5\\n\", \"40.82642450115094\\n\", \"517.7659163185385\\n\", \"5487.2939435157\\n\", \"2785.204368904211\\n\", \"4.385164807134504\\n\", \"1863.4097037615747\\n\", \"3.933981132056603\\n\", \"786.423038600568\\n\", \"13926.607162952774\\n\", \"220.04257247250442\\n\", \"387.5685983184531\\n\", \"497.07313955812333\\n\", \"2738.6273140166404\\n\", \"0.1180339887498949\\n\", \"28.640682074604342\\n\", \"38.5\\n\", \"475.59219163295745\\n\", \"61.763932022500285\\n\", \"95.73385794239596\\n\", \"4698.075276614054\\n\", \"81.394448724536\\n\", \"13.507810593582121\\n\", \"86.69556483806409\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\", \"0.0\\n\"]}", "source": "primeintellect"}
|
So, the Berland is at war with its eternal enemy Flatland again, and Vasya, an accountant, was assigned to fulfil his duty to the nation.
Right now the situation in Berland is dismal — their both cities are surrounded! The armies of flatlanders stand on the borders of circles, the circles' centers are in the surrounded cities. At any moment all points of the flatland ring can begin to move quickly in the direction of the city — that's the strategy the flatlanders usually follow when they besiege cities.
The berlanders are sure that they can repel the enemy's attack if they learn the exact time the attack starts. For that they need to construct a radar that would register any movement at the distance of at most r from it. Thus, we can install a radar at such point, that at least one point of the enemy ring will be in its detecting range (that is, at a distance of at most r). Then the radar can immediately inform about the enemy's attack.
Due to the newest technologies, we can place a radar at any point without any problems. But the problem is that the berlanders have the time to make only one radar. Besides, the larger the detection radius (r) is, the more the radar costs.
That's why Vasya's task (that is, your task) is to find the minimum possible detection radius for the radar. In other words, your task is to find the minimum radius r (r ≥ 0) such, that a radar with radius r can be installed at some point and it can register the start of the movements of both flatland rings from that point.
In this problem you can consider the cities as material points, the attacking enemy rings - as circles with centers in the cities, the radar's detection range — as a disk (including the border) with the center at the point where the radar is placed.
Input
The input files consist of two lines. Each line represents the city and the flatland ring that surrounds it as three space-separated integers xi, yi, ri (|xi|, |yi| ≤ 104; 1 ≤ ri ≤ 104) — the city's coordinates and the distance from the city to the flatlanders, correspondingly.
It is guaranteed that the cities are located at different points.
Output
Print a single real number — the minimum detection radius of the described radar. The answer is considered correct if the absolute or relative error does not exceed 10 - 6.
Examples
Input
0 0 1
6 0 3
Output
1.000000000000000
Input
-10 10 3
10 -10 3
Output
11.142135623730951
Note
The figure below shows the answer to the first sample. In this sample the best decision is to put the radar at point with coordinates (2, 0).
<image>
The figure below shows the answer for the second sample. In this sample the best decision is to put the radar at point with coordinates (0, 0).
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1\\n\", \"4\\n\", \"16677181699666569\\n\", \"52013157885656046\\n\", \"1129718145924\\n\", \"29442431889534807\\n\", \"3\\n\", \"58061299250691018\\n\", \"81\\n\", \"2\\n\", \"10\\n\", \"93886356235159944\\n\", \"72900000000000\\n\", \"243\\n\", \"70414767176369958\\n\", \"5559060566555523\\n\", \"99999999999999997\\n\", \"49664023559436051\\n\", \"8\\n\", \"66708726798666276\\n\", \"108\\n\", \"34391854792828422\\n\", \"205891132094649\\n\", \"100000000000000000\\n\", \"99999999999999999\\n\", \"50031545098999707\\n\", \"97626528902553453\\n\", \"37586570003500923\\n\", \"1290136459530944\\n\", \"29676636410175168\\n\", \"744422128968\\n\", \"17471275008110312\\n\", \"59762955870878174\\n\", \"134\\n\", \"9\\n\", \"58913112379627206\\n\", \"137400064974625\\n\", \"259\\n\", \"132388582992087362\\n\", \"616513766820140\\n\", \"119066802691402319\\n\", \"37571750476483985\\n\", \"106324194433947774\\n\", \"74\\n\", \"4370625371943060\\n\", \"19762873871259\\n\", \"175511684977635088\\n\", \"4845939736310695\\n\", \"99101073768186867\\n\", \"48157762713213842\\n\", \"5\\n\", \"1374486016669718\\n\", \"42327998375756956\\n\", \"1088745798161\\n\", \"976282983829128\\n\", \"75810523336426350\\n\", \"266\\n\", \"69193745078199495\\n\", \"258844947866003\\n\", \"414\\n\", \"66710837504146279\\n\", \"1231482753034472\\n\", \"169782153895473260\\n\", \"29084183820986046\\n\", \"23602146755677917\\n\", \"4837695783482626\\n\", \"11557976627875\\n\", \"315056048456702448\\n\", \"2032374082070849\\n\", \"12782053664654523\\n\", \"64767185898112470\\n\", \"11\\n\", \"17\\n\", \"278804264186214\\n\", \"40600260331330597\\n\", \"532791708628\\n\", \"654281970563690\\n\", \"28073333171338581\\n\", \"34\\n\", \"979923630747748\\n\", \"359582833099366\\n\", \"206\\n\", \"122505763686881776\\n\", \"145786908878261\\n\", \"308381906410013588\\n\", \"41188974820893655\\n\", \"41816413113293548\\n\", \"64\\n\", \"746665964684295\\n\", \"3299475312399\\n\", \"196885015826334776\\n\", \"3413481052392006\\n\", \"25261516147600598\\n\", \"40490293435414477\\n\", \"7\\n\", \"20\\n\", \"6\\n\", \"46\\n\"], \"outputs\": [\" 1\\n\", \" 2\\n\", \"1\", \"880847395988\", \"2\", \"48\", \" 1\\n\", \"32\", \" 1\\n\", \" 1\\n\", \" 4\\n\", \"51\", \"33333333334\", \" 1\\n\", \"13\", \"1\\n\", \"33333333333333333\", \"128191526\", \" 3\\n\", \"2\", \" 2\\n\", \"582429080812\", \"1\", \"33333333333333334\", \"3703703703703704\", \"1\", \"551104613133\", \"548\", \"430045486510315\\n\", \"3297404045575019\\n\", \"82713569886\\n\", \"5823758336036771\\n\", \"19920985290292725\\n\", \"45\\n\", \"1\\n\", \"242440791685709\\n\", \"45800021658209\\n\", \"87\\n\", \"44129527664029121\\n\", \"205504588940047\\n\", \"39688934230467440\\n\", \"12523916825494662\\n\", \"11813799381549753\\n\", \"25\\n\", \"485625041327007\\n\", \"2195874874585\\n\", \"58503894992545030\\n\", \"1615313245436899\\n\", \"11011230418687430\\n\", \"16052587571071281\\n\", \"2\\n\", \"458162005556573\\n\", \"14109332791918986\\n\", \"362915266054\\n\", \"108475887092126\\n\", \"2807797160608384\\n\", \"89\\n\", \"7688193897577722\\n\", \"86281649288668\\n\", \"16\\n\", \"22236945834715427\\n\", \"410494251011491\\n\", \"56594051298491087\\n\", \"3231575980109561\\n\", \"2622460750630880\\n\", \"1612565261160876\\n\", \"3852658875959\\n\", \"3889580845144475\\n\", \"677458027356950\\n\", \"1420228184961614\\n\", \"7196353988679164\\n\", \"4\\n\", \"6\\n\", \"10326083858749\\n\", \"13533420110443533\\n\", \"177597236210\\n\", \"218093990187897\\n\", \"3119259241259843\\n\", \"12\\n\", \"326641210249250\\n\", \"119860944366456\\n\", \"69\\n\", \"40835254562293926\\n\", \"48595636292754\\n\", \"102793968803337863\\n\", \"13729658273631219\\n\", \"13938804371097850\\n\", \"22\\n\", \"82962884964922\\n\", \"366608368045\\n\", \"65628338608778259\\n\", \"379275672488001\\n\", \"8420505382533533\\n\", \"13496764478471493\\n\", \"3\\n\", \"7\\n\", \"1\\n\", \"16\\n\"]}", "source": "primeintellect"}
|
Gerald has been selling state secrets at leisure. All the secrets cost the same: n marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of other denominations. Of course, Gerald likes it when he gets money without the change. And all buyers respect him and try to give the desired sum without change, if possible. But this does not always happen.
One day an unlucky buyer came. He did not have the desired sum without change. Then he took out all his coins and tried to give Gerald a larger than necessary sum with as few coins as possible. What is the maximum number of coins he could get?
The formal explanation of the previous paragraph: we consider all the possible combinations of coins for which the buyer can not give Gerald the sum of n marks without change. For each such combination calculate the minimum number of coins that can bring the buyer at least n marks. Among all combinations choose the maximum of the minimum number of coins. This is the number we want.
Input
The single line contains a single integer n (1 ≤ n ≤ 1017).
Please, do not use the %lld specifier to read or write 64 bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print an integer: the maximum number of coins the unlucky buyer could have paid with.
Examples
Input
1
Output
1
Input
4
Output
2
Note
In the first test case, if a buyer has exactly one coin of at least 3 marks, then, to give Gerald one mark, he will have to give this coin. In this sample, the customer can not have a coin of one mark, as in this case, he will be able to give the money to Gerald without any change.
In the second test case, if the buyer had exactly three coins of 3 marks, then, to give Gerald 4 marks, he will have to give two of these coins. The buyer cannot give three coins as he wants to minimize the number of coins that he gives.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 2\\n-1 1 2\\n\", \"2 3\\n-2 -2\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 216 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 23 183 102 -92 -157 -117 173 47 144 -235 -227 -62 -128 13 -151 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -189 -200 199 -57 -108 -53 269 -101 -134\\n\", \"4 1\\n-1 -1 -1 1\\n\", \"4 2\\n-1 -1 -1 -1\\n\", \"2 2\\n2 2\\n\", \"7 12\\n2 5 -1 -4 -7 4 3\\n\", \"2 2\\n-2 2\\n\", \"1 4\\n-3\\n\", \"1 1\\n1\\n\", \"2 2\\n-1 -1\\n\", \"10 300\\n300 300 300 300 300 300 300 300 300 300\\n\", \"10 7\\n6 4 6 6 -3 4 -1 2 3 3\\n\", \"8 13\\n-11 -1 -11 12 -2 -2 -10 -11\\n\", \"15 16\\n-15 -5 -15 -14 -8 15 -15 -12 -5 -3 5 -7 3 8 -15\\n\", \"2 2\\n1 -1\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 75 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 88 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -112 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 5 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 96 -81 -102 140 -58 -102 132 50 -126 82 6 45 -114 -42\\n\", \"123 222\\n44 -190 -188 -185 -55 17 190 176 157 176 -24 -113 -54 -61 -53 53 -77 68 -12 -114 -217 163 -122 37 -37 20 -108 17 -140 -210 218 19 -89 54 18 197 111 -150 -36 -131 -172 36 67 16 -202 72 169 -137 -34 -122 137 -72 196 -17 -104 180 -102 96 -69 -184 21 -15 217 -61 175 -221 62 173 -93 -106 122 -135 58 7 -110 -108 156 -141 -102 -50 29 -204 -46 -76 101 -33 -190 99 52 -197 175 -71 161 -140 155 10 189 -217 -97 -170 183 -88 83 -149 157 -208 154 -3 77 90 74 165 198 -181 -166 -4 -200 -89 -200 131 100 -61 -149\\n\", \"3 2\\n2 2 2\\n\", \"4 4\\n1 2 3 4\\n\", \"15 5\\n-2 -1 2 -4 -3 4 -4 -2 -2 2 -2 -1 1 -4 -2\\n\", \"1 1\\n-1\\n\", \"2 3\\n-1 1\\n\", \"1 1\\n0\\n\", \"1 1000\\n997\\n\", \"4 3\\n2 -1 -2 -1\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 13 -9 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -1 7 -14 9 -11 -11 13 -4 12 -11 -8 -5 -11 6 10 -2 6 9 9 6 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"2 1\\n1 -1\\n\", \"2 2\\n-1 1\\n\", \"16 11\\n3 -7 7 -9 -2 -3 -4 -2 -6 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -41 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -40 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -51 -32 -51 27 -50 -22 -12 41 3 15 24 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 23 183 102 -92 -157 -117 173 47 144 -235 -227 -62 -128 13 -151 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -189 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 12\\n2 5 -1 -4 -7 6 3\\n\", \"10 300\\n300 300 300 300 300 300 300 155 300 300\\n\", \"10 7\\n2 4 6 6 -3 4 -1 2 3 3\\n\", \"8 13\\n-11 -1 -6 12 -2 -2 -10 -11\\n\", \"15 16\\n-15 -1 -15 -14 -8 15 -15 -12 -5 -3 5 -7 3 8 -15\\n\", \"2 1\\n-1 1\\n\", \"16 11\\n3 -7 7 -9 -2 -4 -4 -2 -6 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -28 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -40 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -51 -32 -51 27 -50 -22 -12 41 3 15 24 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 75 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 88 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -83 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 5 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 96 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"2 2\\n-2 3\\n\", \"2 4\\n-1 -1\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 75 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 88 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -112 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 5 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 96 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"4 4\\n1 2 3 3\\n\", \"15 5\\n-2 -2 2 -4 -3 4 -4 -2 -2 2 -2 -1 1 -4 -2\\n\", \"1 2\\n-1\\n\", \"2 3\\n-1 0\\n\", \"1 1000\\n458\\n\", \"4 3\\n1 -1 -2 -1\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 13 -9 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -1 7 -14 9 -11 -11 13 -4 12 -11 -8 -5 -11 6 10 -2 6 9 9 4 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"2 1\\n1 -2\\n\", \"2 3\\n-2 -3\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 23 183 102 -92 -157 -117 173 47 144 -235 -227 -62 -128 14 -151 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -189 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 2\\n2 5 -1 -4 -7 6 3\\n\", \"2 2\\n-4 3\\n\", \"2 4\\n-1 0\\n\", \"10 300\\n300 300 300 300 300 300 300 289 300 300\\n\", \"10 7\\n2 6 6 6 -3 4 -1 2 3 3\\n\", \"8 13\\n-11 -1 -6 12 -2 -2 -10 -13\\n\", \"15 16\\n-15 -1 -15 -14 -8 15 -15 -12 -5 -3 5 -7 5 8 -15\\n\", \"15 5\\n-2 -2 2 -4 -3 4 -4 -3 -2 2 -2 -1 1 -4 -2\\n\", \"2 3\\n-1 -1\\n\", \"1 1100\\n458\\n\", \"4 6\\n1 -1 -2 -1\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 9 -9 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -1 7 -14 9 -11 -11 13 -4 12 -11 -8 -5 -11 6 10 -2 6 9 9 4 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"2 1\\n-1 0\\n\", \"16 11\\n3 -7 7 -9 -2 -4 -3 -2 -6 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -28 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -2 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -51 -32 -51 27 -50 -22 -12 41 3 15 24 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 23 183 102 -92 -157 -117 173 47 144 -235 -227 -62 -128 14 -17 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -189 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 3\\n2 5 -1 -4 -7 6 3\\n\", \"2 4\\n0 0\\n\", \"10 300\\n300 300 300 300 181 300 300 289 300 300\\n\", \"10 9\\n2 6 6 6 -3 4 -1 2 3 3\\n\", \"8 13\\n-11 -1 -6 12 -2 -2 -16 -13\\n\", \"15 16\\n-15 -1 -15 -14 -8 15 -30 -12 -5 -3 5 -7 5 8 -15\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 75 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 88 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -83 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 5 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 62 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"15 5\\n-2 -2 2 -4 -3 8 -4 -3 -2 2 -2 -1 1 -4 -2\\n\", \"2 3\\n-1 -2\\n\", \"1 1100\\n108\\n\", \"4 6\\n1 -2 -2 -1\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 9 -9 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -1 7 -14 9 -11 -11 13 -7 12 -11 -8 -5 -11 6 10 -2 6 9 9 4 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"2 1\\n-2 0\\n\", \"16 11\\n3 -7 7 -9 -2 -8 -3 -2 -6 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -28 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -2 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -51 -32 -51 27 -50 -22 -12 41 3 15 13 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 23 183 102 -92 -157 -117 173 47 144 -235 -227 -62 -128 14 -17 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -163 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 3\\n2 5 -1 -4 -7 8 3\\n\", \"10 300\\n300 300 311 300 181 300 300 289 300 300\\n\", \"10 9\\n2 6 7 6 -3 4 -1 2 3 3\\n\", \"8 13\\n-9 -1 -6 12 -2 -2 -16 -13\\n\", \"15 16\\n-15 -1 -15 -14 -14 15 -30 -12 -5 -3 5 -7 5 8 -15\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 75 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 88 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -83 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 0 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 62 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"15 5\\n-4 -2 2 -4 -3 8 -4 -3 -2 2 -2 -1 1 -4 -2\\n\", \"1 1000\\n108\\n\", \"4 6\\n1 -2 0 -1\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 9 -9 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -1 7 -14 9 -11 -11 13 -7 12 -11 -8 -5 -11 6 10 0 6 9 9 4 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"16 11\\n3 -7 7 -9 -2 -7 -3 -2 -6 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -28 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -2 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -51 -32 -51 27 -50 -22 -12 66 3 15 13 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 23 183 102 -92 -157 -117 173 47 218 -235 -227 -62 -128 14 -17 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -163 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 3\\n2 5 -1 -4 -4 8 3\\n\", \"10 9\\n2 6 7 6 -3 4 -1 2 3 4\\n\", \"8 13\\n-9 -1 -6 12 -2 -3 -16 -13\\n\", \"15 16\\n-15 -1 -15 -14 -14 6 -30 -12 -5 -3 5 -7 5 8 -15\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 76 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 88 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -83 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 0 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 62 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"15 5\\n-4 -2 2 -4 -3 8 -8 -3 -2 2 -2 -1 1 -4 -2\\n\", \"1 1010\\n108\\n\", \"4 5\\n1 -2 0 -1\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 9 -9 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -2 7 -14 9 -11 -11 13 -7 12 -11 -8 -5 -11 6 10 0 6 9 9 4 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"16 11\\n3 -7 7 -9 -2 -7 -3 -2 -3 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -28 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -2 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -51 -32 -51 27 -50 -22 -12 66 1 15 13 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -150 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 37 183 102 -92 -157 -117 173 47 218 -235 -227 -62 -128 14 -17 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -163 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 3\\n2 5 -2 -4 -4 8 3\\n\", \"10 9\\n2 6 7 6 -3 4 -1 2 4 4\\n\", \"8 13\\n-9 -1 -6 12 -2 -3 -22 -13\\n\", \"15 16\\n-15 -1 -15 -14 -14 6 -30 -12 -5 -3 5 -10 5 8 -15\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 76 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 10 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -83 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 0 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -75 19 108 108 127 141 2 -130 54 62 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"15 5\\n0 -2 2 -4 -3 8 -8 -3 -2 2 -2 -1 1 -4 -2\\n\", \"1 1010\\n120\\n\", \"4 5\\n1 -2 0 -2\\n\", \"67 15\\n-2 -2 6 -4 -7 4 3 9 -15 -4 11 -7 -6 -11 1 11 -1 11 14 10 -8 7 5 11 -13 1 -2 7 -14 9 -11 -11 13 -7 12 -11 -8 -5 -11 6 10 0 6 9 9 4 -11 -2 7 -10 -1 9 -8 -5 1 -7 -2 3 -1 -13 -6 -9 -8 10 13 -3 9\\n\", \"16 11\\n3 -7 7 -9 -4 -7 -3 -2 -3 8 10 7 1 4 6 7\\n\", \"57 53\\n-49 7 -28 7 38 -51 -23 8 45 1 -24 26 37 28 -31 -40 38 25 -32 -47 -3 20 -2 -32 -44 -36 5 33 -16 -5 28 10 -22 3 -10 -24 -32 -51 27 -50 -22 -12 66 1 15 13 30 -12 -34 -15 -29 38 -10 -35 -9 6 -51\\n\", \"93 273\\n-268 -170 -163 19 -69 18 -244 35 -34 125 -224 -48 179 -247 127 -37 271 -49 -102 201 84 -151 -70 -46 -16 317 240 127 3 218 -209 223 -227 -201 228 -8 203 46 -100 -207 126 255 40 -58 -217 93 172 -97 37 183 102 -92 -157 -117 173 47 218 -235 -227 -62 -128 14 -17 158 110 -116 68 -2 -148 -206 -52 79 -152 -223 74 -149 -69 232 38 -70 -256 -213 -236 132 -163 -200 199 -57 -108 -53 269 -101 -134\\n\", \"7 3\\n2 5 -2 -7 -4 8 3\\n\", \"10 9\\n2 3 7 6 -3 4 -1 2 4 4\\n\", \"8 13\\n-9 -1 -6 12 -2 -3 -39 -13\\n\", \"15 29\\n-15 -1 -15 -14 -14 6 -30 -12 -5 -3 5 -10 5 8 -15\\n\", \"130 142\\n58 -50 43 -126 84 -92 -108 -92 57 127 12 -135 -49 89 141 -112 -31 47 76 -19 80 81 -5 17 10 4 -26 68 -102 -10 7 -62 -135 -123 -16 55 -72 -97 -34 21 21 137 130 97 40 -18 110 -52 73 52 85 103 -134 -107 10 30 66 97 126 82 13 125 127 -87 81 22 45 102 13 95 4 10 -35 39 -43 -83 -5 14 -46 19 61 -44 -116 137 -116 -80 -39 92 -75 29 -65 -15 0 -108 -114 -129 -5 52 -21 118 -41 35 -62 -125 130 -95 -11 -15 19 108 108 127 141 2 -130 54 62 -81 -102 140 -58 -102 132 86 -126 82 6 45 -114 -42\\n\", \"15 5\\n0 -2 2 -4 -3 8 -8 -3 -2 3 -2 -1 1 -4 -2\\n\", \"1 1010\\n240\\n\", \"4 5\\n1 0 0 -2\\n\"], \"outputs\": [\"1\\n\", \"2\\n\", \"8\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"10\\n\", \"5\\n\", \"3\\n\", \"6\\n\", \"0\\n\", \"5\\n\", \"8\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"8\\n\", \"7\\n\", \"1\\n\", \"10\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"0\\n\", \"2\\n\", \"8\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"10\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"7\\n\", \"2\\n\", \"0\\n\", \"10\\n\", \"4\\n\", \"3\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"8\\n\", \"7\\n\", \"2\\n\", \"10\\n\", \"4\\n\", \"3\\n\", \"7\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"7\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"7\\n\", \"5\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"7\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"6\\n\", \"2\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
Vanya loves playing. He even has a special set of cards to play with. Each card has a single integer. The number on the card can be positive, negative and can even be equal to zero. The only limit is, the number on each card doesn't exceed x in the absolute value.
Natasha doesn't like when Vanya spends a long time playing, so she hid all of his cards. Vanya became sad and started looking for the cards but he only found n of them. Vanya loves the balance, so he wants the sum of all numbers on found cards equal to zero. On the other hand, he got very tired of looking for cards. Help the boy and say what is the minimum number of cards does he need to find to make the sum equal to zero?
You can assume that initially Vanya had infinitely many cards with each integer number from - x to x.
Input
The first line contains two integers: n (1 ≤ n ≤ 1000) — the number of found cards and x (1 ≤ x ≤ 1000) — the maximum absolute value of the number on a card. The second line contains n space-separated integers — the numbers on found cards. It is guaranteed that the numbers do not exceed x in their absolute value.
Output
Print a single number — the answer to the problem.
Examples
Input
3 2
-1 1 2
Output
1
Input
2 3
-2 -2
Output
2
Note
In the first sample, Vanya needs to find a single card with number -2.
In the second sample, Vanya needs to find two cards with number 2. He can't find a single card with the required number as the numbers on the lost cards do not exceed 3 in their absolute value.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"4\\n1 2 1 2\\n\", \"8\\n2 1 2 1 1 1 1 1\\n\", \"4\\n1 1 1 1\\n\", \"5\\n1 2 1 2 1\\n\", \"82\\n1 1 1 2 2 2 2 1 1 1 2 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 1 1 1 2 2 2 2 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2 2\\n\", \"14\\n2 1 2 1 1 1 1 2 1 1 2 1 2 1\\n\", \"10\\n1 1 2 2 1 1 2 2 1 1\\n\", \"1\\n1\\n\", \"186\\n2 1 2 1 1 1 1 1 2 1 1 2 2 2 1 1 2 2 1 1 1 2 1 1 2 2 1 1 1 2 2 1 1 1 1 1 2 1 1 1 2 1 2 1 1 2 1 1 1 2 2 2 2 2 2 2 1 2 1 2 1 1 2 1 2 2 1 1 1 1 1 2 2 1 2 2 1 2 2 1 1 1 2 2 1 1 2 2 1 2 2 1 2 2 2 2 2 1 1 1 1 2 1 1 2 2 2 2 2 2 1 1 1 1 1 2 1 1 2 2 1 2 2 1 1 1 1 1 2 2 1 1 2 2 1 2 2 2 1 2 1 2 1 1 2 1 2 2 2 2 1 2 1 2 2 1 2 1 1 1 1 1 2 1 1 2 2 1 1 1 2 2 2 1 2 2 1 1 2 1 1 1 1 2 1 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1\\n\", \"1\\n2\\n\", \"20\\n1 1 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1\\n\", \"14\\n2 1 2 1 2 1 1 2 1 1 2 1 2 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1\\n\", \"20\\n1 1 2 2 2 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1\\n\", \"8\\n2 1 2 1 2 1 1 1\\n\", \"5\\n1 2 1 2 2\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1\\n\", \"5\\n1 2 2 2 2\\n\", \"8\\n2 1 1 1 2 1 1 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1\\n\", \"14\\n2 1 2 2 1 1 1 2 1 1 2 1 2 1\\n\", \"8\\n2 2 2 1 1 1 1 1\\n\", \"14\\n2 1 2 2 2 1 1 2 1 1 2 1 2 1\\n\", \"82\\n1 1 1 2 2 2 2 1 1 1 2 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 1 1 1 2 2 2 2 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2 2\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 1 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 1 1\\n\", \"8\\n2 1 1 1 1 1 1 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1\\n\", \"4\\n1 2 2 2\\n\", \"14\\n2 1 2 1 2 1 1 2 2 1 2 1 2 1\\n\", \"5\\n1 1 1 2 2\\n\", \"14\\n2 1 2 2 2 1 1 2 2 1 2 1 2 1\\n\", \"4\\n1 2 1 1\\n\", \"20\\n1 1 2 2 2 1 2 2 2 2 2 2 1 2 2 1 2 1 2 1\\n\", \"8\\n2 1 2 1 2 2 1 1\\n\", \"4\\n1 1 2 2\\n\", \"14\\n2 1 2 2 1 1 1 2 1 1 2 2 2 1\\n\", \"4\\n2 2 1 1\\n\", \"8\\n2 2 2 1 1 1 1 2\\n\", \"20\\n1 1 2 2 2 1 2 2 2 2 2 1 1 2 2 1 2 1 2 1\\n\", \"4\\n2 2 1 2\\n\", \"4\\n2 2 2 2\\n\", \"14\\n2 1 2 1 2 2 1 2 1 1 2 1 2 1\\n\", \"20\\n1 1 1 2 2 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1\\n\", \"8\\n2 2 1 1 2 1 1 1\\n\", \"5\\n2 2 2 2 2\\n\", \"14\\n2 2 2 2 2 1 1 2 2 1 2 1 2 1\\n\", \"20\\n1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 1 2 1 2 1\\n\", \"8\\n2 2 2 1 1 2 1 2\\n\", \"20\\n1 1 1 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 1\\n\", \"8\\n2 2 1 1 2 1 1 2\\n\", \"20\\n1 1 1 2 2 1 2 2 2 2 2 1 2 2 2 1 2 2 2 1\\n\", \"83\\n1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 1 2\\n\", \"20\\n1 1 1 2 2 1 2 2 2 2 2 1 1 2 2 1 2 2 2 1\\n\", \"20\\n1 1 2 2 2 1 2 2 2 2 2 1 1 2 2 1 2 2 2 1\\n\", \"20\\n2 1 2 2 2 1 2 2 2 2 2 1 1 2 2 1 2 2 2 1\\n\", \"20\\n2 1 2 2 1 1 2 2 2 2 2 1 1 2 2 1 2 2 2 1\\n\", \"20\\n2 1 2 2 1 1 2 2 2 2 2 1 1 2 2 1 1 2 2 1\\n\", \"14\\n2 1 2 2 1 1 1 2 2 1 2 1 2 1\\n\", \"5\\n1 2 1 1 1\\n\", \"8\\n2 1 2 1 2 1 1 2\\n\"], \"outputs\": [\"0\\n\", \"3\\n1 6\\n2 3\\n6 1\\n\", \"3\\n1 4\\n2 2\\n4 1\\n\", \"2\\n1 3\\n3 1\\n\", \"0\\n\", \"3\\n1 9\\n3 3\\n9 1\\n\", \"4\\n1 6\\n2 3\\n3 2\\n6 1\\n\", \"1\\n1 1\\n\", \"8\\n1 100\\n2 50\\n6 11\\n8 8\\n19 4\\n25 3\\n40 2\\n100 1\\n\", \"5\\n1 45\\n3 10\\n3 15\\n4 7\\n45 1\\n\", \"1\\n1 1\\n\", \"0\\n\", \"4\\n1 8\\n2 3\\n2 4\\n8 1\\n\", \"4\\n1 44\\n2 22\\n3 10\\n44 1\\n\", \"0\\n\", \"3\\n1 5\\n2 2\\n5 1\\n\", \"2\\n1 3\\n3 1\\n\", \"4\\n1 45\\n3 15\\n4 8\\n45 1\\n\", \"3\\n1 4\\n2 2\\n4 1\\n\", \"4\\n1 6\\n2 3\\n3 2\\n6 1\\n\", \"4\\n1 46\\n2 23\\n5 8\\n46 1\\n\", \"3\\n1 8\\n2 4\\n8 1\\n\", \"2\\n1 5\\n5 1\\n\", \"1\\n2 3\\n\", \"3\\n1 42\\n12 3\\n42 1\\n\", \"7\\n1 45\\n3 10\\n3 13\\n3 15\\n5 8\\n8 4\\n45 1\\n\", \"6\\n1 44\\n2 15\\n2 22\\n4 8\\n8 4\\n44 1\\n\", \"2\\n1 7\\n7 1\\n\", \"4\\n1 46\\n2 23\\n5 7\\n46 1\\n\", \"2\\n1 43\\n43 1\\n\", \"4\\n1 44\\n2 22\\n3 10\\n44 1\\n\", \"2\\n1 3\\n3 1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n1 3\\n3 1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n1 3\\n3 1\\n\", \"3\\n1 4\\n2 2\\n4 1\\n\", \"0\\n\", \"0\\n\", \"2\\n1 5\\n5 1\\n\", \"2\\n1 5\\n5 1\\n\", \"0\\n\", \"0\\n\", \"3\\n1 5\\n2 2\\n5 1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n1 4\\n2 2\\n4 1\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Petya and Gena love playing table tennis. A single match is played according to the following rules: a match consists of multiple sets, each set consists of multiple serves. Each serve is won by one of the players, this player scores one point. As soon as one of the players scores t points, he wins the set; then the next set starts and scores of both players are being set to 0. As soon as one of the players wins the total of s sets, he wins the match and the match is over. Here s and t are some positive integer numbers.
To spice it up, Petya and Gena choose new numbers s and t before every match. Besides, for the sake of history they keep a record of each match: that is, for each serve they write down the winner. Serve winners are recorded in the chronological order. In a record the set is over as soon as one of the players scores t points and the match is over as soon as one of the players wins s sets.
Petya and Gena have found a record of an old match. Unfortunately, the sequence of serves in the record isn't divided into sets and numbers s and t for the given match are also lost. The players now wonder what values of s and t might be. Can you determine all the possible options?
Input
The first line contains a single integer n — the length of the sequence of games (1 ≤ n ≤ 105).
The second line contains n space-separated integers ai. If ai = 1, then the i-th serve was won by Petya, if ai = 2, then the i-th serve was won by Gena.
It is not guaranteed that at least one option for numbers s and t corresponds to the given record.
Output
In the first line print a single number k — the number of options for numbers s and t.
In each of the following k lines print two integers si and ti — the option for numbers s and t. Print the options in the order of increasing si, and for equal si — in the order of increasing ti.
Examples
Input
5
1 2 1 2 1
Output
2
1 3
3 1
Input
4
1 1 1 1
Output
3
1 4
2 2
4 1
Input
4
1 2 1 2
Output
0
Input
8
2 1 2 1 1 1 1 1
Output
3
1 6
2 3
6 1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"1\\n1 1\\n\", \"2\\n0 0\\n1 1\\n\", \"3\\n0 0\\n0 3\\n3 0\\n\", \"3\\n-679 301\\n240 -23\\n-679 -23\\n\", \"2\\n-457 82\\n260 -662\\n\", \"3\\n0 1\\n1 0\\n0 0\\n\", \"1\\n-717 916\\n\", \"4\\n-64 -509\\n-64 960\\n634 -509\\n634 960\\n\", \"3\\n2 1\\n2 4\\n6 1\\n\", \"3\\n1 0\\n1 -1\\n0 0\\n\", \"3\\n-2 -1\\n-1 -1\\n-1 -2\\n\", \"3\\n0 0\\n0 1\\n2 0\\n\", \"3\\n0 1\\n0 0\\n1 1\\n\", \"2\\n-739 -724\\n-739 443\\n\", \"2\\n-748 697\\n671 575\\n\", \"1\\n720 -200\\n\", \"3\\n0 0\\n5 0\\n5 5\\n\", \"3\\n1 5\\n2 2\\n2 5\\n\", \"3\\n0 0\\n0 1\\n1 1\\n\", \"2\\n-1000 -1000\\n0 -1000\\n\", \"4\\n137 -184\\n137 700\\n712 -184\\n712 700\\n\", \"1\\n-188 17\\n\", \"2\\n295 710\\n295 254\\n\", \"3\\n0 0\\n2 0\\n0 2\\n\", \"4\\n5 -952\\n5 292\\n553 -952\\n553 292\\n\", \"2\\n-862 -181\\n-525 -181\\n\", \"4\\n2 0\\n2 8\\n5 8\\n5 0\\n\", \"2\\n-823 358\\n446 358\\n\", \"3\\n0 0\\n1 0\\n1 1\\n\", \"2\\n-187 583\\n25 13\\n\", \"3\\n-282 584\\n696 488\\n-282 488\\n\", \"3\\n-487 838\\n134 691\\n-487 691\\n\", \"4\\n-796 -330\\n-796 758\\n171 -330\\n171 758\\n\", \"3\\n3 5\\n3 2\\n7 2\\n\", \"4\\n-414 -891\\n-414 896\\n346 -891\\n346 896\\n\", \"4\\n-474 -894\\n-474 -833\\n-446 -894\\n-446 -833\\n\", \"3\\n5 0\\n0 0\\n5 5\\n\", \"1\\n858 -279\\n\", \"3\\n1 4\\n4 4\\n4 1\\n\", \"1\\n71 -740\\n\", \"2\\n980 -230\\n980 592\\n\", \"3\\n0 1\\n1 0\\n1 1\\n\", \"2\\n-386 95\\n-386 750\\n\", \"3\\n1 1\\n1 2\\n2 2\\n\", \"1\\n-164 -730\\n\", \"3\\n1 1\\n0 0\\n1 0\\n\", \"4\\n459 -440\\n459 -94\\n872 -440\\n872 -94\\n\", \"4\\n0 0\\n1 0\\n0 1\\n1 1\\n\", \"3\\n0 0\\n2 0\\n0 1\\n\", \"2\\n-414 -431\\n-377 -688\\n\", \"3\\n0 0\\n0 5\\n5 0\\n\", \"4\\n1 1\\n3 3\\n3 1\\n1 3\\n\", \"3\\n1 2\\n1 3\\n2 2\\n\", \"3\\n-639 51\\n-321 -539\\n-639 -539\\n\", \"2\\n0 3\\n3 3\\n\", \"2\\n-559 894\\n314 127\\n\", \"2\\n-337 451\\n32 -395\\n\", \"2\\n0 999\\n100 250\\n\", \"3\\n-890 778\\n-418 296\\n-890 296\\n\", \"2\\n1 0\\n0 1\\n\", \"3\\n0 1\\n0 0\\n1 0\\n\", \"4\\n0 1\\n0 0\\n1 0\\n1 1\\n\", \"2\\n541 611\\n-26 611\\n\", \"2\\n-922 -505\\n712 -683\\n\", \"3\\n1 0\\n0 0\\n0 1\\n\", \"3\\n1 0\\n1 3\\n5 0\\n\", \"2\\n0 0\\n-1 -1\\n\", \"2\\n-612 208\\n326 -559\\n\", \"3\\n1 2\\n1 3\\n2 3\\n\", \"2\\n-257 715\\n102 715\\n\", \"4\\n-56 -858\\n-56 -174\\n778 -858\\n778 -174\\n\", \"2\\n686 664\\n686 -590\\n\", \"2\\n-480 51\\n89 -763\\n\", \"3\\n79 79\\n79 158\\n158 79\\n\", \"2\\n1 0\\n2 1\\n\", \"3\\n1 0\\n5 0\\n5 10\\n\", \"3\\n2 1\\n1 2\\n2 2\\n\", \"3\\n1 1\\n1 2\\n2 1\\n\", \"4\\n-152 198\\n-152 366\\n458 198\\n458 366\\n\", \"4\\n-925 306\\n-925 602\\n398 306\\n398 602\\n\", \"3\\n1 1\\n1 5\\n5 1\\n\", \"1\\n-271 -499\\n\", \"3\\n0 0\\n10 0\\n0 10\\n\", \"4\\n0 0\\n1 0\\n1 1\\n0 1\\n\", \"3\\n576 -659\\n917 -739\\n576 -739\\n\", \"3\\n-318 831\\n450 31\\n-318 31\\n\", \"3\\n0 0\\n2 0\\n2 1\\n\", \"3\\n0 0\\n0 1\\n5 0\\n\", \"3\\n0 0\\n0 -1\\n1 -1\\n\", \"3\\n5 0\\n0 0\\n0 5\\n\", \"3\\n0 0\\n0 5\\n5 5\\n\", \"3\\n-281 598\\n679 -990\\n-281 -990\\n\", \"2\\n-3 0\\n3 3\\n\", \"2\\n380 -849\\n68 -849\\n\", \"1\\n193 304\\n\", \"3\\n258 937\\n395 856\\n258 856\\n\", \"3\\n0 0\\n0 1\\n1 0\\n\", \"4\\n852 -184\\n852 724\\n970 -184\\n970 724\\n\", \"3\\n0 0\\n0 2\\n2 0\\n\", \"3\\n0 4\\n3 4\\n3 1\\n\", \"1\\n627 -250\\n\", \"2\\n14 153\\n566 -13\\n\", \"4\\n259 153\\n259 999\\n266 153\\n266 999\\n\", \"3\\n0 0\\n1 0\\n0 1\\n\", \"3\\n-406 566\\n428 426\\n-406 426\\n\", \"1\\n-841 -121\\n\", \"3\\n4 4\\n1 4\\n4 1\\n\", \"3\\n0 0\\n1 0\\n1 2\\n\", \"2\\n-1000 -1000\\n-1000 0\\n\", \"2\\n-761 907\\n967 907\\n\", \"2\\n-259 -978\\n978 -978\\n\", \"2\\n157 994\\n377 136\\n\", \"3\\n1 1\\n0 1\\n1 0\\n\", \"3\\n1 1\\n2 1\\n1 2\\n\", \"1\\n-227 -825\\n\", \"2\\n56 31\\n704 -121\\n\", \"4\\n0 0\\n0 1\\n1 1\\n1 0\\n\", \"3\\n1 1\\n1 3\\n3 1\\n\", \"3\\n-686 695\\n-547 308\\n-686 308\\n\", \"2\\n115 730\\n562 -546\\n\", \"2\\n247 -457\\n434 -921\\n\", \"2\\n-457 82\\n422 -662\\n\", \"1\\n-717 1347\\n\", \"2\\n-748 697\\n671 638\\n\", \"2\\n-823 358\\n446 509\\n\", \"2\\n-187 583\\n25 14\\n\", \"3\\n-282 88\\n696 488\\n-282 488\\n\", \"3\\n5 0\\n1 0\\n5 5\\n\", \"3\\n1 4\\n4 4\\n4 0\\n\", \"2\\n-414 -431\\n-377 -1000\\n\", \"3\\n0 0\\n0 5\\n6 0\\n\", \"2\\n-559 377\\n314 127\\n\", \"2\\n-148 451\\n32 -395\\n\", \"2\\n0 1542\\n100 250\\n\", \"2\\n1 0\\n-1 1\\n\", \"2\\n-922 -505\\n712 -85\\n\", \"2\\n-612 208\\n326 -1109\\n\", \"2\\n-257 715\\n102 510\\n\", \"2\\n-387 51\\n89 -763\\n\", \"3\\n79 79\\n79 185\\n158 79\\n\", \"2\\n1 0\\n4 1\\n\", \"3\\n1 0\\n5 0\\n5 20\\n\", \"3\\n0 0\\n6 0\\n0 10\\n\", \"2\\n-6 0\\n3 3\\n\", \"2\\n20 153\\n566 -13\\n\", \"3\\n-406 566\\n156 426\\n-406 426\\n\", \"2\\n157 994\\n106 136\\n\", \"2\\n56 31\\n704 -228\\n\", \"3\\n1 1\\n1 3\\n6 1\\n\", \"2\\n115 730\\n562 -135\\n\", \"2\\n247 -457\\n44 -921\\n\", \"2\\n-386 82\\n422 -662\\n\", \"2\\n-851 -990\\n-739 443\\n\", \"2\\n-748 697\\n671 320\\n\", \"2\\n-840 358\\n446 509\\n\", \"2\\n-187 583\\n20 14\\n\", \"3\\n-282 174\\n696 488\\n-282 488\\n\", \"3\\n2 4\\n4 4\\n4 0\\n\", \"2\\n-609 -431\\n-377 -1000\\n\", \"2\\n-559 377\\n314 38\\n\", \"2\\n-288 451\\n32 -395\\n\", \"2\\n1 1542\\n100 250\\n\", \"2\\n1 0\\n-1 2\\n\", \"2\\n-922 -82\\n712 -85\\n\", \"2\\n-612 208\\n526 -1109\\n\", \"2\\n-277 715\\n102 510\\n\", \"2\\n-387 51\\n89 -1303\\n\", \"3\\n0 0\\n6 0\\n0 20\\n\", \"2\\n-739 -990\\n-739 443\\n\", \"1\\n55 -200\\n\", \"2\\n-1980 -1000\\n0 -1000\\n\", \"1\\n-188 24\\n\", \"2\\n295 710\\n295 397\\n\", \"2\\n-1188 -181\\n-525 -181\\n\", \"1\\n858 -553\\n\", \"1\\n71 -752\\n\", \"2\\n980 -221\\n980 592\\n\", \"2\\n-386 95\\n-386 1230\\n\", \"1\\n-164 -668\\n\", \"2\\n541 611\\n-24 611\\n\", \"3\\n2 0\\n0 0\\n0 1\\n\", \"2\\n0 0\\n-1 0\\n\", \"3\\n1 1\\n1 3\\n2 3\\n\", \"2\\n686 664\\n686 -968\\n\", \"1\\n-271 -777\\n\", \"3\\n4 0\\n0 0\\n0 5\\n\", \"2\\n8 -849\\n68 -849\\n\", \"1\\n14 304\\n\", \"1\\n627 -411\\n\", \"1\\n-841 -113\\n\", \"3\\n4 4\\n1 4\\n4 0\\n\", \"2\\n-1015 907\\n967 907\\n\", \"2\\n-259 -978\\n1314 -978\\n\", \"1\\n-227 -283\\n\", \"1\\n0 1\\n\", \"2\\n0 -1\\n1 1\\n\", \"1\\n-717 520\\n\", \"1\\n51 -200\\n\", \"2\\n-1232 -1000\\n0 -1000\\n\", \"1\\n-299 24\\n\", \"2\\n295 710\\n295 61\\n\", \"2\\n-1188 -181\\n-310 -181\\n\", \"1\\n1125 -553\\n\", \"1\\n15 -752\\n\", \"2\\n980 -221\\n980 930\\n\", \"2\\n-386 162\\n-386 1230\\n\", \"1\\n-164 -726\\n\", \"2\\n941 611\\n-24 611\\n\", \"3\\n1 0\\n0 0\\n0 2\\n\", \"2\\n1 0\\n-1 0\\n\", \"2\\n686 242\\n686 -968\\n\", \"2\\n1 0\\n0 0\\n\", \"1\\n-271 -969\\n\", \"3\\n6 0\\n0 0\\n0 5\\n\", \"2\\n-6 0\\n3 0\\n\", \"2\\n11 -849\\n68 -849\\n\", \"1\\n15 304\\n\"], \"outputs\": [\"-1\\n\", \"1\\n\", \"9\\n\", \"297756\\n\", \"533448\\n\", \"1\\n\", \"-1\\n\", \"1025362\\n\", \"12\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"-1\\n\", \"173118\\n\", \"-1\\n\", \"25\\n\", \"3\\n\", \"1\\n\", \"-1\\n\", \"508300\\n\", \"-1\\n\", \"-1\\n\", \"4\\n\", \"681712\\n\", \"-1\\n\", \"24\\n\", \"-1\\n\", \"1\\n\", \"120840\\n\", \"93888\\n\", \"91287\\n\", \"1052096\\n\", \"12\\n\", \"1358120\\n\", \"1708\\n\", \"25\\n\", \"-1\\n\", \"9\\n\", \"-1\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"142898\\n\", \"1\\n\", \"2\\n\", \"9509\\n\", \"25\\n\", \"4\\n\", \"1\\n\", \"187620\\n\", \"-1\\n\", \"669591\\n\", \"312174\\n\", \"74900\\n\", \"227504\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"290852\\n\", \"1\\n\", \"12\\n\", \"1\\n\", \"719446\\n\", \"1\\n\", \"-1\\n\", \"570456\\n\", \"-1\\n\", \"463166\\n\", \"6241\\n\", \"1\\n\", \"40\\n\", \"1\\n\", \"1\\n\", \"102480\\n\", \"391608\\n\", \"16\\n\", \"-1\\n\", \"100\\n\", \"1\\n\", \"27280\\n\", \"614400\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"25\\n\", \"25\\n\", \"1524480\\n\", \"18\\n\", \"-1\\n\", \"-1\\n\", \"11097\\n\", \"1\\n\", \"107144\\n\", \"4\\n\", \"9\\n\", \"-1\\n\", \"91632\\n\", \"5922\\n\", \"1\\n\", \"116760\\n\", \"-1\\n\", \"9\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"188760\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"98496\\n\", \"1\\n\", \"4\\n\", \"53793\\n\", \"570372\\n\", \"86768\\n\", \"653976\\n\", \"-1\\n\", \"83721\\n\", \"191619\\n\", \"120628\\n\", \"391200\\n\", \"20\\n\", \"12\\n\", \"21053\\n\", \"30\\n\", \"218250\\n\", \"152280\\n\", \"129200\\n\", \"2\\n\", \"686280\\n\", \"1235346\\n\", \"73595\\n\", \"387464\\n\", \"8374\\n\", \"3\\n\", \"80\\n\", \"60\\n\", \"27\\n\", \"90636\\n\", \"78680\\n\", \"43758\\n\", \"167832\\n\", \"10\\n\", \"386655\\n\", \"94192\\n\", \"601152\\n\", \"160496\\n\", \"534963\\n\", \"194186\\n\", \"117783\\n\", \"307092\\n\", \"8\\n\", \"132008\\n\", \"295947\\n\", \"270720\\n\", \"127908\\n\", \"4\\n\", \"4902\\n\", \"1498746\\n\", \"77695\\n\", \"644504\\n\", \"120\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"20\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"12\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"30\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\"]}", "source": "primeintellect"}
|
After making bad dives into swimming pools, Wilbur wants to build a swimming pool in the shape of a rectangle in his backyard. He has set up coordinate axes, and he wants the sides of the rectangle to be parallel to them. Of course, the area of the rectangle must be positive. Wilbur had all four vertices of the planned pool written on a paper, until his friend came along and erased some of the vertices.
Now Wilbur is wondering, if the remaining n vertices of the initial rectangle give enough information to restore the area of the planned swimming pool.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 4) — the number of vertices that were not erased by Wilbur's friend.
Each of the following n lines contains two integers xi and yi ( - 1000 ≤ xi, yi ≤ 1000) —the coordinates of the i-th vertex that remains. Vertices are given in an arbitrary order.
It's guaranteed that these points are distinct vertices of some rectangle, that has positive area and which sides are parallel to the coordinate axes.
Output
Print the area of the initial rectangle if it could be uniquely determined by the points remaining. Otherwise, print - 1.
Examples
Input
2
0 0
1 1
Output
1
Input
1
1 1
Output
-1
Note
In the first sample, two opposite corners of the initial rectangle are given, and that gives enough information to say that the rectangle is actually a unit square.
In the second sample there is only one vertex left and this is definitely not enough to uniquely define the area.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"2 -1 0 5 3\\n0 2\\n5 2\\n\", \"4 0 0 5 0\\n9 4\\n8 3\\n-1 0\\n1 4\\n\", \"10 -68 10 87 22\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n21 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"1 -10000000 -10000000 -10000000 -9999999\\n10000000 10000000\\n\", \"5 -6 -4 0 10\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n-8 10\\n\", \"10 -18 10 87 22\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n21 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"5 -6 -4 -1 10\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n-8 10\\n\", \"2 -1 0 5 4\\n0 2\\n5 2\\n\", \"4 0 0 3 0\\n9 4\\n8 3\\n-1 0\\n1 4\\n\", \"2 -1 0 5 6\\n0 2\\n5 2\\n\", \"5 -6 -4 -1 8\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n0 10\\n\", \"2 -1 0 6 6\\n0 2\\n5 2\\n\", \"10 -17 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"5 -6 -4 -1 11\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n0 10\\n\", \"4 0 0 3 -1\\n9 4\\n8 4\\n-1 0\\n1 4\\n\", \"10 -25 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -27\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -27\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -7\\n-98 -14\\n-4 31\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -14\\n-150 -6\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -14\\n-288 -6\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -379\\n-52 25\\n142 -28\\n-5 95\\n20 25\\n4 -1\\n45 -28\\n-288 -6\\n-4 59\\n\", \"10 -68 10 87 22\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n21 25\\n2 -3\\n45 -9\\n-98 -56\\n-15 16\\n\", \"1 -10000000 -10000000 -10000000 -6994405\\n10000000 10000000\\n\", \"5 -6 -4 0 17\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n-8 10\\n\", \"4 0 0 5 0\\n9 4\\n8 6\\n-1 0\\n1 4\\n\", \"10 -18 10 87 22\\n30 89\\n40 -97\\n-52 25\\n76 -22\\n-20 95\\n21 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"5 -6 -4 -1 13\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n-8 10\\n\", \"2 -1 0 5 4\\n1 2\\n5 2\\n\", \"2 -1 0 5 9\\n0 2\\n5 2\\n\", \"5 -6 -6 -1 8\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n0 10\\n\", \"2 -1 0 8 6\\n0 2\\n5 2\\n\", \"5 -6 -4 -1 11\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n0 0\\n\", \"10 -49 10 87 36\\n30 89\\n25 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"10 -49 10 81 36\\n30 89\\n82 -97\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -56\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -53\\n-4 16\\n\", \"10 -18 10 87 22\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"5 -6 -4 -1 10\\n-7 6\\n-9 7\\n-5 -1\\n-2 1\\n0 10\\n\", \"4 0 0 3 0\\n9 4\\n8 3\\n-1 0\\n0 4\\n\", \"10 -18 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"4 0 0 3 0\\n9 4\\n8 4\\n-1 0\\n1 4\\n\", \"10 -17 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"4 0 0 3 -1\\n9 4\\n8 4\\n-1 0\\n2 4\\n\", \"10 -17 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"4 0 0 3 -1\\n9 4\\n8 4\\n-1 0\\n2 2\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -56\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -14\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n45 -7\\n-98 -14\\n-4 31\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -7\\n-98 -14\\n-4 31\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -7\\n-98 -14\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -14\\n-98 -14\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n76 -28\\n-5 95\\n20 25\\n4 -1\\n45 -14\\n-98 -6\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n133 -28\\n-5 95\\n20 25\\n4 -1\\n45 -14\\n-288 -6\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n142 -28\\n-5 95\\n20 25\\n4 -1\\n45 -14\\n-288 -6\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -200\\n-52 25\\n142 -28\\n-5 95\\n20 25\\n4 -1\\n45 -28\\n-288 -6\\n-4 59\\n\", \"10 -49 10 87 36\\n30 89\\n82 -379\\n-52 25\\n142 -28\\n-5 95\\n20 25\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 89\\n82 -379\\n-52 25\\n142 -38\\n-5 95\\n20 25\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 89\\n82 -379\\n-52 25\\n142 -38\\n-5 95\\n20 14\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 114\\n82 -379\\n-52 25\\n142 -38\\n-5 95\\n20 14\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 114\\n82 -379\\n-52 25\\n142 -38\\n-5 95\\n20 20\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 95\\n20 20\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n4 -1\\n45 -28\\n-288 -6\\n-4 45\\n\", \"10 -49 10 87 36\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n4 -1\\n45 -28\\n-288 -6\\n-2 45\\n\", \"10 -49 10 87 36\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n45 -28\\n-288 -6\\n-2 45\\n\", \"10 -49 10 104 36\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n45 -28\\n-288 -6\\n-2 45\\n\", \"10 -49 10 180 36\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n45 -28\\n-288 -6\\n-2 45\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n45 -28\\n-288 -6\\n-2 45\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n45 -28\\n-393 -6\\n-2 45\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n45 -28\\n-143 -6\\n-2 45\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n51 -28\\n-143 -6\\n-2 45\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 -1\\n51 -28\\n-143 -6\\n-2 2\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 25\\n142 -38\\n-5 138\\n20 20\\n5 0\\n51 -28\\n-143 -6\\n-2 2\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 13\\n142 -38\\n-5 138\\n20 20\\n5 0\\n51 -28\\n-143 -6\\n-2 2\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 13\\n142 -38\\n-5 138\\n20 20\\n8 0\\n51 -28\\n-143 -6\\n-2 2\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-49 2\\n142 -38\\n-5 138\\n20 20\\n8 0\\n51 -28\\n-143 -6\\n-2 2\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-56 2\\n142 -38\\n-5 138\\n20 20\\n8 0\\n51 -28\\n-143 -6\\n-2 2\\n\", \"10 -49 10 180 60\\n30 114\\n82 -379\\n-56 1\\n142 -38\\n-5 138\\n20 20\\n8 0\\n51 -28\\n-143 -6\\n-2 2\\n\", \"2 -2 0 5 3\\n0 2\\n5 2\\n\", \"4 1 0 3 0\\n9 4\\n8 3\\n-1 0\\n1 4\\n\", \"10 -18 10 87 22\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n3 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"4 0 1 3 0\\n9 4\\n8 3\\n-1 0\\n0 4\\n\", \"10 -18 10 87 36\\n30 89\\n82 -97\\n-23 25\\n76 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"4 -1 0 3 0\\n9 4\\n8 4\\n-1 0\\n1 4\\n\", \"10 -17 10 87 36\\n30 89\\n82 -97\\n-52 25\\n99 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-15 16\\n\", \"4 0 0 3 -1\\n9 4\\n8 4\\n-1 0\\n1 2\\n\", \"10 -17 10 87 57\\n30 89\\n82 -97\\n-52 25\\n76 -22\\n-20 95\\n20 25\\n2 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"10 -17 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -13\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"4 0 0 3 -1\\n9 4\\n0 4\\n-1 0\\n2 2\\n\", \"10 -25 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -23\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-26 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n4 -22\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -97\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -3\\n45 -7\\n-98 -56\\n-4 2\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n7 -1\\n45 -7\\n-98 -27\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-20 95\\n20 0\\n4 -1\\n45 -7\\n-98 -14\\n-4 16\\n\", \"10 -49 10 87 36\\n30 89\\n82 -187\\n-52 25\\n76 -28\\n-20 95\\n20 25\\n4 -1\\n81 -7\\n-98 -14\\n-4 31\\n\"], \"outputs\": [\"6\\n\", \"33\\n\", \"22034\\n\", \"799999960000001\\n\", \"100\\n\", \"21449\\n\", \"92\\n\", \"9\\n\", \"52\\n\", \"21\\n\", \"75\\n\", \"22\\n\", \"21250\\n\", \"111\\n\", \"61\\n\", \"22898\\n\", \"24471\\n\", \"21484\\n\", \"49754\\n\", \"55721\\n\", \"57933\\n\", \"61261\\n\", \"168482\\n\", \"22034\\n\", \"688809801304025\\n\", \"200\\n\", \"45\\n\", \"14813\\n\", \"141\\n\", \"12\\n\", \"40\\n\", \"91\\n\", \"30\\n\", \"130\\n\", \"16925\\n\", \"24447\\n\", \"24084\\n\", \"21449\\n\", \"92\\n\", \"52\\n\", \"21449\\n\", \"52\\n\", \"21250\\n\", \"61\\n\", \"21250\\n\", \"61\\n\", \"24471\\n\", \"24471\\n\", \"24471\\n\", \"49754\\n\", \"49754\\n\", \"49754\\n\", \"55721\\n\", \"55721\\n\", \"55721\\n\", \"61261\\n\", \"61261\\n\", \"61261\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"168482\\n\", \"9\\n\", \"52\\n\", \"21449\\n\", \"52\\n\", \"21449\\n\", \"52\\n\", \"21250\\n\", \"61\\n\", \"21250\\n\", \"21250\\n\", \"61\\n\", \"22898\\n\", \"24471\\n\", \"24471\\n\", \"49754\\n\", \"49754\\n\", \"49754\\n\"]}", "source": "primeintellect"}
|
A flowerbed has many flowers and two fountains.
You can adjust the water pressure and set any values r1(r1 ≥ 0) and r2(r2 ≥ 0), giving the distances at which the water is spread from the first and second fountain respectively. You have to set such r1 and r2 that all the flowers are watered, that is, for each flower, the distance between the flower and the first fountain doesn't exceed r1, or the distance to the second fountain doesn't exceed r2. It's OK if some flowers are watered by both fountains.
You need to decrease the amount of water you need, that is set such r1 and r2 that all the flowers are watered and the r12 + r22 is minimum possible. Find this minimum value.
Input
The first line of the input contains integers n, x1, y1, x2, y2 (1 ≤ n ≤ 2000, - 107 ≤ x1, y1, x2, y2 ≤ 107) — the number of flowers, the coordinates of the first and the second fountain.
Next follow n lines. The i-th of these lines contains integers xi and yi ( - 107 ≤ xi, yi ≤ 107) — the coordinates of the i-th flower.
It is guaranteed that all n + 2 points in the input are distinct.
Output
Print the minimum possible value r12 + r22. Note, that in this problem optimal answer is always integer.
Examples
Input
2 -1 0 5 3
0 2
5 2
Output
6
Input
4 0 0 5 0
9 4
8 3
-1 0
1 4
Output
33
Note
The first sample is (r12 = 5, r22 = 1): <image> The second sample is (r12 = 1, r22 = 32): <image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"2 9 2 3\\n6 4\\n\", \"3 10 1 3\\n3 4 7\\n\", \"3 12000 2000 245\\n3000 9003 7001\\n\", \"13 91 1 3\\n5 12 17 22 29 36 43 49 57 64 70 74 84\\n\", \"9 82 14 4\\n10 18 28 38 46 55 64 74 79\\n\", \"8 51 2 1\\n6 14 20 26 29 35 40 48\\n\", \"3 20000 4000 3502\\n5000 8500 15000\\n\", \"4 10 1 7\\n2 4 6 8\\n\", \"12 89 14 9\\n6 11 18 24 33 37 45 51 60 69 71 80\\n\", \"10 42 1 3\\n1 6 10 15 17 22 24 29 33 38\\n\", \"2 14 8 8\\n5 9\\n\", \"15 56 1 5\\n5 10 15 20 21 25 29 31 34 37 38 41 43 47 52\\n\", \"7 36 11 4\\n6 11 17 19 22 24 30\\n\", \"10 100 2 8\\n93 35 24 87 39 46 86 37 73 33\\n\", \"6 22 5 7\\n4 6 10 13 15 18\\n\", \"1 2 1 5\\n1\\n\", \"1 3 1 2\\n2\\n\", \"2 1000000000 2 4\\n5 8\\n\", \"7 28 10 2\\n5 10 14 19 21 23 27\\n\", \"2 1000000000 2 5\\n5 8\\n\", \"11 65 1 7\\n7 11 14 21 24 30 37 44 50 56 59\\n\", \"5 25 10 2\\n6 12 13 15 22\\n\", \"3 24 2 6\\n6 12 17\\n\", \"6 35 12 4\\n7 12 17 21 24 28\\n\", \"1 10 2 9\\n5\\n\", \"3 20000 4000 3502\\n5000 8501 15000\\n\", \"1 5 1 2\\n2\\n\", \"9 40 6 3\\n5 10 14 18 22 27 30 31 36\\n\", \"100 600 1 4\\n9 536 518 59 229 377 72 203 81 309 304 321 55 439 287 505 3 410 582 351 440 568 584 259 22 415 348 147 404 277 477 323 537 75 548 324 338 198 145 182 271 496 256 329 592 132 291 222 115 587 54 158 154 103 356 15 36 76 402 27 223 551 267 527 51 34 417 573 479 398 425 71 485 20 262 566 467 131 524 352 330 541 146 53 322 436 366 86 88 272 96 456 388 319 149 470 129 162 353 346\\n\", \"8 56 2 9\\n7 11 20 28 34 39 40 48\\n\", \"12 13 6 7\\n1 2 3 4 5 6 7 8 9 10 11 12\\n\", \"9 57 2 2\\n5 11 15 21 24 30 36 43 50\\n\", \"1 1000000000 1 1000000000\\n2\\n\", \"4 31 12 9\\n7 13 21 28\\n\", \"15 97 4 4\\n3 7 13 23 29 35 39 45 49 50 60 68 72 81 87\\n\", \"4 30000 5000 6000\\n6000 16000 15000 21001\\n\", \"4 10000 500 500\\n700 601 1099 2000\\n\", \"5 28 6 8\\n3 9 15 21 25\\n\", \"10 1000000000 8905990 20319560\\n233244997 997992814 242452779 497363176 572234096 126615858 886769539 662035052 989086824 716655858\\n\", \"12 78 3 1\\n4 11 19 22 30 38 43 51 56 59 67 73\\n\", \"1 9 6 4\\n4\\n\", \"14 109 10 1\\n8 15 25 29 38 48 57 65 70 79 81 89 94 100\\n\", \"5 19 7 10\\n3 7 9 12 16\\n\", \"10 82 2 5\\n9 17 27 37 44 51 57 62 67 72\\n\", \"8 46 4 5\\n3 6 15 21 24 26 36 42\\n\", \"1 10 1 2\\n9\\n\", \"2 1000000000 1 2\\n5 8\\n\", \"3 21 6 2\\n7 11 16\\n\", \"1 10 7 4\\n5\\n\", \"6 55 3 5\\n10 18 24 34 39 45\\n\", \"100 1000 1 4\\n228 420 360 642 442 551 940 343 24 83 928 110 663 548 704 461 942 799 283 746 371 204 435 209 986 489 918 526 496 321 233 643 208 717 806 18 291 431 521 631 3 450 711 602 401 60 680 930 625 891 161 279 510 529 546 338 473 925 446 786 384 952 260 649 865 916 789 71 103 997 484 89 408 129 953 670 568 55 287 511 369 225 950 539 652 567 730 499 687 90 779 848 801 606 82 853 967 776 951 329\\n\", \"4 36 8 4\\n4 13 19 27\\n\", \"11 69 4 9\\n7 14 20 26 29 35 40 46 52 58 64\\n\", \"11 77 10 10\\n7 14 17 24 29 34 38 47 56 64 69\\n\", \"2 14 4 2\\n2 7\\n\", \"2 1000000000 1 4\\n5 8\\n\", \"3 29 3 4\\n7 16 19\\n\", \"14 62 11 4\\n5 10 15 18 22 26 31 34 39 42 44 47 52 57\\n\", \"1 1000000000 1000000000 2\\n999999999\\n\", \"100 1000 1 5\\n204 233 384 776 450 649 473 717 55 90 208 951 499 551 916 18 539 103 420 521 730 779 360 546 746 953 484 82 110 789 161 950 71 806 928 652 510 287 997 967 329 786 643 431 321 663 279 291 799 986 848 680 89 225 918 801 567 369 687 209 602 401 952 930 442 853 606 338 129 631 228 24 3 925 940 711 496 625 548 446 891 283 60 83 529 511 568 704 371 343 670 435 461 865 408 642 260 526 489 942\\n\", \"13 87 5 6\\n7 10 18 24 31 40 41 48 54 63 69 78 81\\n\", \"2 1000000000 1 3\\n5 8\\n\", \"13 46 2 4\\n1 4 9 13 15 19 21 23 25 30 35 37 42\\n\", \"14 93 1 1\\n8 15 19 21 28 36 44 51 56 63 67 74 79 85\\n\", \"2 23 12 8\\n8 16\\n\", \"10 44 6 2\\n4 8 13 19 23 29 32 33 37 41\\n\", \"4 30000 5000 1654\\n6000 16000 14999 21002\\n\", \"15 77 4 8\\n7 14 16 20 26 33 36 43 44 48 52 59 61 66 70\\n\", \"3 12000 2000 3000\\n3000 9002 7001\\n\", \"7 51 6 1\\n8 17 18 23 27 33 42\\n\", \"1 100 1 1\\n4\\n\", \"4 10000 500 500\\n700 600 1099 2000\\n\", \"13 91 1 3\\n5 12 17 22 29 36 43 49 57 64 70 79 84\\n\", \"8 51 2 1\\n6 14 20 26 19 35 40 48\\n\", \"2 14 0 8\\n5 9\\n\", \"10 100 2 12\\n93 35 24 87 39 46 86 37 73 33\\n\", \"2 1000000000 3 5\\n5 8\\n\", \"11 65 1 7\\n7 11 14 21 24 30 37 34 50 56 59\\n\", \"1 7 1 2\\n2\\n\", \"8 56 2 9\\n7 11 20 28 34 39 40 26\\n\", \"1 1000000001 1 1000000000\\n2\\n\", \"15 97 1 4\\n3 7 13 23 29 35 39 45 49 50 60 68 72 81 87\\n\", \"4 30000 5000 6000\\n6000 16000 29080 21001\\n\", \"10 82 2 5\\n9 17 27 37 44 51 57 62 19 72\\n\", \"1 14 1 2\\n9\\n\", \"2 1000000000 1 2\\n5 11\\n\", \"100 1000 1 5\\n204 233 384 776 450 649 473 717 55 90 208 951 499 551 916 18 539 103 420 521 730 779 360 546 746 953 484 82 110 789 161 950 71 806 928 652 510 287 997 967 329 786 643 431 321 663 279 291 799 986 848 680 131 225 918 801 567 369 687 209 602 401 952 930 442 853 606 338 129 631 228 24 3 925 940 711 496 625 548 446 891 283 60 83 529 511 568 704 371 343 670 435 461 865 408 642 260 526 489 942\\n\", \"2 1000000001 1 3\\n5 8\\n\", \"4 30000 5000 1654\\n7119 16000 14999 21002\\n\", \"3 12000 2000 3000\\n4703 9002 7001\\n\", \"10 100 2 12\\n93 35 40 87 39 46 86 37 73 33\\n\", \"2 1000000000 0 3\\n5 8\\n\", \"11 65 1 7\\n7 11 14 21 24 30 37 34 50 56 58\\n\", \"12 89 14 9\\n6 11 18 24 33 70 45 51 60 69 71 80\\n\", \"10 42 1 3\\n1 6 10 15 17 22 24 29 16 38\\n\", \"7 36 11 4\\n6 14 17 19 22 24 30\\n\", \"6 22 5 7\\n4 6 10 13 6 18\\n\", \"1 3 1 2\\n0\\n\", \"2 1000000000 2 3\\n5 8\\n\", \"7 28 10 2\\n5 10 14 36 21 23 27\\n\", \"5 25 10 2\\n1 12 13 15 22\\n\", \"1 10 2 9\\n1\\n\", \"9 40 12 3\\n5 10 14 18 22 27 30 31 36\\n\", \"100 600 1 4\\n9 536 518 59 229 377 72 203 81 309 304 321 55 439 287 505 3 410 582 351 440 568 584 259 22 415 348 147 404 277 477 323 537 75 548 324 338 198 145 182 271 496 256 329 592 132 291 222 115 587 54 158 154 103 356 15 36 76 402 27 223 551 267 527 51 34 417 573 479 398 425 71 485 20 262 566 467 131 524 352 330 541 146 53 322 436 366 86 88 272 158 456 388 319 149 470 129 162 353 346\\n\", \"12 13 6 7\\n1 2 3 4 4 6 7 8 9 10 11 12\\n\", \"9 57 2 2\\n5 11 15 21 24 30 50 43 50\\n\", \"5 28 6 8\\n3 17 15 21 25\\n\", \"1 9 6 6\\n4\\n\", \"14 109 10 1\\n8 16 25 29 38 48 57 65 70 79 81 89 94 100\\n\", \"5 38 7 10\\n3 7 9 12 16\\n\", \"8 46 4 5\\n3 6 15 21 24 26 36 6\\n\", \"3 21 6 2\\n7 20 16\\n\", \"1 10 7 8\\n5\\n\", \"100 1000 1 4\\n228 420 360 642 442 551 940 343 24 83 928 110 663 548 704 461 942 799 283 746 371 204 435 209 986 489 918 526 496 321 233 643 208 717 806 18 291 431 521 631 3 450 711 84 401 60 680 930 625 891 161 279 510 529 546 338 473 925 446 786 384 952 260 649 865 916 789 71 103 997 484 89 408 129 953 670 568 55 287 511 369 225 950 539 652 567 730 499 687 90 779 848 801 606 82 853 967 776 951 329\\n\", \"4 36 8 4\\n0 13 19 27\\n\", \"11 77 10 10\\n7 6 17 24 29 34 38 47 56 64 69\\n\", \"2 14 8 2\\n2 7\\n\", \"3 29 3 0\\n7 16 19\\n\", \"14 62 11 4\\n5 10 15 18 22 48 31 34 39 42 44 47 52 57\\n\", \"1 1000000000 1000100000 2\\n999999999\\n\", \"13 87 5 6\\n7 10 18 24 31 40 75 48 54 63 69 78 81\\n\", \"13 46 2 4\\n1 4 9 13 30 19 21 23 25 30 35 37 42\\n\", \"14 131 1 1\\n8 15 19 21 28 36 44 51 56 63 67 74 79 85\\n\", \"10 44 6 2\\n4 6 13 19 23 29 32 33 37 41\\n\", \"15 77 4 8\\n7 14 16 20 26 33 36 43 44 48 52 59 61 68 70\\n\", \"1 100 2 1\\n4\\n\", \"13 91 2 3\\n5 12 17 22 29 36 43 49 57 64 70 79 84\\n\", \"12 89 14 9\\n6 10 18 24 33 70 45 51 60 69 71 80\\n\", \"10 42 1 3\\n1 9 10 15 17 22 24 29 16 38\\n\", \"7 28 10 2\\n5 10 1 36 21 23 27\\n\", \"2 1000000000 3 8\\n5 8\\n\"], \"outputs\": [\"IMPOSSIBLE\\n\", \"RUN 2\\nJUMP 3\\nRUN 1\\nJUMP 2\\nRUN 2\\n\", \"RUN 2999\\nJUMP 2\\nRUN 3999\\nJUMP 2\\nRUN 2000\\nJUMP 2\\nRUN 2996\\n\", \"RUN 4\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 6\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4999\\nJUMP 3502\\nRUN 6498\\nJUMP 2\\nRUN 4999\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 3\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 4\\nRUN 1\\nJUMP 2\\nRUN 1\\nJUMP 3\\nRUN 1\\nJUMP 4\\nRUN 2\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\n\", \"IMPOSSIBLE\\n\", \"RUN 23\\nJUMP 2\\nRUN 7\\nJUMP 8\\nRUN 5\\nJUMP 2\\nRUN 25\\nJUMP 2\\nRUN 11\\nJUMP 3\\nRUN 4\\nJUMP 2\\nRUN 6\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 1\\nJUMP 2\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 5\\nRUN 999999991\\n\", \"RUN 6\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\n\", \"IMPOSSIBLE\\n\", \"RUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 6\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 4\\n\", \"IMPOSSIBLE\\n\", \"RUN 1\\nJUMP 2\\nRUN 2\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 6\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 3\\nJUMP 3\\nRUN 6\\nJUMP 2\\nRUN 7\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 1\\nJUMP 2\\nRUN 999999997\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 600\\nJUMP 500\\nRUN 899\\nJUMP 2\\nRUN 7999\\n\", \"IMPOSSIBLE\\n\", \"RUN 126615857\\nJUMP 2\\nRUN 106629137\\nJUMP 2\\nRUN 9207780\\nJUMP 2\\nRUN 254910395\\nJUMP 2\\nRUN 74870918\\nJUMP 2\\nRUN 89800954\\nJUMP 2\\nRUN 54620804\\nJUMP 2\\nRUN 170113679\\nJUMP 2\\nRUN 102317283\\nJUMP 8905992\\nRUN 2007185\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 8\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 9\\n\", \"IMPOSSIBLE\\n\", \"RUN 8\\nJUMP 2\\n\", \"RUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 999999991\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 9\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 9\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 6\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 4\\nJUMP 5\\nRUN 4\\nJUMP 7\\nRUN 4\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 4\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 999999991\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 2\\nJUMP 2\\nRUN 13\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 29\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 9\\nJUMP 3\\nRUN 4\\nJUMP 3\\nRUN 11\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 30\\nJUMP 2\\nRUN 41\\nJUMP 2\\nRUN 2\\nJUMP 3\\nRUN 14\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 25\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 28\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 15\\nJUMP 2\\nRUN 7\\nJUMP 4\\nRUN 11\\nJUMP 2\\nRUN 15\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 10\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 10\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 9\\nJUMP 3\\nRUN 8\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 5\\nJUMP 4\\nRUN 1\\nJUMP 2\\nRUN 14\\nJUMP 3\\nRUN 32\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 9\\nJUMP 3\\nRUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 15\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 11\\nJUMP 2\\nRUN 14\\nJUMP 2\\nRUN 28\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 8\\nJUMP 4\\nRUN 3\\nJUMP 2\\nRUN 40\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 10\\nJUMP 2\\nRUN 24\\nJUMP 2\\nRUN 23\\nJUMP 4\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 4\\nRUN 8\\nJUMP 4\\nRUN 6\\nJUMP 5\\nRUN 12\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 2\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 999999991\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 5999\\nJUMP 2\\nRUN 8997\\nJUMP 1003\\nRUN 5000\\nJUMP 2\\nRUN 8997\\n\", \"IMPOSSIBLE\\n\", \"RUN 2999\\nJUMP 2\\nRUN 3999\\nJUMP 2003\\nRUN 2997\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 6\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 4\\n\", \"RUN 23\\nJUMP 2\\nRUN 7\\nJUMP 8\\nRUN 5\\nJUMP 2\\nRUN 25\\nJUMP 2\\nRUN 11\\nJUMP 3\\nRUN 4\\nJUMP 2\\nRUN 6\\n\", \"RUN 4\\nJUMP 5\\nRUN 999999991\\n\", \"RUN 6\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 11\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\n\", \"RUN 1\\nJUMP 2\\nRUN 4\\n\", \"RUN 6\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 4\\nJUMP 4\\nRUN 4\\nJUMP 2\\nRUN 3\\nJUMP 3\\nRUN 15\\n\", \"RUN 1\\nJUMP 2\\nRUN 999999998\\n\", \"RUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 2\\nJUMP 3\\nRUN 8\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 9\\n\", \"RUN 5999\\nJUMP 2\\nRUN 9998\\nJUMP 5003\\nRUN 8077\\nJUMP 2\\nRUN 919\\n\", \"RUN 8\\nJUMP 2\\nRUN 6\\nJUMP 4\\nRUN 6\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 9\\n\", \"RUN 8\\nJUMP 2\\nRUN 4\\n\", \"RUN 4\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 999999988\\n\", \"RUN 2\\nJUMP 2\\nRUN 13\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 29\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 9\\nJUMP 3\\nRUN 5\\nJUMP 2\\nRUN 11\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 17\\nJUMP 4\\nRUN 28\\nJUMP 2\\nRUN 41\\nJUMP 2\\nRUN 2\\nJUMP 3\\nRUN 14\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 25\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 28\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 15\\nJUMP 2\\nRUN 7\\nJUMP 4\\nRUN 11\\nJUMP 2\\nRUN 15\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 10\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 10\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 9\\nJUMP 3\\nRUN 8\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 5\\nJUMP 4\\nRUN 1\\nJUMP 2\\nRUN 14\\nJUMP 3\\nRUN 32\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 9\\nJUMP 3\\nRUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 8\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 15\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 11\\nJUMP 2\\nRUN 14\\nJUMP 2\\nRUN 28\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 8\\nJUMP 4\\nRUN 3\\nJUMP 2\\nRUN 40\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 10\\nJUMP 2\\nRUN 24\\nJUMP 2\\nRUN 23\\nJUMP 4\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 4\\nRUN 8\\nJUMP 4\\nRUN 6\\nJUMP 5\\nRUN 12\\nJUMP 2\\nRUN 17\\nJUMP 2\\nRUN 9\\nJUMP 2\\nRUN 2\\n\", \"RUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 999999992\\n\", \"RUN 7118\\nJUMP 2\\nRUN 7878\\nJUMP 1003\\nRUN 5000\\nJUMP 2\\nRUN 8997\\n\", \"RUN 4702\\nJUMP 2\\nRUN 2296\\nJUMP 2003\\nRUN 2997\\n\", \"RUN 32\\nJUMP 9\\nRUN 4\\nJUMP 2\\nRUN 25\\nJUMP 2\\nRUN 11\\nJUMP 3\\nRUN 4\\nJUMP 2\\nRUN 6\\n\", \"RUN 4\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 999999991\\n\", \"RUN 6\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 2\\nJUMP 2\\nRUN 1\\nJUMP 2\\nRUN 11\\nJUMP 2\\nRUN 4\\nJUMP 4\\nRUN 6\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 6\\nJUMP 2\\nRUN 5\\nJUMP 2\\nRUN 4\\nJUMP 2\\nRUN 7\\nJUMP 2\\nRUN 3\\nJUMP 2\\nRUN 6\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"IMPOSSIBLE\\n\", \"RUN 4\\nJUMP 5\\nRUN 999999991\\n\"]}", "source": "primeintellect"}
|
A sportsman starts from point xstart = 0 and runs to point with coordinate xfinish = m (on a straight line). Also, the sportsman can jump — to jump, he should first take a run of length of not less than s meters (in this case for these s meters his path should have no obstacles), and after that he can jump over a length of not more than d meters. Running and jumping is permitted only in the direction from left to right. He can start andfinish a jump only at the points with integer coordinates in which there are no obstacles. To overcome some obstacle, it is necessary to land at a point which is strictly to the right of this obstacle.
On the way of an athlete are n obstacles at coordinates x1, x2, ..., xn. He cannot go over the obstacles, he can only jump over them. Your task is to determine whether the athlete will be able to get to the finish point.
Input
The first line of the input containsd four integers n, m, s and d (1 ≤ n ≤ 200 000, 2 ≤ m ≤ 109, 1 ≤ s, d ≤ 109) — the number of obstacles on the runner's way, the coordinate of the finishing point, the length of running before the jump and the maximum length of the jump, correspondingly.
The second line contains a sequence of n integers a1, a2, ..., an (1 ≤ ai ≤ m - 1) — the coordinates of the obstacles. It is guaranteed that the starting and finishing point have no obstacles, also no point can have more than one obstacle, The coordinates of the obstacles are given in an arbitrary order.
Output
If the runner cannot reach the finishing point, print in the first line of the output "IMPOSSIBLE" (without the quotes).
If the athlete can get from start to finish, print any way to do this in the following format:
* print a line of form "RUN X>" (where "X" should be a positive integer), if the athlete should run for "X" more meters;
* print a line of form "JUMP Y" (where "Y" should be a positive integer), if the sportsman starts a jump and should remain in air for "Y" more meters.
All commands "RUN" and "JUMP" should strictly alternate, starting with "RUN", besides, they should be printed chronologically. It is not allowed to jump over the finishing point but it is allowed to land there after a jump. The athlete should stop as soon as he reaches finish.
Examples
Input
3 10 1 3
3 4 7
Output
RUN 2
JUMP 3
RUN 1
JUMP 2
RUN 2
Input
2 9 2 3
6 4
Output
IMPOSSIBLE
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 90\\n1 11\\n\", \"3 50\\n4 2 1\\n\", \"14 6\\n256 465 759 589 242 824 638 985 506 128 809 105 301 827\\n\", \"1 20\\n784\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 866 379 1 723 880 992 9 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 381 130 820 357 911 884 735 460 428 764 187 344 760 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 819 30\\n\", \"10 20\\n812 896 36 596 709 641 679 778 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 591 420 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 504 618 292 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 743 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 675 942 952 610 574 633 758 999\\n\", \"12 71\\n472 111 924 103 975 527 807 618 400 523 607 424\\n\", \"13 89\\n19 944 341 846 764 676 222 957 953 481 708 920 950\\n\", \"5 45\\n964 515 454 623 594\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 135 106 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 802 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 968 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 515 702 811 877 286\\n\", \"11 1\\n235 280 196 670 495 379 391 280 847 875 506\\n\", \"5 26\\n42 65 23 43 64\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 692 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 829 683 345 706 294 901 238 606 12 24 89 882 203 962 804 745 166 425 393 252 415 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 98 35 347 799 313 40 821 118 786 31 587 888 84 88 751 98 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 252 508 722 380 922 634 911 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 430 171\\n\", \"10 83\\n689 759 779 927 15 231 976 943 604 917\\n\", \"14 6\\n256 465 354 589 242 824 638 985 506 128 809 105 301 827\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 866 379 1 723 880 992 11 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 381 130 820 357 911 884 735 460 428 764 187 344 760 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 819 30\\n\", \"10 20\\n812 896 36 596 709 1277 679 778 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 591 420 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 504 618 292 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 743 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n472 111 924 103 975 527 807 618 400 523 163 424\\n\", \"13 89\\n19 944 341 846 764 676 92 957 953 481 708 920 950\\n\", \"5 45\\n964 980 454 623 594\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 135 106 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 802 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 27 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 515 702 811 877 286\\n\", \"11 1\\n235 280 264 670 495 379 391 280 847 875 506\\n\", \"5 28\\n42 65 23 43 64\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 692 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 238 606 12 24 89 882 203 962 804 745 166 425 393 252 415 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 98 35 347 799 313 40 821 118 786 31 587 888 84 88 751 98 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 252 508 722 719 922 634 911 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 430 171\\n\", \"10 83\\n689 759 779 927 15 231 976 943 604 652\\n\", \"2 90\\n1 2\\n\", \"3 75\\n4 2 1\\n\", \"14 6\\n256 465 354 589 242 824 781 985 506 128 809 105 301 827\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 866 379 1 723 880 992 11 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 760 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 819 30\\n\", \"10 20\\n812 896 36 596 709 1277 679 589 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 591 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 504 618 292 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 743 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n472 111 924 103 975 527 807 618 521 523 163 424\\n\", \"13 89\\n19 944 341 846 764 676 92 957 953 481 708 904 950\\n\", \"5 45\\n964 980 454 945 594\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 135 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 802 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 27 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 515 702 811 877 286\\n\", \"11 1\\n235 524 264 670 495 379 391 280 847 875 506\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 692 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 238 606 12 24 89 1706 203 962 804 745 166 425 393 252 415 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 98 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 252 508 722 719 922 634 911 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 430 171\\n\", \"10 83\\n689 759 779 927 15 231 976 1161 604 652\\n\", \"14 6\\n256 465 354 589 242 824 781 1730 506 128 809 105 301 827\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 866 379 1 723 880 992 11 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 819 30\\n\", \"10 20\\n812 896 36 596 709 1277 679 1066 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 591 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 504 618 538 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 743 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n472 111 924 167 975 527 807 618 521 523 163 424\\n\", \"13 89\\n19 944 341 846 60 676 92 957 953 481 708 904 950\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 135 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 802 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 27 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"11 1\\n235 524 264 670 495 379 391 280 1583 875 506\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 1057 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 238 606 12 24 89 1706 203 962 804 745 166 425 393 252 415 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 98 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 252 508 722 719 922 634 911 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"10 83\\n689 759 570 927 15 231 976 1161 604 652\\n\", \"14 6\\n256 465 354 589 242 1553 781 1730 506 128 809 105 301 827\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 819 30\\n\", \"10 20\\n812 896 11 596 709 1277 679 1066 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 591 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 868 618 538 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 743 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n472 111 924 167 975 527 807 618 502 523 163 424\\n\", \"13 89\\n19 944 341 846 60 676 92 957 953 481 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 135 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 27 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"11 1\\n283 524 264 670 495 379 391 280 1583 875 506\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 1057 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 238 606 12 24 89 1706 203 962 804 745 166 425 393 252 811 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 98 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 252 508 722 719 922 634 1669 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"14 6\\n256 465 354 589 242 1553 781 1730 506 128 809 61 301 827\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 1267 30\\n\", \"10 20\\n812 896 11 596 709 890 679 1066 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 591 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 868 618 538 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 793 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n472 111 924 167 975 781 807 618 502 523 163 424\\n\", \"13 89\\n15 944 341 846 60 676 92 957 953 481 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 254 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 27 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 1057 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 291 606 12 24 89 1706 203 962 804 745 166 425 393 252 811 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 46 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 252 508 722 719 922 634 1669 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"14 6\\n256 465 354 589 232 1553 781 1730 506 128 809 61 301 827\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 157 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 1267 30\\n\", \"10 20\\n812 254 11 596 709 890 679 1066 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 1151 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 868 618 538 699 203 959 218 788 285 602 83 104 41 562 272 806 4 582 780 87 639 793 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n445 111 924 167 975 781 807 618 502 523 163 424\\n\", \"13 89\\n15 944 341 846 60 676 92 957 953 489 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 254 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 2 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 57 1057 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 291 606 12 24 89 1706 203 962 804 745 166 425 393 252 811 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 46 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 135 508 722 719 922 634 1669 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 536 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"14 6\\n256 465 354 589 232 1553 781 1730 506 128 809 61 301 391\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 106 371 574 862 967 581 543 330 348 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 157 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 1267 30\\n\", \"10 20\\n812 254 11 424 709 890 679 1066 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 1151 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 329 671 127 494 868 618 538 699 203 959 218 788 285 602 83 85 41 562 272 806 4 582 780 87 639 793 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n445 111 924 167 1411 781 807 618 502 523 163 424\\n\", \"13 89\\n23 944 341 846 60 676 92 957 953 489 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 254 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 111 135 254 519 896 227 224 2 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 106 405 594 693 339 43 57 1057 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 291 606 12 24 89 1706 203 962 804 745 166 425 393 252 811 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 46 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 135 508 722 719 922 634 1669 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 498 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"14 6\\n256 465 354 589 232 1553 1060 1730 506 128 809 61 301 391\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 106 371 574 862 967 581 543 330 70 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 157 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 1267 30\\n\", \"10 20\\n812 254 11 424 709 890 679 1508 738 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 1151 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 509 671 127 494 868 618 538 699 203 959 218 788 285 602 83 85 41 562 272 806 4 582 780 87 639 793 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n445 111 924 167 1411 781 807 618 502 523 163 330\\n\", \"13 89\\n23 944 341 846 60 676 92 957 1526 489 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 95 668 64 651 110 515 482 401 170 971 623 672 254 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 111 135 254 519 896 227 224 2 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 106 405 594 693 339 43 57 1057 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 61 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 291 606 12 24 89 1706 203 962 804 745 166 425 393 252 811 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 46 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 135 508 722 719 922 634 1669 102 384 346 212 705 380 220 221 492 421 244 591 758 631 370 866 641 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"14 6\\n256 465 354 589 232 1553 1060 1730 506 128 809 61 399 391\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 106 371 574 862 967 581 543 330 70 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 157 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 339 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 1267 30\\n\", \"10 20\\n812 254 11 424 709 890 679 1508 31 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 435 317 854 353 222 851 1151 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 509 671 127 494 868 63 538 699 203 959 218 788 285 602 83 85 41 562 272 806 4 582 780 87 639 793 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n445 111 924 167 1411 781 807 823 502 523 163 330\\n\", \"13 89\\n23 944 341 846 18 676 92 957 1526 489 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 95 668 64 651 110 515 482 401 170 971 623 672 254 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 111 135 254 519 896 227 224 2 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 184 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\", \"103 26\\n33 455 273 884 569 636 360 69 802 106 405 594 693 339 43 57 1057 514 217 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 61 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 984 683 345 706 294 901 291 606 12 24 89 1706 203 962 804 745 166 425 393 252 811 195 571 596 41 486 445\\n\", \"100 95\\n154 444 715 46 35 347 799 313 40 821 118 786 31 587 888 84 88 751 21 86 321 720 201 247 302 518 663 904 482 385 139 646 581 995 847 775 173 135 508 722 719 922 634 1669 102 384 346 212 705 380 220 318 492 421 244 591 758 631 370 866 641 872 294 152 337 810 761 235 789 839 365 366 623 897 905 249 685 838 380 873 702 379 865 68 215 168 425 264 652 228 167 498 733 41 502 21 565 956 85 171\\n\", \"14 6\\n256 465 354 589 232 1553 1060 1730 506 128 809 61 280 391\\n\", \"102 99\\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 106 371 574 862 390 581 543 330 70 221 640 378 250 500 428 514 379 1 723 880 992 11 419 0 157 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 518 130 820 357 911 884 735 460 428 764 187 344 837 339 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 1267 30\\n\", \"10 20\\n812 254 11 424 521 890 679 1508 31 302\\n\", \"104 54\\n683 252 125 813 874 835 651 424 826 139 397 323 143 153 326 941 536 682 317 854 353 222 851 1151 836 415 190 872 178 311 612 635 174 505 153 81 559 815 805 414 378 62 75 929 208 942 254 670 509 671 127 494 868 63 538 699 203 959 218 788 285 602 83 85 41 562 272 806 4 582 780 87 639 793 811 263 83 632 230 984 826 304 133 142 612 413 310 985 594 309 787 930 541 92 461 663 791 942 952 610 574 633 758 999\\n\", \"12 71\\n445 011 924 167 1411 781 807 823 502 523 163 330\\n\", \"13 89\\n23 944 341 846 18 676 92 957 1215 489 708 904 1794\\n\", \"101 71\\n113 551 568 26 650 547 95 668 64 651 110 515 482 401 170 971 623 672 254 167 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 1582 667 665 206 774 573 499 361 202 620 522 72 220 739 868 111 135 254 519 896 227 120 2 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 184 733 576 840 683 417 709 569 432 556 702 811 877 286\\n\"], \"outputs\": [\"1.9090909088\\n\", \"2.0000000001\\n\", \"523.4270986753\\n\", \"783.9999999996\\n\", \"68.7029204433\\n\", \"597.2558139539\\n\", \"399.4309034622\\n\", \"413.2495543673\\n\", \"361.9243902446\\n\", \"594.1097560978\\n\", \"343.0472848177\\n\", \"467.5863013707\\n\", \"45.4151785716\\n\", \"419.9226594311\\n\", \"179.0750000007\\n\", \"406.8392857149\\n\", \"494.72164948453604\\n\", \"68.90433031218522\\n\", \"656.4186046511627\\n\", \"400.18181818181824\\n\", \"360.3030303030303\\n\", \"327.22741433021804\\n\", \"668.3414634146341\\n\", \"333.96767639453265\\n\", \"473.7963470319635\\n\", \"45.24324324324324\\n\", \"421.2195838986886\\n\", \"179.78125\\n\", \"393.4315476190476\\n\", \"1.0909090909090908\\n\", \"1.6666666666666665\\n\", \"504.62002945508095\\n\", \"69.03846153846158\\n\", \"637.7045454545454\\n\", \"402.87475372924285\\n\", \"366.5579322638146\\n\", \"326.6791277258567\\n\", \"722.4520547945204\\n\", \"335.0931631722881\\n\", \"496.05296803652965\\n\", \"428.0872302158272\\n\", \"176.57291666666663\\n\", \"404.4613095238095\\n\", \"555.9677419354838\\n\", \"69.10897435897435\\n\", \"683.1136363636364\\n\", \"405.3284174702212\\n\", \"377.96613190730835\\n\", \"249.90243902439022\\n\", \"335.3099361896079\\n\", \"562.5086599817685\\n\", \"431.12306657700077\\n\", \"172.37083333333325\\n\", \"393.88690476190476\\n\", \"606.1313868613139\\n\", \"68.7653575025176\\n\", \"680.2727272727273\\n\", \"407.702779353375\\n\", \"376.9839572192513\\n\", \"272.54634146341465\\n\", \"339.43391066545104\\n\", \"566.8842297174111\\n\", \"434.45707240529055\\n\", \"173.91382765531066\\n\", \"602.9197080291971\\n\", \"69.1968864468864\\n\", \"644.3023255813953\\n\", \"408.0289279636983\\n\", \"390.11408199643495\\n\", \"271.57073170731707\\n\", \"341.60346399270736\\n\", \"435.05110961667805\\n\", \"171.78333333333342\\n\", \"602.1897810218977\\n\", \"69.19139194139191\\n\", \"576.6279069767442\\n\", \"411.6817923993194\\n\", \"388.7183600713012\\n\", \"271.7853658536585\\n\", \"341.1476754785778\\n\", \"435.0959426137639\\n\", \"170.11458333333334\\n\", \"571.4072992700729\\n\", \"68.84290030211476\\n\", \"557.5227272727273\\n\", \"411.4123652864434\\n\", \"411.2566844919786\\n\", \"273.7365853658536\\n\", \"341.3299908842296\\n\", \"432.80945976238485\\n\", \"170.03541666666672\\n\", \"590.5436046511628\\n\", \"68.56294058408862\\n\", \"597.7045454545454\\n\", \"413.2297220646624\\n\", \"397.8148734177215\\n\", \"289.109756097561\\n\", \"341.4393801276207\\n\", \"428.7472378804962\\n\", \"170.33333333333334\\n\", \"597.6656976744185\\n\", \"68.48841893252764\\n\", \"522.2666666666667\\n\", \"406.9293817356779\\n\", \"407.2215189873417\\n\", \"278.86585365853654\\n\", \"338.47228221742256\\n\", \"425.02562949640287\\n\", \"170.53541666666672\\n\", \"589.017441860465\\n\", \"67.90735146022158\\n\", \"505.55555555555554\\n\", \"408.5405558706747\\n\", \"391.3987341772152\\n\", \"270.5219512195122\\n\", \"336.60043196544274\\n\"]}", "source": "primeintellect"}
|
It is well known that the planet suffers from the energy crisis. Little Petya doesn't like that and wants to save the world. For this purpose he needs every accumulator to contain the same amount of energy. Initially every accumulator has some amount of energy: the i-th accumulator has ai units of energy. Energy can be transferred from one accumulator to the other. Every time x units of energy are transferred (x is not necessarily an integer) k percent of it is lost. That is, if x units were transferred from one accumulator to the other, amount of energy in the first one decreased by x units and in other increased by <image> units.
Your task is to help Petya find what maximum equal amount of energy can be stored in each accumulator after the transfers.
Input
First line of the input contains two integers n and k (1 ≤ n ≤ 10000, 0 ≤ k ≤ 99) — number of accumulators and the percent of energy that is lost during transfers.
Next line contains n integers a1, a2, ... , an — amounts of energy in the first, second, .., n-th accumulator respectively (0 ≤ ai ≤ 1000, 1 ≤ i ≤ n).
Output
Output maximum possible amount of energy that can remain in each of accumulators after the transfers of energy.
The absolute or relative error in the answer should not exceed 10 - 6.
Examples
Input
3 50
4 2 1
Output
2.000000000
Input
2 90
1 11
Output
1.909090909
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"1 3\\n\", \"4 3\\n\", \"3 2\\n\", \"27811605053083586 516548918254320722\\n\", \"121125188014443608 400338158982406735\\n\", \"768753603103944226 868940\\n\", \"545838312215845682 715670\\n\", \"160986032904427725 153429\\n\", \"78305076165311264 280970\\n\", \"452811696339558207 443394\\n\", \"472663767432643850 601411\\n\", \"871286622346211738 836848346410668404\\n\", \"605838195283987989 198026\\n\", \"494956757081479349 760223\\n\", \"565690379013964030 914981\\n\", \"901928035250255660 465555\\n\", \"37774758680708184 156713778825283978\\n\", \"59 576460752303423488\\n\", \"216434772356360296 67212780306228770\\n\", \"70181875975239647 504898544415017211\\n\", \"851434559843060686 397746475431992189\\n\", \"525829538418947209 501264136399411409\\n\", \"274151686958873391 747281437213482980\\n\", \"616183854421159004 962643186273781485\\n\", \"500001 1000002\\n\", \"821919374090247584 554985827995633347\\n\", \"802067302997161941 115883952721989836\\n\", \"266928247763555270 547878\\n\", \"1000000000000000000 1000000000000000000\\n\", \"473120513399321115 489435\\n\", \"17922687587622540 3728\\n\", \"876625063841174080 360793239109880865\\n\", \"59 576460752303423489\\n\", \"24858346330090877 523038\\n\", \"172714899512474455 414514930706102803\\n\", \"269600543342663655 10645\\n\", \"625690262082106337 220453546754437119\\n\", \"904600330829364045 969618\\n\", \"98157142963429612 169605644318211774\\n\", \"389313338098908426 99564\\n\", \"973122623649224625 850102328697987938\\n\", \"218718983913330026 55198\\n\", \"412663884364501543 401745061547424998\\n\", \"852560778404356914 258808\\n\", \"2 4\\n\", \"555344724171760311 567396824985513364\\n\", \"471994290543057591 972026\\n\", \"364505998666117889 208660487087853057\\n\", \"620154000220554572 802783\\n\", \"859411744555329603 932262\\n\", \"301399940652446487 937011639371661304\\n\", \"329600422115838666 166731855158215181\\n\", \"711481618561526208 858685\\n\", \"1000003 1000002\\n\", \"756878725313062090 497297\\n\", \"467708499092938957 59762\\n\", \"831301534196025310 690475\\n\", \"659003966270291348 426245\\n\", \"940197003483178269 77403\\n\", \"884360180009107043 795255840146329784\\n\", \"180838095407578776 715935\\n\", \"211479504016655403 861717213151744108\\n\", \"397362961182592931 814397\\n\", \"698408060898630904 50803201495883240\\n\", \"1234567891234 100005\\n\", \"902777085738878599 348432\\n\", \"58453009367192916 164246\\n\", \"422627037992126141 41909917823420958\\n\", \"369461267005822782 537061\\n\", \"88268234087903158 290389\\n\", \"198866921410178974 492694\\n\", \"486125404822710514 109107\\n\", \"164699049675494044 325434\\n\", \"884748259736278401 407112\\n\", \"116185964671062513 620234\\n\", \"341930258137049567 734173670740688701\\n\", \"955093801941591723 462827230953066080\\n\", \"588270344337806667 964906185404883662\\n\", \"728223285619341145 791009\\n\", \"455483991918666592 947456\\n\", \"639151895177205704 416747737792752265\\n\", \"468804735183774830 244864585447548924\\n\", \"286780314561673617 664601\\n\", \"467127505571092085 905135971539044394\\n\", \"231331570814773750 77447051570611803\\n\", \"496942725996835031 761030666233908048\\n\", \"318967795893595104 976829166597314361\\n\", \"1000002 1000003\\n\", \"685403173770208801 962607\\n\", \"57626821183859235 372443612949184377\\n\", \"649040812642666750 821314\\n\", \"782215240494010889 417929\\n\", \"935241735143473375 247097392534198386\\n\", \"665551106972090453 845883\\n\", \"758864689933450475 128294949711869852\\n\", \"83260344505016157 935999340494020219\\n\", \"500001 1000003\\n\", \"96333897872944166 462217\\n\", \"563321908884029228 664734\\n\", \"922629148242029651 787671\\n\", \"512524612322627967 897562435047674890\\n\", \"1000002 1000002\\n\", \"176573931761343475 697077\\n\", \"505977467325861565 285534302275511011\\n\", \"708371214526255502 632992\\n\", \"13491088710006829 715337619732144903\\n\", \"460788885346794419 634257\\n\", \"517924802132493346 67413\\n\", \"718716873663426516 872259572564867078\\n\", \"426597183791521709 928925\\n\", \"532376674825779019 113292273466542585\\n\", \"615057631564895479 807178821338760482\\n\", \"748901536305825878 347728\\n\", \"371745482857759808 590068361140585059\\n\", \"269212459320525000 680451979144466763\\n\", \"523157242839838824 310837164758318823\\n\", \"324064160254286900 898448\\n\", \"688519152023104450 70486\\n\", \"2016 2016\\n\", \"394409702459600222 851414284237789752\\n\", \"575196786674911363 36374\\n\", \"236286839154478644 282942618725096464\\n\", \"2016 2017\\n\", \"93223502427608051 790744\\n\", \"15266076338626979 913942576088954168\\n\", \"831582488749975043 182016637013124494\\n\", \"864508113210988695 17803\\n\", \"781827160766839530 885639453855244191\\n\", \"703820075205013062 862025309890418636\\n\", \"314682004443476471 544443468582510377\\n\", \"841928147887146057 620004\\n\", \"960049070281296616 235421\\n\", \"417215023685743983 376900\\n\", \"73371431334522407 674020\\n\", \"751573831884934263 851791\\n\", \"648371335753080490 787441\\n\", \"569660524813359598 814752357830129986\\n\", \"91237529217285074 672878442653097259\\n\", \"20506891020332316 516548918254320722\\n\", \"44363793938196165 400338158982406735\\n\", \"768753603103944226 84651\\n\", \"545838312215845682 1340303\\n\", \"109749788729122513 153429\\n\", \"86904287621265186 280970\\n\", \"452811696339558207 523537\\n\", \"472663767432643850 894417\\n\", \"644383370002866787 836848346410668404\\n\", \"1169600543608376130 198026\\n\", \"494956757081479349 950144\\n\", \"565690379013964030 193236\\n\", \"680228391146208544 465555\\n\", \"37774758680708184 108569621387333695\\n\", \"59 43496016578516310\\n\", \"299038194522214531 67212780306228770\\n\", \"125930982302171292 504898544415017211\\n\", \"1002926547994558173 397746475431992189\\n\", \"525829538418947209 629703928994725053\\n\", \"272016344257673110 747281437213482980\\n\", \"494282 1000002\\n\", \"821919374090247584 20298046175892998\\n\", \"1473775137370162486 115883952721989836\\n\", \"266928247763555270 47062\\n\", \"1000000000000000010 1000000000000000000\\n\", \"511530325403590189 489435\\n\", \"1242565614479896 3728\\n\", \"1012211293915181675 360793239109880865\\n\", \"83 576460752303423489\\n\", \"24858346330090877 463220\\n\", \"172714899512474455 196456042120768002\\n\", \"269600543342663655 8754\\n\", \"258754647913324970 220453546754437119\\n\", \"904600330829364045 1708110\\n\", \"150449192290603078 169605644318211774\\n\", \"417677919895383458 99564\\n\", \"589286351113543512 850102328697987938\\n\", \"1343285506794963 55198\\n\", \"412663884364501543 349526029531750143\\n\", \"1243899219782032638 258808\\n\", \"424738843652749488 567396824985513364\\n\", \"547033032511504106 972026\\n\", \"380286210819371042 208660487087853057\\n\", \"620154000220554572 1199702\\n\", \"859411744555329603 1552620\\n\", \"70811258311680878 166731855158215181\\n\", \"137063881668184731 858685\\n\", \"1736866 1000002\\n\", \"1216284756724805506 497297\\n\", \"627296117987996156 59762\\n\", \"831301534196025310 941292\\n\", \"659003966270291348 397463\\n\", \"940197003483178269 65577\\n\", \"1641700108221654888 795255840146329784\\n\", \"343380071539185828 715935\\n\", \"185431135750698109 814397\\n\"], \"outputs\": [\"1 1\", \"23 128\", \"1 8\\n\", \"894732 894732\", \"199488 199488\", \"118118 118118\", \"156176 156176\", \"100374 100374\", \"293282 624669\", \"474530 348263\", \"203104 203104\", \"530710 530710\", \"929969 156402\", \"586955 423513\", \"547343 547343\", \"586380 781987\", \"73122 73122\", \"840218 840218\", \"995572 995572\", \"79176 79176\", \"314138 314138\", \"715564 715564\", \"977029 977029\", \"149006 149006\", \"998979 999491\", \"854880 854880\", \"928705 928705\", \"817352 54712\", \"906300 906300\", \"57896 535051\", \"478998 792943\", \"34117 34117\", \"1 1\", \"5846 5846\", \"626500 626500\", \"913809 282202\", \"741435 741435\", \"245893 245893\", \"409023 409023\", \"205907 386429\", \"781676 781676\", \"99469 89622\", \"228503 228503\", \"775128 775128\", \"29 32\", \"666610 666610\", \"215668 215668\", \"83777 83777\", \"163153 163153\", \"859175 859175\", \"165989 165989\", \"242921 242921\", \"929035 929035\", \"256 256\", \"641345 641345\", \"283212 204310\", \"964028 964028\", \"795318 278062\", \"119089 181418\", \"541758 541758\", \"378695 378695\", \"196797 196797\", \"155345 155345\", \"750308 750308\", \"173817 722464\", \"396798 564327\", \"317900 341568\", \"268735 268735\", \"97003 97003\", \"566668 88331\", \"847137 847137\", \"832669 164722\", \"170498 994561\", \"25714 811489\", \"798435 622171\", \"21530 21530\", \"999170 999170\", \"544853 544853\", \"764528 274644\", \"570626 570626\", \"135045 135045\", \"365451 365451\", \"654850 654850\", \"608084 608084\", \"578654 578654\", \"746587 746587\", \"750015 750015\", \"256 256\", \"135409 135409\", \"802451 802451\", \"57323 57323\", \"665887 270857\", \"181888 181888\", \"623684 623684\", \"37325 37325\", \"138293 138293\", \"256 256\", \"367832 367832\", \"883734 883734\", \"164442 164442\", \"614855 614855\", \"512 512\", \"389281 749563\", \"782797 782797\", \"615316 615316\", \"719453 719453\", \"660266 660266\", \"954073 995488\", \"401470 401470\", \"835709 835709\", \"36122 36122\", \"52078 52078\", \"80599 80599\", \"748215 748215\", \"868951 868951\", \"726051 726051\", \"18338 18338\", \"476402 371144\", \"1564 227035\", \"419420 419420\", \"88076 806040\", \"187677 187677\", \"360153 815112\", \"983387 983387\", \"506165 506165\", \"159828 159828\", \"107443 838933\", \"627074 627074\", \"982260 982260\", \"279665 279665\", \"151333 51640\", \"274784 325200\", \"122689 122689\", \"899111 372106\", \"905743 905743\", \"228932 228932\", \"780635 780635\", \"988072 988072\\n\", \"108747 108747\\n\", \"236433 236433\\n\", \"433339 811571\\n\", \"736738 736738\\n\", \"346046 581197\\n\", \"983825 251387\\n\", \"814697 706668\\n\", \"606879 606879\\n\", \"779805 779805\\n\", \"670559 880870\\n\", \"567983 567983\\n\", \"811548 811548\\n\", \"200431 200431\\n\", \"19867 19867\\n\", \"216491 216491\\n\", \"869881 869881\\n\", \"659411 659411\\n\", \"145788 145788\\n\", \"133468 133468\\n\", \"234446 234446\\n\", \"101701 101701\\n\", \"911648 911648\\n\", \"302682 302682\\n\", \"509932 526757\\n\", \"954414 954414\\n\", \"84127 84127\\n\", \"921457 204644\\n\", \"545123 545123\\n\", \"193421 193421\\n\", \"868281 868281\\n\", \"528194 528194\\n\", \"757777 823363\\n\", \"982964 982964\\n\", \"774309 774309\\n\", \"551122 551122\\n\", \"255157 267406\\n\", \"667435 667435\\n\", \"888252 355970\\n\", \"622396 622396\\n\", \"757730 249731\\n\", \"935272 935272\\n\", \"313779 313779\\n\", \"247619 247619\\n\", \"613980 613980\\n\", \"446232 446232\\n\", \"724510 724510\\n\", \"122788 122788\\n\", \"589677 589677\\n\", \"641398 641398\\n\", \"666288 151269\\n\", \"144598 144598\\n\", \"117547 35727\\n\", \"512179 352766\\n\", \"769226 769226\\n\", \"950276 950276\\n\", \"779269 779269\\n\"]}", "source": "primeintellect"}
|
ZS the Coder has recently found an interesting concept called the Birthday Paradox. It states that given a random set of 23 people, there is around 50% chance that some two of them share the same birthday. ZS the Coder finds this very interesting, and decides to test this with the inhabitants of Udayland.
In Udayland, there are 2n days in a year. ZS the Coder wants to interview k people from Udayland, each of them has birthday in one of 2n days (each day with equal probability). He is interested in the probability of at least two of them have the birthday at the same day.
ZS the Coder knows that the answer can be written as an irreducible fraction <image>. He wants to find the values of A and B (he does not like to deal with floating point numbers). Can you help him?
Input
The first and only line of the input contains two integers n and k (1 ≤ n ≤ 1018, 2 ≤ k ≤ 1018), meaning that there are 2n days in a year and that ZS the Coder wants to interview exactly k people.
Output
If the probability of at least two k people having the same birthday in 2n days long year equals <image> (A ≥ 0, B ≥ 1, <image>), print the A and B in a single line.
Since these numbers may be too large, print them modulo 106 + 3. Note that A and B must be coprime before their remainders modulo 106 + 3 are taken.
Examples
Input
3 2
Output
1 8
Input
1 3
Output
1 1
Input
4 3
Output
23 128
Note
In the first sample case, there are 23 = 8 days in Udayland. The probability that 2 people have the same birthday among 2 people is clearly <image>, so A = 1, B = 8.
In the second sample case, there are only 21 = 2 days in Udayland, but there are 3 people, so it is guaranteed that two of them have the same birthday. Thus, the probability is 1 and A = B = 1.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 1\\na := 1\\nbb := 0\\ncx := ? OR a\\nd := ? XOR ?\\ne := d AND bb\\n\", \"3 3\\na := 101\\nb := 011\\nc := ? XOR b\\n\", \"2 109\\na := 1010101010100000000000011111111111111111111111111111111111111111111000000000000000000000000000111111111111111\\nb := ? XOR a\\n\", \"12 14\\na := 01100010000111\\nb := ? XOR a\\nc := 01101111001010\\nd := ? XOR c\\ne := 10000011101111\\nf := ? XOR e\\ng := 10100011001010\\nh := ? XOR g\\ni := 10010110111111\\nj := ? XOR i\\nk := 10000111110001\\nl := ? XOR k\\n\", \"1 10\\na := 0110110011\\n\", \"13 6\\na := 111010\\nb := 100100\\nc := 001110\\nd := b AND b\\ne := c AND ?\\nf := e OR c\\ng := 011110\\nh := d XOR ?\\ni := 010111\\nj := 000011\\nk := d OR ?\\nl := 011101\\nm := b OR j\\n\", \"22 9\\na := 100101111\\nb := 010001100\\nc := b AND b\\nd := 111000010\\ne := c AND a\\nf := a OR e\\ng := e AND ?\\nh := 000010001\\ni := b OR ?\\nj := d AND ?\\nk := g AND h\\nl := 010100000\\nm := a AND a\\nn := j AND ?\\no := m OR n\\np := o AND ?\\nq := f OR ?\\nr := 000011011\\ns := 001110011\\nt := 100111100\\nu := l AND p\\nv := g OR h\\n\", \"1 6\\na := ? OR ?\\n\", \"14 14\\na := 10000100110000\\nb := 01111011001111\\nc := 11110001111101\\nd := 00001110000010\\ne := 00111100000010\\nf := 11000011111101\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 11110011011001\\nn := ? XOR m\\n\", \"29 2\\naa := 10\\nba := 11\\nca := 01\\nda := aa AND ?\\nea := ba OR ?\\nfa := da XOR ?\\nga := 11\\nha := fa XOR ea\\nia := 01\\nja := ca OR ha\\nka := ha XOR ia\\nla := ha OR ?\\nma := ba AND ba\\nna := ma OR ?\\noa := 11\\npa := oa OR ba\\nqa := 00\\nra := qa AND ia\\nsa := fa OR ?\\nta := ha OR ga\\nua := 00\\nva := 00\\nwa := 11\\nxa := 10\\nya := ja XOR ?\\nza := 00\\nab := 00\\nbb := pa OR qa\\ncb := bb AND ?\\n\", \"16 3\\na := 011\\nb := 110\\nc := a XOR b\\nd := 110\\ne := a XOR b\\nf := b XOR a\\ng := b XOR e\\nh := 111\\ni := a XOR h\\nj := f XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"10 3\\na := 011\\nb := ? OR a\\nc := 000\\nd := ? AND c\\ne := 101\\nf := ? AND e\\ng := 001\\nh := ? XOR g\\ni := 001\\nj := ? XOR i\\n\", \"12 3\\na := 101\\nb := a XOR ?\\nc := b XOR b\\nd := b XOR a\\ne := c XOR ?\\nf := e XOR ?\\ng := c XOR f\\nh := 100\\ni := c XOR h\\nj := c XOR i\\nk := b XOR ?\\nl := 111\\n\", \"2 10\\nb := 0100101101\\na := ? XOR b\\n\", \"14 8\\na := 01010000\\nb := 10101111\\nc := 01100100\\nd := 10011011\\ne := 01001100\\nf := 10110011\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 00101111\\nn := ? XOR m\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000010110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"1 10\\na := 0110110111\\n\", \"10 3\\na := 011\\nb := ? OR a\\nc := 000\\nd := ? AND c\\ne := 101\\nf := ? AND e\\ng := 101\\nh := ? XOR g\\ni := 001\\nj := ? XOR i\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"1 3\\na := 0110110011\\n\", \"13 6\\na := 111010\\nb := 100100\\nc := 001110\\nd := b AND b\\ne := c AND ?\\nf := e OR c\\ng := 011110\\nh := d XOR ?\\ni := 010111\\nj := 000011\\nk := d OR ?\\nl := 010101\\nm := b OR j\\n\", \"14 14\\na := 10000100110000\\nb := 01111011001111\\nc := 10110001111101\\nd := 00001110000010\\ne := 00111100000010\\nf := 11000011111101\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 11110011011001\\nn := ? XOR m\\n\", \"16 3\\na := 011\\nb := 110\\nc := a XOR b\\nd := 110\\ne := a XOR b\\nf := b XOR a\\ng := b XOR e\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"3 3\\na := 101\\nb := 111\\nc := ? XOR b\\n\", \"10 3\\na := 010\\nb := ? OR a\\nc := 000\\nd := ? AND c\\ne := 101\\nf := ? AND e\\ng := 101\\nh := ? XOR g\\ni := 001\\nj := ? XOR i\\n\", \"17 5\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"3 3\\na := 001\\nb := 110\\nc := ? XOR b\\n\", \"22 9\\na := 100101111\\nb := 010001100\\nc := b AND b\\nd := 111000010\\ne := c AND a\\nf := a OR e\\ng := e AND ?\\nh := 000010001\\ni := b OR ?\\nj := d AND ?\\nk := g AND h\\nl := 010100000\\nm := a AND a\\nn := j AND ?\\no := m OR n\\np := o AND ?\\nq := f OR ?\\nr := 000011011\\ns := 001010011\\nt := 100111100\\nu := l AND p\\nv := g OR h\\n\", \"1 6\\nb := ? OR ?\\n\", \"14 14\\na := 10000100110000\\nb := 01111011001111\\nc := 11110001111101\\nd := 00001110001010\\ne := 00111100000010\\nf := 11000011111101\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 11110011011001\\nn := ? XOR m\\n\", \"14 14\\na := 10000100110000\\nb := 01111011001111\\nc := 10111001111101\\nd := 00001110000010\\ne := 00111100000010\\nf := 11000011111101\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 11110011011001\\nn := ? XOR m\\n\", \"14 14\\na := 10000100110000\\nb := 01111011001111\\nc := 11110001111101\\nd := 00001110001010\\ne := 00111100000010\\nf := 11000011111101\\ng := ? XOR a\\nh := c XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 11110011011001\\nn := ? XOR m\\n\", \"12 14\\na := 01100010000111\\nb := ? XOR a\\nc := 01101111001010\\nd := ? XOR c\\ne := 10000011101111\\nf := ? XOR e\\ng := 10100011001010\\nh := ? XOR g\\ni := 10010110111111\\nj := ? XOR i\\nk := 10001111110001\\nl := ? XOR k\\n\", \"14 8\\na := 01010000\\nb := 10101111\\nc := 01100100\\nd := 10011011\\ne := 01001100\\nf := 10110011\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR c\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 00101111\\nn := ? XOR l\\n\", \"14 14\\na := 10000100110000\\nb := 01111011001111\\nc := 10111001111101\\nd := 00001110000010\\ne := 00111100000010\\nf := 11000011111101\\ng := ? XOR a\\nh := b XOR ?\\ni := ? XOR b\\nj := d XOR ?\\nk := ? XOR e\\nl := f XOR ?\\nm := 11110011011001\\nn := ? XOR m\\n\", \"1 10\\na := 0110110110\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011011011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"17 15\\na := 000000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000010110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"1 10\\na := 0110110101\\n\", \"16 3\\na := 011\\nb := 110\\nc := a XOR b\\nd := 110\\ne := a XOR b\\nf := b XOR a\\ng := b XOR f\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"17 15\\na := 000000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000010110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110111001\\nq := 000100110001000\\n\", \"3 3\\na := 001\\nb := 111\\nc := ? XOR b\\n\", \"16 3\\na := 011\\nb := 110\\nc := b XOR b\\nd := 110\\ne := a XOR b\\nf := b XOR a\\ng := b XOR f\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"16 3\\na := 011\\nb := 110\\nc := b XOR b\\nd := 010\\ne := a XOR b\\nf := b XOR a\\ng := b XOR f\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"0 3\\na := 101\\nb := 011\\nc := ? XOR b\\n\", \"1 10\\na := 0100110111\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101010\\nn := 011011011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"16 3\\na := 001\\nb := 110\\nc := a XOR b\\nd := 110\\ne := a XOR b\\nf := b XOR a\\ng := b XOR e\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"16 3\\na := 011\\nb := 111\\nc := b XOR b\\nd := 010\\ne := a XOR b\\nf := b XOR a\\ng := b XOR f\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"0 3\\na := 101\\nb := 111\\nc := ? XOR b\\n\", \"1 10\\na := 0110010011\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000010110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011101011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"1 10\\na := 0110111111\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010110001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"17 15\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000011101101000\\nn := 011011011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"1 3\\nb := 0110110011\\n\", \"17 15\\na := 000000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000010110\\nf := 011001110111110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 100010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"17 5\\na := 010000111111110\\nb := 101100110000100\\nc := 100101100100111\\nd := 010110101110110\\ne := 111111000110110\\nf := 011001110011110\\ng := 110011010100101\\nh := 000001010010001\\ni := 110000111001011\\nj := 000010000010111\\nk := 110110111110110\\nl := 010000110000100\\nm := 000111101101000\\nn := 011111011000111\\no := 010110110010100\\np := 111001110011001\\nq := 000100110001000\\n\", \"16 3\\na := 011\\nb := 110\\nc := b XOR b\\nd := 110\\ne := a XOR b\\nf := a XOR a\\ng := b XOR f\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 100\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"16 3\\na := 011\\nb := 110\\nc := b XOR b\\nd := 010\\ne := a XOR b\\nf := b XOR a\\ng := b XOR f\\nh := 111\\ni := a XOR h\\nj := g XOR ?\\nk := 110\\nl := 000\\nm := 100\\nn := 110\\no := 110\\np := 110\\n\", \"0 3\\na := 101\\nb := 011\\nc := ? XOR c\\n\"], \"outputs\": [\"0\\n0\\n\", \"011\\n100\\n\", \"1010101010100000000000011111111111111111111111111111111111111111111000000000000000000000000000111111111111111\\n0101010101011111111111100000000000000000000000000000000000000000000111111111111111111111111111000000000000000\\n\", \"10000011001011\\n01011000010000\\n\", \"0000000000\\n0000000000\\n\", \"100000\\n011011\\n\", \"000000000\\n111111111\\n\", \"000000\\n111111\\n\", \"11110011011001\\n00001100100110\\n\", \"00\\n11\\n\", \"101\\n010\\n\", \"001\\n110\\n\", \"000\\n111\\n\", \"0100101101\\n1011010010\\n\", \"00101111\\n11010000\\n\", \"000000000000000\\n000000000000000\\n\", \"0000000000\\n0000000000\\n\", \"001\\n110\\n\", \"000000000000000\\n000000000000000\\n\", \"000\\n000\\n\", \"100000\\n011011\\n\", \"10110011011001\\n01001100100110\\n\", \"011\\n100\\n\", \"111\\n000\\n\", \"000\\n110\\n\", \"00000\\n00000\\n\", \"110\\n001\\n\", \"000000000\\n111111111\\n\", \"000000\\n111111\\n\", \"11110011011001\\n00001100100110\\n\", \"10111011011001\\n01000100100110\\n\", \"11110001111001\\n00001110000110\\n\", \"10000011001011\\n01011000010000\\n\", \"00000000\\n00000000\\n\", \"01111011001011\\n10000100110100\\n\", \"0000000000\\n0000000000\\n\", \"000000000000000\\n000000000000000\\n\", \"000000000000000\\n000000000000000\\n\", \"0000000000\\n0000000000\\n\", \"011\\n100\\n\", \"000000000000000\\n000000000000000\\n\", \"111\\n000\\n\", \"011\\n100\\n\", \"011\\n100\\n\", \"000\\n000\\n\", \"0000000000\\n0000000000\\n\", \"000000000000000\\n000000000000000\\n\", \"001\\n110\\n\", \"011\\n100\\n\", \"000\\n000\\n\", \"0000000000\\n0000000000\\n\", \"000000000000000\\n000000000000000\\n\", \"0000000000\\n0000000000\\n\", \"000000000000000\\n000000000000000\\n\", \"000000000000000\\n000000000000000\\n\", \"000\\n000\\n\", \"000000000000000\\n000000000000000\\n\", \"00000\\n00000\\n\", \"110\\n001\\n\", \"011\\n100\\n\", \"000\\n000\\n\"]}", "source": "primeintellect"}
|
Bob recently read about bitwise operations used in computers: AND, OR and XOR. He have studied their properties and invented a new game.
Initially, Bob chooses integer m, bit depth of the game, which means that all numbers in the game will consist of m bits. Then he asks Peter to choose some m-bit number. After that, Bob computes the values of n variables. Each variable is assigned either a constant m-bit number or result of bitwise operation. Operands of the operation may be either variables defined before, or the number, chosen by Peter. After that, Peter's score equals to the sum of all variable values.
Bob wants to know, what number Peter needs to choose to get the minimum possible score, and what number he needs to choose to get the maximum possible score. In both cases, if there are several ways to get the same score, find the minimum number, which he can choose.
Input
The first line contains two integers n and m, the number of variables and bit depth, respectively (1 ≤ n ≤ 5000; 1 ≤ m ≤ 1000).
The following n lines contain descriptions of the variables. Each line describes exactly one variable. Description has the following format: name of a new variable, space, sign ":=", space, followed by one of:
1. Binary number of exactly m bits.
2. The first operand, space, bitwise operation ("AND", "OR" or "XOR"), space, the second operand. Each operand is either the name of variable defined before or symbol '?', indicating the number chosen by Peter.
Variable names are strings consisting of lowercase Latin letters with length at most 10. All variable names are different.
Output
In the first line output the minimum number that should be chosen by Peter, to make the sum of all variable values minimum possible, in the second line output the minimum number that should be chosen by Peter, to make the sum of all variable values maximum possible. Both numbers should be printed as m-bit binary numbers.
Examples
Input
3 3
a := 101
b := 011
c := ? XOR b
Output
011
100
Input
5 1
a := 1
bb := 0
cx := ? OR a
d := ? XOR ?
e := d AND bb
Output
0
0
Note
In the first sample if Peter chooses a number 0112, then a = 1012, b = 0112, c = 0002, the sum of their values is 8. If he chooses the number 1002, then a = 1012, b = 0112, c = 1112, the sum of their values is 15.
For the second test, the minimum and maximum sum of variables a, bb, cx, d and e is 2, and this sum doesn't depend on the number chosen by Peter, so the minimum Peter can choose is 0.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n111\\n\", \"9\\n110011101\\n\", \"5\\n10001\\n\", \"1\\n1\\n\", \"8\\n10101010\\n\", \"2\\n10\\n\", \"14\\n11001100011000\\n\", \"31\\n1000011111111100011110111111111\\n\", \"53\\n10110111011110111110111111011111110111111110111111111\\n\", \"10\\n1000000000\\n\", \"3\\n100\\n\", \"89\\n11111111101111111110111111111011111111101111111110111111111011111111101111111110111111111\\n\", \"4\\n1110\\n\", \"8\\n10101110\\n\", \"14\\n11000100011000\\n\", \"53\\n10110111011110111110111111011111110111111110011111111\\n\", \"10\\n1000000010\\n\", \"3\\n110\\n\", \"4\\n1010\\n\", \"9\\n110010101\\n\", \"8\\n10101111\\n\", \"14\\n11010100011000\\n\", \"10\\n1010000010\\n\", \"4\\n1000\\n\", \"9\\n110010111\\n\", \"14\\n11010100011001\\n\", \"4\\n1011\\n\", \"9\\n110010110\\n\", \"14\\n10010100011001\\n\", \"4\\n1111\\n\", \"9\\n110000111\\n\", \"14\\n10010100011000\\n\", \"14\\n10010100011100\\n\", \"14\\n10010100011101\\n\", \"14\\n10011100011101\\n\", \"14\\n10110100011101\\n\", \"14\\n11110100011101\\n\", \"14\\n11110100011111\\n\", \"5\\n10101\\n\", \"8\\n10111010\\n\", \"14\\n11011100011000\\n\", \"31\\n1000011111111100011110111111110\\n\", \"53\\n10110111011110101110111111011111110111111110111111111\\n\", \"10\\n1000010000\\n\", \"3\\n101\\n\", \"9\\n111011101\\n\", \"8\\n10111110\\n\", \"53\\n10110111011110111110111111011111110111111111011111111\\n\", \"10\\n1000001010\\n\", \"9\\n100010101\\n\", \"14\\n11010100010000\\n\", \"10\\n1010000011\\n\", \"9\\n110110101\\n\", \"14\\n11010110011001\\n\", \"4\\n1100\\n\", \"14\\n10010100011111\\n\", \"4\\n1101\\n\", \"14\\n11010100011010\\n\", \"14\\n10010100001100\\n\", \"14\\n10010110011111\\n\", \"14\\n10011100001101\\n\", \"14\\n10110100010101\\n\", \"14\\n11010100011111\\n\", \"8\\n10110010\\n\", \"14\\n11010101011000\\n\", \"10\\n1000011000\\n\", \"9\\n101011101\\n\", \"8\\n10011110\\n\", \"53\\n10110111111110111110111111011111110111111111011111111\\n\", \"10\\n1000001011\\n\", \"9\\n111011111\\n\", \"14\\n11010101010000\\n\", \"14\\n10110100011111\\n\", \"14\\n11011100011010\\n\", \"14\\n10010100011110\\n\", \"14\\n10001100001101\\n\", \"14\\n10110100010001\\n\", \"14\\n11010100001111\\n\", \"8\\n10110011\\n\", \"14\\n11000101011000\\n\", \"10\\n1000111000\\n\", \"9\\n101010101\\n\", \"53\\n10010111111110111110111111011111110111111111011111111\\n\", \"10\\n1001001011\\n\", \"9\\n101011111\\n\", \"14\\n11010100111010\\n\"], \"outputs\": [\"3\\n\", \"2031\\n\", \"1001\\n\", \"1\\n\", \"11110\\n\", \"10\\n\", \"202002000\\n\", \"100090049\\n\", \"123456789\\n\", \"1000000000\\n\", \"100\\n\", \"999999999\\n\", \"30\\n\", \"1130\\n\", \"2001002000\\n\", \"1234567808\\n\", \"100000010\\n\", \"20\\n\", \"110\\n\", \"20111\\n\", \"114\\n\", \"211002000\\n\", \"11000010\\n\", \"1000\\n\", \"2013\\n\", \"21100201\\n\", \"12\\n\", \"20120\\n\", \"101100201\\n\", \"4\\n\", \"20003\\n\", \"1011002000\\n\", \"101100300\\n\", \"10110031\\n\", \"1030031\\n\", \"1210031\\n\", \"410031\\n\", \"41005\\n\", \"111\\n\", \"1310\\n\", \"23002000\\n\", \"1000900480\\n\", \"1234136789\\n\", \"100010000\\n\", \"11\\n\", \"331\\n\", \"150\\n\", \"123456798\\n\", \"10000110\\n\", \"100111\\n\", \"2110010000\\n\", \"1100002\\n\", \"2211\\n\", \"2120201\\n\", \"200\\n\", \"1011005\\n\", \"21\\n\", \"21100210\\n\", \"1011000200\\n\", \"101205\\n\", \"10300021\\n\", \"12100111\\n\", \"211005\\n\", \"12010\\n\", \"21112000\\n\", \"10002000\\n\", \"1131\\n\", \"1040\\n\", \"12856798\\n\", \"1000012\\n\", \"35\\n\", \"211110000\\n\", \"121005\\n\", \"2300210\\n\", \"10110040\\n\", \"100200021\\n\", \"121001001\\n\", \"2110004\\n\", \"1202\\n\", \"200112000\\n\", \"1003000\\n\", \"11111\\n\", \"101856798\\n\", \"101012\\n\", \"115\\n\", \"2110310\\n\"]}", "source": "primeintellect"}
|
Polycarp has just invented a new binary protocol for data transmission. He is encoding positive integer decimal number to binary string using following algorithm:
* Each digit is represented with number of '1' characters equal to the value of that digit (for 0 it is zero ones).
* Digits are written one by one in order corresponding to number and separated by single '0' character.
Though Polycarp learnt how to encode the numbers, he has no idea how to decode them back. Help him calculate the decoded number.
Input
The first line contains one integer number n (1 ≤ n ≤ 89) — length of the string s.
The second line contains string s — sequence of '0' and '1' characters, number in its encoded format. It is guaranteed that the number corresponding to the string is positive and doesn't exceed 109. The string always starts with '1'.
Output
Print the decoded number.
Examples
Input
3
111
Output
3
Input
9
110011101
Output
2031
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n4:2,5,3,4\\n1:4-1:1-2:5,3\\n4:4,5,2,1\\n4:2,1,3,5\\n1:3-3:4,2,1\\n\", \"3\\n1:2-1:3\\n1:1-1:3\\n1:1-1:2\\n\", \"3\\n2:3,2\\n1:1-1:3\\n2:1,2\\n\", \"4\\n2:2,3-1:4\\n3:4,3,1\\n3:2,4,1\\n1:2-2:1,3\\n\", \"10\\n2:7,4-2:5,8-1:3-1:6-1:2-2:10,9\\n9:6,7,3,4,10,8,9,5,1\\n9:2,1,7,6,9,4,8,10,5\\n8:5,2,1,3,6,9,10,8-1:7\\n1:8-8:9,10,2,6,3,1,7,4\\n9:8,4,1,2,10,9,7,3,5\\n9:1,3,6,2,9,10,5,8,4\\n9:5,2,7,3,6,4,10,1,9\\n9:3,7,6,8,10,5,1,2,4\\n1:9-8:2,7,3,6,8,5,1,4\\n\", \"4\\n3:2,3,4\\n1:1-2:3,4\\n2:1,2-1:4\\n3:1,2,3\\n\", \"5\\n4:3,5,4,2\\n4:5,3,4,1\\n3:4,1,5-1:2\\n2:3,2-2:1,5\\n1:1-3:2,3,4\\n\", \"4\\n1:4-1:2-1:3\\n3:1,3,4\\n3:1,4,2\\n3:1,2,3\\n\", \"4\\n3:2,3,4\\n1:1-1:3-1:4\\n2:1,2-1:4\\n3:1,2,3\\n\", \"4\\n3:2,3,4\\n1:3-1:4-1:1\\n1:4-1:1-1:2\\n1:2-1:3-1:1\\n\", \"5\\n1:3-1:2-2:4,5\\n4:1,3,4,5\\n4:2,4,1,5\\n3:3,1,2-1:5\\n4:1,3,4,2\\n\", \"5\\n4:3,5,2,4\\n3:4,3,1-1:5\\n3:2,1,5-1:4\\n1:2-2:3,5-1:1\\n2:4,3-2:1,2\\n\", \"4\\n3:3,4,2\\n1:3-2:1,4\\n3:1,4,2\\n2:2,3-1:1\\n\", \"4\\n1:3-2:4,2\\n2:3,1-1:4\\n3:4,2,1\\n2:2,3-1:1\\n\", \"3\\n1:3-1:2\\n2:3,1\\n2:2,1\\n\", \"4\\n3:2,4,3\\n2:1,4-1:3\\n2:1,4-1:2\\n2:1,2-1:3\\n\", \"5\\n2:4,5-2:2,3\\n4:1,5,4,3\\n1:2-3:5,4,1\\n1:5-3:2,1,3\\n1:2-3:1,4,3\\n\", \"4\\n3:2,4,3\\n3:3,4,1\\n2:2,1-1:4\\n2:3,2-1:1\\n\", \"5\\n1:4-1:2-1:3-1:5\\n4:1,4,5,3\\n4:2,5,4,1\\n4:5,3,1,2\\n4:2,1,3,4\\n\", \"4\\n1:2-1:4-1:3\\n3:4,3,1\\n1:2-1:1-1:4\\n1:1-1:3-1:2\\n\", \"3\\n2:3,2\\n1:1-1:3\\n1:1-1:2\\n\", \"5\\n1:4-2:3,5-1:2\\n4:1,4,3,5\\n4:2,5,1,4\\n4:1,3,5,2\\n3:1,2,4-1:3\\n\", \"5\\n4:2,4,5,3\\n2:3,5-2:1,4\\n3:2,4,1-1:5\\n1:1-3:2,3,5\\n4:1,4,2,3\\n\", \"4\\n3:2,3,4\\n1:1-2:3,4\\n1:1-1:2-1:4\\n3:1,2,3\\n\", \"2\\n1:2\\n1:1\\n\", \"4\\n3:2,4,3\\n3:3,4,1\\n2:2,1-1:4\\n2:3,1-1:2\\n\", \"4\\n3:2,3,4\\n1:1-2:3,4\\n2:1,2-1:4\\n3:2,1,3\\n\", \"5\\n4:3,4,5,2\\n4:5,3,4,1\\n3:4,1,5-1:2\\n2:3,2-2:1,5\\n1:1-3:2,3,4\\n\", \"5\\n4:5,2,3,4\\n1:4-1:1-2:5,3\\n4:4,5,2,1\\n4:2,1,3,5\\n1:3-3:4,2,1\\n\", \"4\\n1:4-1:2-1:3\\n3:3,1,4\\n3:1,4,2\\n3:1,2,3\\n\", \"5\\n1:3-1:2-2:4,5\\n4:1,3,4,5\\n4:2,1,4,5\\n3:3,1,2-1:5\\n4:1,3,4,2\\n\", \"3\\n1:3-1:2\\n2:3,1\\n2:1,2\\n\", \"4\\n3:2,4,3\\n1:3-1:4-1:1\\n1:4-1:1-1:2\\n1:2-1:3-1:1\\n\", \"4\\n3:2,4,3\\n1:3-1:4-1:1\\n1:3-1:1-1:2\\n1:2-1:3-1:1\\n\", \"4\\n3:2,4,3\\n3:2,4,1\\n2:2,1-1:4\\n2:3,1-1:2\\n\", \"4\\n3:2,3,4\\n1:1-2:3,4\\n2:1,2-1:4\\n3:3,1,2\\n\", \"4\\n3:2,3,4\\n1:2-2:3,4\\n1:1-1:2-1:4\\n3:1,2,3\\n\", \"5\\n4:3,4,5,2\\n4:5,3,1,4\\n3:4,1,5-1:2\\n2:3,2-2:1,5\\n1:1-3:2,3,4\\n\", \"4\\n3:2,4,3\\n1:2-1:4-1:1\\n1:3-1:1-1:2\\n1:2-1:3-1:1\\n\", \"4\\n1:3-2:4,2\\n2:3,1-1:4\\n3:3,2,1\\n2:2,3-1:1\\n\", \"4\\n3:2,4,3\\n3:2,4,1\\n2:2,1-1:4\\n2:2,1-1:2\\n\", \"4\\n1:2-1:4-1:3\\n3:4,3,1\\n1:4-1:1-1:2\\n1:1-1:3-1:2\\n\", \"5\\n4:3,4,5,2\\n4:4,3,5,1\\n3:4,1,5-1:2\\n2:3,2-2:1,5\\n1:1-3:2,3,4\\n\", \"5\\n2:4,5-2:2,3\\n4:1,5,3,4\\n1:2-3:5,4,1\\n1:5-3:2,1,3\\n1:2-3:1,4,3\\n\", \"5\\n2:4,3-2:2,5\\n4:1,5,4,3\\n1:2-3:5,4,1\\n1:5-3:2,1,3\\n1:2-3:1,4,3\\n\", \"4\\n3:2,4,3\\n1:3-1:3-1:1\\n1:3-1:1-1:2\\n1:2-1:3-1:1\\n\", \"4\\n3:3,4,3\\n3:2,4,1\\n2:2,1-1:4\\n2:2,1-1:2\\n\", \"4\\n3:2,3,4\\n1:1-1:3-1:4\\n2:1,3-1:4\\n3:1,2,3\\n\", \"4\\n3:2,4,3\\n1:3-1:4-1:1\\n1:3-1:1-1:2\\n1:2-1:4-1:1\\n\", \"4\\n1:3-2:4,2\\n2:3,1-1:4\\n3:3,1,1\\n2:2,3-1:1\\n\", \"4\\n3:2,3,4\\n1:1-1:3-1:4\\n2:1,3-1:4\\n3:1,3,3\\n\"], \"outputs\": [\"4\\n1 2\\n2 4\\n2 5\\n3 5\\n\", \"-1\\n\", \"2\\n1 2\\n2 3\\n\", \"-1\\n\", \"9\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n1 10\\n4 7\\n5 8\\n9 10\\n\", \"3\\n1 2\\n2 3\\n3 4\\n\", \"4\\n1 5\\n2 3\\n3 4\\n4 5\\n\", \"3\\n1 2\\n1 3\\n1 4\\n\", \"-1\\n\", \"-1\\n\", \"4\\n1 2\\n1 3\\n1 4\\n4 5\\n\", \"-1\\n\", \"3\\n1 4\\n2 3\\n2 4\\n\", \"-1\\n\", \"2\\n1 2\\n1 3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"4\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"-1\\n\", \"-1\\n\", \"4\\n1 2\\n1 4\\n1 5\\n3 5\\n\", \"4\\n1 4\\n2 3\\n2 4\\n3 5\\n\", \"-1\\n\", \"1\\n1 2\\n\", \"-1\\n\", \"3\\n1 2\\n2 3\\n3 4\\n\", \"4\\n1 5\\n2 3\\n3 4\\n4 5\\n\", \"4\\n1 2\\n2 4\\n2 5\\n3 5\\n\", \"3\\n1 2\\n1 3\\n1 4\\n\", \"4\\n1 2\\n1 3\\n1 4\\n4 5\\n\", \"2\\n1 2\\n1 3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"3\\n1 2\\n2 3\\n3 4\\n\", \"-1\\n\", \"4\\n1 5\\n2 3\\n3 4\\n4 5\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"4\\n1 5\\n2 3\\n3 4\\n4 5\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\"]}", "source": "primeintellect"}
|
In the computer network of the Berland State University there are n routers numbered from 1 to n. Some pairs of routers are connected by patch cords. Information can be transmitted over patch cords in both direction. The network is arranged in such a way that communication between any two routers (directly or through other routers) is possible. There are no cycles in the network, so there is only one path between each pair of routers over patch cords.
Unfortunately, the exact topology of the network was lost by administrators. In order to restore it, the following auxiliary information was collected.
For each patch cord p, directly connected to the router i, list of routers located behind the patch cord p relatively i is known. In other words, all routers path from which to the router i goes through p are known. So for each router i there are ki lists, where ki is the number of patch cords connected to i.
For example, let the network consists of three routers connected in chain 1 - 2 - 3. Then:
* the router 1: for the single patch cord connected to the first router there is a single list containing two routers: 2 and 3;
* the router 2: for each of the patch cords connected to the second router there is a list: one list contains the router 1 and the other — the router 3;
* the router 3: for the single patch cord connected to the third router there is a single list containing two routers: 1 and 2.
Your task is to help administrators to restore the network topology, i. e. to identify all pairs of routers directly connected by a patch cord.
Input
The first line contains a single integer n (2 ≤ n ≤ 1000) — the number of routers in the network.
The i-th of the following n lines contains a description of the lists for the router i.
The description of each list begins with the number of routers in it. Then the symbol ':' follows, and after that the numbers of routers from the list are given. This numbers are separated by comma. Lists are separated by symbol '-'.
It is guaranteed, that for each router i the total number of routers in its lists equals to n - 1 and all the numbers in lists of each router are distinct. For each router i lists do not contain the number i.
Output
Print -1 if no solution exists.
In the other case print to the first line n - 1 — the total number of patch cords in the network. In each of the following n - 1 lines print two integers — the routers which are directly connected by a patch cord. Information about each patch cord must be printed exactly once.
Patch cords and routers can be printed in arbitrary order.
Examples
Input
3
2:3,2
1:1-1:3
2:1,2
Output
2
2 1
2 3
Input
5
4:2,5,3,4
1:4-1:1-2:5,3
4:4,5,2,1
4:2,1,3,5
1:3-3:4,2,1
Output
4
2 1
2 4
5 2
3 5
Input
3
1:2-1:3
1:1-1:3
1:1-1:2
Output
-1
Note
The first example is analyzed in the statement.
The answer to the second example is shown on the picture.
<image>
The first router has one list, which contains all other routers. The second router has three lists: the first — the single router 4, the second — the single router 1, the third — two routers 3 and 5. The third router has one list, which contains all other routers. The fourth router also has one list, which contains all other routers. The fifth router has two lists: the first — the single router 3, the second — three routers 1, 2 and 4.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n1\\n2\\n3\\n\\nSAMPLE\", \"3\\n1\\n2\\n4\\n\\nSAMPLE\", \"3\\n1\\n4\\n4\\n\\nSAMPLE\", \"3\\n1\\n4\\n7\\n\\nSALPME\", \"3\\n1\\n2\\n5\\n\\nSAMPLE\", \"3\\n1\\n1\\n4\\n\\nSAMPLE\", \"3\\n1\\n4\\n1\\n\\nSALPME\", \"3\\n1\\n4\\n6\\n\\nSALPME\", \"3\\n1\\n2\\n9\\n\\nSAMPLE\", \"3\\n2\\n1\\n4\\n\\nSAMPLE\", \"3\\n2\\n4\\n1\\n\\nSALPME\", \"3\\n1\\n8\\n6\\n\\nSALPME\", \"3\\n1\\n1\\n9\\n\\nSAMPLE\", \"3\\n2\\n4\\n2\\n\\nSALPME\", \"3\\n3\\n4\\n2\\n\\nSALPME\", \"3\\n1\\n8\\n1\\n\\nEMPLAS\", \"3\\n3\\n7\\n2\\n\\nSALPME\", \"3\\n1\\n7\\n1\\n\\nEMPLAS\", \"3\\n1\\n10\\n1\\n\\nEMPLAS\", \"3\\n3\\n1\\n2\\n\\nEMPLAS\", \"3\\n1\\n5\\n1\\n\\nEMPLAS\", \"3\\n3\\n2\\n2\\n\\nEMPLAS\", \"3\\n1\\n5\\n2\\n\\nEMPLAS\", \"3\\n3\\n3\\n2\\n\\nEMPLAS\", \"3\\n2\\n3\\n2\\n\\nSALPME\", \"3\\n1\\n4\\n2\\n\\nEMALPS\", \"3\\n2\\n6\\n2\\n\\nSALPME\", \"3\\n2\\n6\\n3\\n\\nSALPME\", \"3\\n2\\n4\\n4\\n\\nELALPS\", \"3\\n4\\n6\\n3\\n\\nSALPMF\", \"3\\n4\\n4\\n4\\n\\nELALPS\", \"3\\n4\\n3\\n3\\n\\nSALPMF\", \"3\\n1\\n6\\n4\\n\\nELALPS\", \"3\\n4\\n3\\n1\\n\\nRALPMG\", \"3\\n4\\n3\\n2\\n\\nRALPMG\", \"3\\n4\\n5\\n2\\n\\nRAPLMG\", \"3\\n4\\n5\\n1\\n\\nRAPLMG\", \"3\\n1\\n2\\n3\\n\\nSMAPLE\", \"3\\n1\\n3\\n4\\n\\nSAMPLE\", \"3\\n1\\n6\\n7\\n\\nSALPME\", \"3\\n1\\n2\\n2\\n\\nSAMPLE\", \"3\\n1\\n1\\n3\\n\\nSAMPLE\", \"3\\n2\\n4\\n6\\n\\nSALPME\", \"3\\n1\\n2\\n16\\n\\nSAMPLE\", \"3\\n1\\n8\\n4\\n\\nEMPLAS\", \"3\\n3\\n11\\n2\\n\\nSALPME\", \"3\\n2\\n1\\n9\\n\\nSBEPLM\", \"3\\n3\\n7\\n4\\n\\nSALPME\", \"3\\n3\\n12\\n2\\n\\nEMPLAS\", \"3\\n1\\n10\\n2\\n\\nEMPLAS\", \"3\\n3\\n3\\n3\\n\\nEMPLAS\", \"3\\n1\\n3\\n2\\n\\nSALPME\", \"3\\n1\\n7\\n2\\n\\nEMALPS\", \"3\\n2\\n1\\n3\\n\\nSALPME\", \"3\\n2\\n6\\n5\\n\\nSALPMF\", \"3\\n1\\n3\\n3\\n\\nSALPMF\", \"3\\n4\\n4\\n2\\n\\nRALPMG\", \"3\\n7\\n3\\n2\\n\\nRAPLMG\", \"3\\n8\\n5\\n2\\n\\nRAPLMG\", \"3\\n4\\n1\\n1\\n\\nRAPLMG\", \"3\\n7\\n5\\n1\\n\\nRAPLMF\", \"3\\n2\\n6\\n4\\n\\nSALPLE\", \"3\\n1\\n1\\n2\\n\\nSAMPLE\", \"3\\n1\\n1\\n1\\n\\nSAMPLE\", \"3\\n1\\n4\\n5\\n\\nSAMPLF\", \"3\\n1\\n3\\n7\\n\\nSALLPE\", \"3\\n1\\n3\\n16\\n\\nSAMPLE\", \"3\\n2\\n2\\n4\\n\\nTAMPLE\", \"3\\n2\\n8\\n4\\n\\nEMPLAS\", \"3\\n2\\n11\\n2\\n\\nSALPME\", \"3\\n1\\n7\\n4\\n\\nSALPME\", \"3\\n3\\n1\\n1\\n\\nFMPLAS\", \"3\\n2\\n3\\n3\\n\\nEMPLAS\", \"3\\n6\\n3\\n2\\n\\nEMPLAR\", \"3\\n3\\n6\\n2\\n\\nSAKPME\", \"3\\n2\\n4\\n9\\n\\nELALPS\", \"3\\n2\\n4\\n3\\n\\nELALPS\", \"3\\n8\\n6\\n3\\n\\nSAMPMF\", \"3\\n4\\n4\\n1\\n\\nQALPMG\", \"3\\n4\\n1\\n3\\n\\nRALPMG\", \"3\\n7\\n1\\n2\\n\\nRAPLMG\", \"3\\n7\\n5\\n2\\n\\nRAPLMF\", \"3\\n2\\n2\\n2\\n\\nSAMPEL\", \"3\\n2\\n6\\n1\\n\\nSALPLE\", \"3\\n2\\n3\\n16\\n\\nSAMPLE\", \"3\\n2\\n3\\n4\\n\\nTAMPLE\", \"3\\n2\\n8\\n6\\n\\nSALQMF\", \"3\\n1\\n1\\n13\\n\\nDLPMBS\", \"3\\n4\\n11\\n2\\n\\nSALPME\", \"3\\n2\\n1\\n12\\n\\nSBEPMM\", \"3\\n1\\n12\\n2\\n\\nENPLAS\", \"3\\n1\\n6\\n2\\n\\nSAKPME\", \"3\\n4\\n4\\n8\\n\\nELAKPT\", \"3\\n3\\n4\\n1\\n\\nQALPMG\", \"3\\n7\\n10\\n2\\n\\nRAPLMF\", \"3\\n4\\n2\\n2\\n\\nSAMPEL\", \"3\\n2\\n8\\n1\\n\\nSALPLE\", \"3\\n2\\n3\\n7\\n\\nSALLPD\", \"3\\n2\\n12\\n6\\n\\nSALQMF\", \"3\\n1\\n1\\n10\\n\\nDLPMBS\", \"3\\n4\\n1\\n12\\n\\nSBEPMM\"], \"outputs\": [\"1\\n4\\n7\\n\", \"1\\n4\\n10\\n\", \"1\\n10\\n10\\n\", \"1\\n10\\n20\\n\", \"1\\n4\\n13\\n\", \"1\\n1\\n10\\n\", \"1\\n10\\n1\\n\", \"1\\n10\\n17\\n\", \"1\\n4\\n28\\n\", \"4\\n1\\n10\\n\", \"4\\n10\\n1\\n\", \"1\\n24\\n17\\n\", \"1\\n1\\n28\\n\", \"4\\n10\\n4\\n\", \"7\\n10\\n4\\n\", \"1\\n24\\n1\\n\", \"7\\n20\\n4\\n\", \"1\\n20\\n1\\n\", \"1\\n32\\n1\\n\", \"7\\n1\\n4\\n\", \"1\\n13\\n1\\n\", \"7\\n4\\n4\\n\", \"1\\n13\\n4\\n\", \"7\\n7\\n4\\n\", \"4\\n7\\n4\\n\", \"1\\n10\\n4\\n\", \"4\\n17\\n4\\n\", \"4\\n17\\n7\\n\", \"4\\n10\\n10\\n\", \"10\\n17\\n7\\n\", \"10\\n10\\n10\\n\", \"10\\n7\\n7\\n\", \"1\\n17\\n10\\n\", \"10\\n7\\n1\\n\", \"10\\n7\\n4\\n\", \"10\\n13\\n4\\n\", \"10\\n13\\n1\\n\", \"1\\n4\\n7\\n\", \"1\\n7\\n10\\n\", \"1\\n17\\n20\\n\", \"1\\n4\\n4\\n\", \"1\\n1\\n7\\n\", \"4\\n10\\n17\\n\", \"1\\n4\\n58\\n\", \"1\\n24\\n10\\n\", \"7\\n35\\n4\\n\", \"4\\n1\\n28\\n\", \"7\\n20\\n10\\n\", \"7\\n41\\n4\\n\", \"1\\n32\\n4\\n\", \"7\\n7\\n7\\n\", \"1\\n7\\n4\\n\", \"1\\n20\\n4\\n\", \"4\\n1\\n7\\n\", \"4\\n17\\n13\\n\", \"1\\n7\\n7\\n\", \"10\\n10\\n4\\n\", \"20\\n7\\n4\\n\", \"24\\n13\\n4\\n\", \"10\\n1\\n1\\n\", \"20\\n13\\n1\\n\", \"4\\n17\\n10\\n\", \"1\\n1\\n4\\n\", \"1\\n1\\n1\\n\", \"1\\n10\\n13\\n\", \"1\\n7\\n20\\n\", \"1\\n7\\n58\\n\", \"4\\n4\\n10\\n\", \"4\\n24\\n10\\n\", \"4\\n35\\n4\\n\", \"1\\n20\\n10\\n\", \"7\\n1\\n1\\n\", \"4\\n7\\n7\\n\", \"17\\n7\\n4\\n\", \"7\\n17\\n4\\n\", \"4\\n10\\n28\\n\", \"4\\n10\\n7\\n\", \"24\\n17\\n7\\n\", \"10\\n10\\n1\\n\", \"10\\n1\\n7\\n\", \"20\\n1\\n4\\n\", \"20\\n13\\n4\\n\", \"4\\n4\\n4\\n\", \"4\\n17\\n1\\n\", \"4\\n7\\n58\\n\", \"4\\n7\\n10\\n\", \"4\\n24\\n17\\n\", \"1\\n1\\n44\\n\", \"10\\n35\\n4\\n\", \"4\\n1\\n41\\n\", \"1\\n41\\n4\\n\", \"1\\n17\\n4\\n\", \"10\\n10\\n24\\n\", \"7\\n10\\n1\\n\", \"20\\n32\\n4\\n\", \"10\\n4\\n4\\n\", \"4\\n24\\n1\\n\", \"4\\n7\\n20\\n\", \"4\\n41\\n17\\n\", \"1\\n1\\n32\\n\", \"10\\n1\\n41\\n\"]}", "source": "primeintellect"}
|
Little Monty is very fond of Fibonacci numbers and challenges his friend Lopa
that he can solve any question regarding the same. Lopa however is jealous
and after thinking for a long time came up with a problem.
She says given
N(the number of fibonacci numbers) one has to count all the multiples of all
the fibonacci numbers. This statement can be quite confusing hence look at the
mathematical definition and test cases for better understanding.
Let M(x) denote the number of multiple of x in the sequence and F(y) denote
the yth fibonacci number. The required answer is:
Take the first two number of the sequence to be 1 and 1.
Input Format
The first line contains T i.e. the number of test cases.
T lines follow, each line containing an integer, N.
(The sample fibonacci series for n=5 is 1, 1, 2, 3, 5)
Output Format
For each testcase, print the output that Lopa wants in one line.
Constraints
1 ≤ T ≤ 1000
1 ≤ N ≤ 1000
SAMPLE INPUT
3
1
2
3
SAMPLE OUTPUT
1
4
7
Explanation
For N=1. The fibonacci number is 1. The multiple of 1 is 1(itself). Hence the answer is 1.
For N=2. The fibonacci number is 1, 1. The multiple of 1(first fibonacci number) is 1(first fibonacci number) and 1(second fibonacci number). The multiple of 1(second fibonacci number) is 1(first fibonacci number) and 1(second fibonacci number). Hence the answer is 4.
For n=3. The fibonacci sequence is 1, 1, 2 . The multiples of 1(first fibonacci number) is 1(itself) and 1(second fibonacci number) and 2. The multiples of 1(second fibonacci number) is 1(first fibonacci number), 1(itself) and 2. The multiple of 2 is 2(itself). Hence the answer is 7.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"4 3\\n3543\", \"20 11\\n33883322005544116655\", \"4 2\\n2020\", \"20 8\\n33883322005544116655\", \"20 5\\n33883322005544116655\", \"20 5\\n35091597582718018558\", \"20 3\\n35091597582718018558\", \"20 5\\n34713145004890865366\", \"20 5\\n63523169932268849551\", \"20 2\\n33883322005544116655\", \"20 5\\n39199232665812066366\", \"20 1\\n33883322005544116655\", \"20 5\\n47579150395957846029\", \"20 5\\n49062164197271661909\", \"20 5\\n21039509252647103775\", \"4 3\\n2919\", \"20 11\\n36673895194000463959\", \"4 1\\n2020\", \"20 12\\n33883322005544116655\", \"20 4\\n56634154780773330382\", \"20 5\\n45700466732094913207\", \"20 5\\n80262801877286319154\", \"4 3\\n1541\", \"20 12\\n10763178948652303319\", \"20 3\\n56634154780773330382\", \"20 16\\n10763178948652303319\", \"20 3\\n46641478607660491854\", \"20 6\\n33883322005544116655\", \"20 2\\n63481141552985125698\", \"20 9\\n34713145004890865366\", \"20 5\\n78241045045927541728\", \"20 5\\n56634154780773330382\", \"20 5\\n70910203754927152255\", \"20 5\\n68623237005374317174\", \"4 3\\n3041\", \"20 5\\n64233050277017797062\", \"20 5\\n64082820716121964551\", \"4 2\\n3041\", \"20 5\\n120786170909293573286\", \"20 7\\n64082820716121964551\", \"20 5\\n25463205115636900601\", \"20 2\\n35091597582718018558\", \"20 7\\n34713145004890865366\", \"20 8\\n36673895194000463959\", \"20 2\\n46641478607660491854\", \"20 6\\n54563765835862962500\", \"20 2\\n91616890468299060863\", \"20 5\\n33400284924017557751\", \"20 3\\n70910203754927152255\", \"4 6\\n1793\", \"20 6\\n86811575049688112831\", \"4 4\\n3041\", \"4 2\\n1173\", \"20 5\\n142844074699528851997\", \"20 4\\n35091597582718018558\", \"20 6\\n22559860210561303756\", \"4 2\\n2058\", \"20 2\\n24851507063065426885\", \"20 9\\n46280926482052991001\", \"20 9\\n20264339970364027228\", \"20 2\\n35707963453301215040\", \"20 11\\n53465107063652597527\", \"20 13\\n33883322005544116655\", \"20 2\\n15884722865080868051\", \"20 5\\n61221862348494034783\", \"20 5\\n40485206747914683040\", \"20 2\\n45333253375453954057\", \"20 5\\n46641478607660491854\", \"20 7\\n56382348392986817014\", \"20 5\\n234661398276925987704\", \"20 2\\n44266490953809705498\", \"20 3\\n83069831581883249798\", \"4 2\\n1688\", \"20 13\\n49082328226971304044\", \"20 9\\n14018019523705439643\", \"20 7\\n62409452523044762298\", \"20 2\\n85996213811074399494\", \"20 8\\n59304693997605481538\", \"20 2\\n83760232926677939238\", \"20 14\\n31343362464311470441\", \"20 2\\n65120561418738561623\", \"20 7\\n69579549294736319522\", \"20 26\\n11177936417238695657\", \"20 43\\n11177936417238695657\", \"20 2\\n22087475858737814107\", \"20 22\\n18749369940970223561\", \"20 5\\n37782958109119482755\", \"20 2\\n29038608160197666750\", \"20 5\\n103090319159265902647\", \"20 2\\n57355150744928513664\", \"20 2\\n30828626758953297040\", \"20 2\\n30979043201770128342\", \"20 2\\n26815384055013021233\", \"20 16\\n46280926482052991001\", \"20 5\\n11124332407574166405\", \"20 5\\n53239178134672239910\", \"20 2\\n40786224234492210774\", \"20 12\\n69966438306858691658\", \"20 2\\n89468721425438927062\", \"20 13\\n66925254151992414938\", \"20 2\\n83069831581883249798\", \"20 2\\n137675936412705515509\", \"20 2\\n17543487021090060035\"], \"outputs\": [\"6\", \"68\", \"10\", \"171\\n\", \"81\\n\", \"72\\n\", \"66\\n\", \"58\\n\", \"40\\n\", \"103\\n\", \"26\\n\", \"210\\n\", \"60\\n\", \"22\\n\", \"62\\n\", \"4\\n\", \"19\\n\", \"10\\n\", \"53\\n\", \"190\\n\", \"42\\n\", \"28\\n\", \"2\\n\", \"57\\n\", \"67\\n\", \"136\\n\", \"64\\n\", \"59\\n\", \"93\\n\", \"23\\n\", \"49\\n\", \"36\\n\", \"79\\n\", \"30\\n\", \"3\\n\", \"51\\n\", \"48\\n\", \"5\\n\", \"39\\n\", \"33\\n\", \"80\\n\", \"90\\n\", \"27\\n\", \"153\\n\", \"135\\n\", \"70\\n\", \"149\\n\", \"71\\n\", \"76\\n\", \"1\\n\", \"63\\n\", \"6\\n\", \"0\\n\", \"37\\n\", \"172\\n\", \"82\\n\", \"7\\n\", \"142\\n\", \"31\\n\", \"24\\n\", \"105\\n\", \"20\\n\", \"13\\n\", \"151\\n\", \"15\\n\", \"52\\n\", \"54\\n\", \"43\\n\", \"38\\n\", \"35\\n\", \"108\\n\", \"75\\n\", \"9\\n\", \"16\\n\", \"34\\n\", \"32\\n\", \"85\\n\", \"154\\n\", \"95\\n\", \"25\\n\", \"104\\n\", \"29\\n\", \"14\\n\", \"8\\n\", \"87\\n\", \"18\\n\", \"56\\n\", \"119\\n\", \"55\\n\", \"113\\n\", \"118\\n\", \"120\\n\", \"91\\n\", \"139\\n\", \"61\\n\", \"21\\n\", \"131\\n\", \"88\\n\", \"138\\n\", \"12\\n\", \"100\\n\", \"69\\n\", \"128\\n\"]}", "source": "primeintellect"}
|
Takahashi has a string S of length N consisting of digits from `0` through `9`.
He loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N \times (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.
Here substrings starting with a `0` also count, and substrings originated from different positions in S are distinguished, even if they are equal as strings or integers.
Compute this count to help Takahashi.
Constraints
* 1 \leq N \leq 2 \times 10^5
* S consists of digits.
* |S| = N
* 2 \leq P \leq 10000
* P is a prime number.
Input
Input is given from Standard Input in the following format:
N P
S
Output
Print the number of non-empty (contiguous) substrings of S that are divisible by P when regarded as an integer written in base ten.
Examples
Input
4 3
3543
Output
6
Input
4 2
2020
Output
10
Input
20 11
33883322005544116655
Output
68
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 10\\n4 1\\n3 1\\n4 1\", \"6 4\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\\n1 1\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n319670097 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n122253639 1\\n824646518 2\\n902554792 2\", \"1 10\\n10 1\", \"3 15\\n4 1\\n3 1\\n4 1\", \"6 4\\n1 1\\n0 1\\n1 1\\n1 1\\n1 1\\n1 1\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n122253639 1\\n824646518 2\\n902554792 2\", \"2 10\\n10 1\", \"3 15\\n4 1\\n3 1\\n6 1\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n902554792 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n902554792 2\", \"3 28\\n8 1\\n3 1\\n6 1\", \"3 28\\n10 1\\n3 1\\n6 1\", \"12 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"6 4\\n1 1\\n1 1\\n1 1\\n1 1\\n2 1\\n1 1\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n122253639 1\\n824646518 2\\n902554792 2\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n151289162 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n902554792 2\", \"3 28\\n8 1\\n1 1\\n6 1\", \"12 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n1074360 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n156162414 1\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n483976928 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n170856517 1\\n335134457 1\\n49245790 1\\n1257975903 4\\n902554792 2\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n319670097 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 2\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n78312281 1\\n824646518 2\\n902554792 2\", \"6 4\\n1 1\\n0 1\\n1 1\\n1 1\\n2 0\\n1 2\", \"3 28\\n1 1\\n1 1\\n6 1\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 2\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"20 987654321\\n258828350 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n902554792 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 3\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n176383857 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n1140334472 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n546482988 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n156162414 1\\n458437539 1\\n258406183 3\\n202863355 0\\n112218745 1\\n485744751 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n191442573 2\\n202863355 0\\n112218745 1\\n348732033 1\\n194021488 2\\n382398703 1\\n55854389 0\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n170856517 1\\n335134457 1\\n65071767 1\\n1257975903 4\\n902554792 2\", \"20 987654321\\n50221307 1\\n162021979 1\\n458437539 1\\n319670097 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 2\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n78312281 1\\n824646518 2\\n902554792 2\", \"20 987654321\\n258828350 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n96996012 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n175006048 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n13178737 1\\n283445191 1\\n151300613 1\\n693338042 2\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 2\\n902554792 2\", \"10 987654321\\n129662684 2\\n101758273 2\\n458437539 2\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"6 987654321\\n129662684 2\\n162021979 1\\n175006048 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n13178737 1\\n283445191 1\\n151300613 1\\n693338042 2\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 2\\n902554792 2\", \"10 987654321\\n129662684 2\\n140067724 2\\n458437539 2\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n80500056 1\\n563556861 0\\n151300613 1\\n693338042 2\\n174929831 2\\n386707193 1\\n204580036 1\\n553684838 1\\n49245790 1\\n824646518 6\\n902554792 2\", \"10 987654321\\n176654507 2\\n228720281 1\\n253603396 1\\n483976928 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 1\\n386707193 1\\n170856517 0\\n335134457 1\\n49245790 1\\n1257975903 4\\n902554792 2\", \"20 987654321\\n258828350 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n96996012 2\", \"3 54\\n2 1\\n0 1\\n7 1\", \"12 987654321\\n129662684 0\\n164601024 1\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n546482988 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"13 987654321\\n129662684 2\\n140067724 2\\n458437539 2\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n156162414 1\\n458437539 1\\n258406183 3\\n202863355 0\\n112218745 1\\n485744751 1\\n323036578 2\\n382398703 1\\n10279910 1\\n427763169 0\\n151300613 1\\n693338042 2\\n279240448 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"20 987654321\\n258828350 2\\n79353943 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n96996012 2\", \"6 987654321\\n129662684 2\\n162021979 1\\n266870585 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n15396583 1\\n283445191 1\\n151300613 1\\n693338042 2\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 2\\n902554792 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n96996012 2\", \"12 987654321\\n129662684 0\\n102812229 1\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n546482988 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n73143007 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"13 987654321\\n129662684 4\\n140067724 2\\n458437539 2\\n258406183 2\\n330090240 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n258406183 0\\n346660608 1\\n126102326 1\\n1074360 1\\n323036578 2\\n382398703 2\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 4\\n386707193 1\\n264650101 1\\n335134457 1\\n126287332 1\\n824646518 4\\n1583142159 2\", \"13 987654321\\n129662684 4\\n140067724 2\\n458437539 2\\n258406183 2\\n330090240 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n75474834 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"17 987654321\\n129662684 4\\n140067724 2\\n458437539 2\\n258406183 2\\n330090240 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n75474834 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n189599958 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n80500056 1\\n661753608 0\\n151300613 1\\n693338042 2\\n174929831 2\\n386707193 1\\n204580036 1\\n553684838 0\\n49245790 1\\n1212555348 6\\n362803241 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n82753736 2\\n824646518 2\\n96996012 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n137553404 2\\n56157703 1\\n204580036 1\\n335134457 1\\n82753736 1\\n824646518 2\\n96996012 2\", \"6 845437684\\n129662684 2\\n162021979 1\\n266870585 1\\n296393966 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n15396583 1\\n283445191 1\\n151300613 1\\n693338042 0\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 1\\n902554792 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n137553404 2\\n56157703 1\\n204580036 1\\n335134457 1\\n82753736 1\\n824646518 2\\n147476715 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n137553404 2\\n56157703 1\\n204580036 1\\n335134457 1\\n97080858 1\\n824646518 2\\n147476715 3\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n137553404 2\\n56157703 1\\n324486806 1\\n335134457 1\\n97080858 1\\n824646518 2\\n147476715 3\", \"12 987654321\\n125837218 0\\n102812229 1\\n458437539 2\\n258406183 -1\\n202863355 1\\n62079242 1\\n348732033 1\\n323036578 2\\n382398703 1\\n8652337 2\\n546482988 2\\n151300613 1\\n139859119 3\\n269900371 4\\n386707193 1\\n6166041 2\\n99760870 1\\n38590089 1\\n824646518 1\\n902554792 2\", \"2 782361618\\n390916614 5\\n176290976 1\\n458437539 1\\n15600532 2\\n1827839 1\\n186561424 0\\n466931608 2\\n460526366 2\\n77208630 1\\n17327151 4\\n19862349 -2\\n141479926 0\\n743958581 0\\n556689387 0\\n386707193 1\\n107021330 1\\n335134457 1\\n226471030 2\\n1014066981 3\\n41223664 5\", \"2 782361618\\n390916614 5\\n158223686 1\\n458437539 1\\n23628194 2\\n1827839 1\\n186561424 0\\n466931608 2\\n460526366 2\\n77208630 1\\n17327151 4\\n37157364 -2\\n185631984 0\\n2242790132 0\\n556689387 0\\n386707193 1\\n107021330 1\\n335134457 1\\n142444970 2\\n1014066981 0\\n41223664 5\", \"2 782361618\\n390916614 5\\n295009694 1\\n458437539 1\\n23628194 2\\n1827839 1\\n186561424 0\\n466931608 2\\n460526366 4\\n77208630 1\\n17327151 4\\n12398386 -2\\n29862040 0\\n2242790132 0\\n556689387 0\\n386707193 1\\n107021330 1\\n335134457 1\\n278452014 2\\n1014066981 0\\n41223664 5\", \"2 782361618\\n390916614 5\\n308705932 1\\n458437539 1\\n23628194 2\\n1827839 1\\n186561424 0\\n466931608 4\\n460526366 4\\n77208630 1\\n17327151 4\\n12398386 -2\\n29862040 0\\n4142736599 0\\n556689387 0\\n386707193 1\\n107021330 1\\n335134457 1\\n278452014 2\\n1014066981 -1\\n41223664 5\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n283445191 1\\n109180659 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n902554792 2\", \"3 28\\n1 1\\n3 1\\n6 1\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n281923594 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 2\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"20 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n319670097 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 2\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n220635430 1\\n824646518 2\\n902554792 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 2\\n458437539 1\\n483976928 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n170856517 1\\n335134457 1\\n49245790 1\\n1257975903 4\\n902554792 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n283445191 1\\n115540513 1\\n693338042 2\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 2\\n902554792 2\", \"10 987654321\\n190039677 2\\n228720281 1\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n553684838 1\\n49245790 1\\n824646518 6\\n902554792 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 3\\n202863355 1\\n112218745 2\\n348732033 1\\n323036578 2\\n176383857 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n1140334472 2\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n546482988 2\\n123295001 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 2\\n680521146 2\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n458437539 1\\n483976928 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n253794953 1\\n55854389 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 1\\n386707193 1\\n170856517 0\\n335134457 1\\n49245790 1\\n1257975903 4\\n902554792 2\", \"20 987654321\\n258828350 2\\n162021979 1\\n211781862 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n96996012 2\", \"12 987654321\\n129662684 2\\n178726839 1\\n175006048 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n13178737 1\\n283445191 1\\n151300613 1\\n693338042 2\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 2\\n902554792 2\", \"10 987654321\\n129662684 2\\n228720281 1\\n150573388 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n563556861 0\\n151300613 1\\n693338042 2\\n174929831 2\\n386707193 1\\n204580036 1\\n553684838 1\\n49245790 1\\n824646518 6\\n902554792 2\", \"3 10\\n3 1\\n3 2\\n10 2\", \"12 987654321\\n129662684 0\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 0\\n215375601 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n546482988 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n140067724 2\\n458437539 2\\n258406183 2\\n202863355 0\\n112218745 1\\n43334447 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n176654507 2\\n228720281 1\\n253603396 1\\n483976928 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n28199130 1\\n283445191 0\\n151300613 1\\n693338042 2\\n269900371 1\\n386707193 1\\n170856517 0\\n335134457 1\\n49245790 1\\n1257975903 4\\n902554792 2\", \"20 987654321\\n50221307 1\\n162021979 1\\n458437539 1\\n319670097 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 2\\n100903370 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n78312281 1\\n1013891425 2\\n902554792 2\", \"12 987654321\\n129662684 0\\n164601024 1\\n458437539 1\\n258406183 2\\n366988544 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n546482988 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"10 987654321\\n129662684 2\\n127536468 1\\n458437539 1\\n258406183 3\\n202863355 0\\n112218745 1\\n485744751 1\\n323036578 2\\n382398703 1\\n10279910 1\\n427763169 0\\n151300613 1\\n693338042 2\\n279240448 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"6 987654321\\n129662684 2\\n162021979 1\\n17695860 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 1\\n382398703 1\\n15396583 1\\n283445191 1\\n151300613 1\\n693338042 2\\n16463560 2\\n386707193 1\\n204580036 1\\n335134457 1\\n246951404 1\\n824646518 2\\n902554792 2\", \"12 987654321\\n129767156 2\\n228720281 1\\n458437539 1\\n258406183 2\\n346660608 1\\n126102326 1\\n1074360 1\\n323036578 2\\n382398703 2\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 4\\n386707193 1\\n264650101 1\\n335134457 1\\n126287332 1\\n824646518 4\\n1583142159 2\", \"13 987654321\\n129662684 4\\n140067724 2\\n458437539 2\\n258406183 2\\n32341222 0\\n112218745 1\\n348732033 1\\n234435584 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"12 987654321\\n129662684 0\\n102812229 1\\n458437539 1\\n258406183 2\\n202863355 0\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n96632773 1\\n546482988 2\\n151300613 1\\n693338042 2\\n269900371 2\\n386707193 1\\n73143007 1\\n114997513 1\\n126287332 1\\n824646518 4\\n902554792 2\", \"20 987654321\\n258828350 2\\n183142297 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 1\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n96996012 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n122253639 2\\n824646518 2\\n144188474 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n191178308 2\\n56157703 1\\n204580036 1\\n335134457 1\\n8496737 1\\n824646518 2\\n96996012 2\", \"20 987654321\\n258828350 2\\n116315472 1\\n458437539 1\\n258406183 2\\n202863355 1\\n79647013 1\\n348732033 1\\n410822061 1\\n121120687 1\\n55854389 1\\n39406026 1\\n151300613 2\\n693338042 2\\n137553404 2\\n88694429 1\\n204580036 1\\n335134457 1\\n82753736 1\\n824646518 2\\n147476715 3\", \"12 987654321\\n198119443 0\\n102812229 1\\n458437539 2\\n258406183 0\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n8652337 1\\n546482988 2\\n151300613 1\\n139859119 3\\n269900371 4\\n386707193 1\\n6166041 2\\n99760870 1\\n38590089 1\\n824646518 1\\n902554792 2\", \"12 987654321\\n125837218 0\\n102812229 1\\n458437539 2\\n258406183 -1\\n202863355 1\\n122813460 1\\n348732033 1\\n323036578 2\\n382398703 1\\n8652337 2\\n963533009 2\\n151300613 1\\n109517069 3\\n269900371 4\\n386707193 1\\n6166041 2\\n99760870 1\\n38590089 2\\n824646518 1\\n902554792 2\", \"20 682742322\\n41742564 2\\n116315472 2\\n85043212 1\\n258406183 2\\n202863355 1\\n79647013 1\\n24975779 0\\n145259444 0\\n65194965 1\\n67914729 0\\n75038829 1\\n170312817 2\\n266601184 1\\n137553404 1\\n36225868 1\\n324486806 1\\n335134457 1\\n97080858 1\\n595319643 2\\n147476715 3\", \"2 782361618\\n390916614 5\\n100488605 1\\n458437539 1\\n23628194 2\\n1827839 1\\n186561424 0\\n466931608 2\\n460526366 2\\n77208630 1\\n17327151 4\\n37157364 -2\\n305456909 0\\n2242790132 0\\n556689387 0\\n386707193 1\\n107021330 1\\n335134457 1\\n278452014 2\\n1014066981 0\\n41223664 5\", \"6 4\\n1 1\\n0 1\\n1 1\\n1 1\\n1 0\\n1 1\", \"2 6\\n10 1\", \"3 15\\n8 1\\n3 1\\n6 1\", \"2 6\\n5 1\", \"12 987654321\\n129662684 2\\n162021979 1\\n458437539 1\\n258406183 2\\n202863355 1\\n112218745 1\\n348732033 1\\n323036578 2\\n382398703 1\\n55854389 1\\n283445191 1\\n151300613 1\\n693338042 2\\n191178308 2\\n386707193 1\\n204580036 1\\n335134457 1\\n126287332 1\\n824646518 2\\n902554792 2\"], \"outputs\": [\"26\", \"12\", \"14829091348\", \"-1\", \"22\\n\", \"10\\n\", \"14829091348\\n\", \"-1\\n\", \"26\\n\", \"14837158734\\n\", \"6391132539\\n\", \"34\\n\", \"38\\n\", \"6524529143\\n\", \"5543889398\\n\", \"14\\n\", \"13841437027\\n\", \"13849504413\\n\", \"30\\n\", \"5536874822\\n\", \"5398773664\\n\", \"6531543719\\n\", \"14741208632\\n\", \"12\\n\", \"16\\n\", \"4867634994\\n\", \"14099768359\\n\", \"5515186996\\n\", \"6811896478\\n\", \"6386427985\\n\", \"4654087798\\n\", \"14582325878\\n\", \"12488650799\\n\", \"5753490314\\n\", \"4613710978\\n\", \"2080357988\\n\", \"4690329880\\n\", \"5593180732\\n\", \"5637873044\\n\", \"11500996478\\n\", \"18\\n\", \"6817054568\\n\", \"6946497572\\n\", \"6295279027\\n\", \"11335660406\\n\", \"2264087062\\n\", \"11409583464\\n\", \"6693476978\\n\", \"7200951342\\n\", \"5162328500\\n\", \"6785010628\\n\", \"10441615391\\n\", \"4984726327\\n\", \"11330583658\\n\", \"10342929337\\n\", \"2498682184\\n\", \"10443890743\\n\", \"10472544987\\n\", \"11460199308\\n\", \"6685826046\\n\", \"1134415180\\n\", \"1098280600\\n\", \"1371852616\\n\", \"1399245092\\n\", \"6306892631\\n\", \"20\\n\", \"7378786860\\n\", \"5473110155\\n\", \"15343240337\\n\", \"6279984402\\n\", \"6460764476\\n\", \"6319612339\\n\", \"5664643384\\n\", \"5403478218\\n\", \"6755885254\\n\", \"5311802208\\n\", \"5642564799\\n\", \"11924560202\\n\", \"5786900034\\n\", \"4857381853\\n\", \"32\\n\", \"7799550799\\n\", \"4035358706\\n\", \"5582562526\\n\", \"14960815692\\n\", \"7804708889\\n\", \"6238027135\\n\", \"1765737612\\n\", \"6524738087\\n\", \"6605453306\\n\", \"6769197264\\n\", \"11543237114\\n\", \"11503968388\\n\", \"11182069660\\n\", \"11431545064\\n\", \"6830390496\\n\", \"7673480367\\n\", \"7184949936\\n\", \"982810438\\n\", \"10\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"6391132539\\n\"]}", "source": "primeintellect"}
|
There is a railroad in Takahashi Kingdom. The railroad consists of N sections, numbered 1, 2, ..., N, and N+1 stations, numbered 0, 1, ..., N. Section i directly connects the stations i-1 and i. A train takes exactly A_i minutes to run through section i, regardless of direction. Each of the N sections is either single-tracked over the whole length, or double-tracked over the whole length. If B_i = 1, section i is single-tracked; if B_i = 2, section i is double-tracked. Two trains running in opposite directions can cross each other on a double-tracked section, but not on a single-tracked section. Trains can also cross each other at a station.
Snuke is creating the timetable for this railroad. In this timetable, the trains on the railroad run every K minutes, as shown in the following figure. Here, bold lines represent the positions of trains running on the railroad. (See Sample 1 for clarification.)
<image>
When creating such a timetable, find the minimum sum of the amount of time required for a train to depart station 0 and reach station N, and the amount of time required for a train to depart station N and reach station 0. It can be proved that, if there exists a timetable satisfying the conditions in this problem, this minimum sum is always an integer.
Formally, the times at which trains arrive and depart must satisfy the following:
* Each train either departs station 0 and is bound for station N, or departs station N and is bound for station 0.
* Each train takes exactly A_i minutes to run through section i. For example, if a train bound for station N departs station i-1 at time t, the train arrives at station i exactly at time t+A_i.
* Assume that a train bound for station N arrives at a station at time s, and departs the station at time t. Then, the next train bound for station N arrives at the station at time s+K, and departs the station at time t+K. Additionally, the previous train bound for station N arrives at the station at time s-K, and departs the station at time t-K. This must also be true for trains bound for station 0.
* Trains running in opposite directions must not be running on the same single-tracked section (except the stations at both ends) at the same time.
Constraints
* 1 \leq N \leq 100000
* 1 \leq K \leq 10^9
* 1 \leq A_i \leq 10^9
* A_i is an integer.
* B_i is either 1 or 2.
Input
The input is given from Standard Input in the following format:
N K
A_1 B_1
A_2 B_2
:
A_N B_N
Output
Print an integer representing the minimum sum of the amount of time required for a train to depart station 0 and reach station N, and the amount of time required for a train to depart station N and reach station 0. If it is impossible to create a timetable satisfying the conditions, print -1 instead.
Examples
Input
3 10
4 1
3 1
4 1
Output
26
Input
1 10
10 1
Output
-1
Input
6 4
1 1
1 1
1 1
1 1
1 1
1 1
Output
12
Input
20 987654321
129662684 2
162021979 1
458437539 1
319670097 2
202863355 1
112218745 1
348732033 1
323036578 1
382398703 1
55854389 1
283445191 1
151300613 1
693338042 2
191178308 2
386707193 1
204580036 1
335134457 1
122253639 1
824646518 2
902554792 2
Output
14829091348
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"the cost of one peach is higher than that of one apple.\", \"the cost of one peach is higher than th`t of one apple.\", \"the cost of ooe peach is higher than th`t of one apple.\", \"the cost of ooe peach is higher than th`t of eno apple.\", \"the cpst of ooe peach is higher than th`t of eno apple.\", \"the cpst of ooe peach is higher than t`ht of eno apple.\", \"eht cpst of ooe peach is higher than t`ht of eno apple.\", \"eht dpst of ooe peach is higher than t`ht of eno apple.\", \"the dpst of ooe peach is higher than t`ht of eno apple.\", \"the tspd of ooe peach is higher than t`ht of eno apple.\", \"eht tspd of ooe peach is higher than t`ht of eno apple.\", \"eht tspd of ooe peach is higher than t`ht of enn apple.\", \"the cost nf one peach is higher than that of one apple.\", \"tie cost of one peach is higher than th`t of one apple.\", \"the cost of ooe peach is higher than th`t of noe apple.\", \"the cost of ooe peach is higher than th`t of eno `pple.\", \"the cpst of ooe peach is higher than th`t of eno bpple.\", \"the cpst of ooe peach is hiehgr than t`ht of eno apple.\", \"eht cpst of ooe peach is higher than t`it of eno apple.\", \"eht dpst of ooe peach is higher nhat t`ht of eno apple.\", \"the dpst of ooe peach is rehgih than t`ht of eno apple.\", \"eht tspd of ooe hcaep is higher than t`ht of eno apple.\", \"eht tsqd of ooe peach is higher than t`ht of enn apple.\", \"the cost nf one peach is higher than taht of one apple.\", \"tie cost of one peach is higher than th`t nf one apple.\", \"the cost of ooe peach is higher than t`ht of noe apple.\", \"the soct of ooe peach is higher than th`t of eno `pple.\", \"the cpst of ooe peach is higher than th`t of neo bpple.\", \"eht cpst of ooe peach is higher tnah t`it of eno apple.\", \"eht dpst of poe peach is higher nhat t`ht of eno apple.\", \"the dpst of ooe peach is rehgih than th`t of eno apple.\", \"egt tspd of ooe hcaep is higher than t`ht of eno apple.\", \"eht tsqd of ooe peach si higher than t`ht of enn apple.\", \"the cost nf one peach is higher than taht nf one apple.\", \"tie cost of one peacg is higher than th`t nf one apple.\", \"the cost of ooe peach is higher than s`ht of noe apple.\", \"the soct og ooe peach is higher than th`t of eno `pple.\", \"the cpst of ooe peach is higher than `htt of neo bpple.\", \"eht cpst of ooe peach is higher tnah t_it of eno apple.\", \"eht dtsp of poe peach is higher nhat t`ht of eno apple.\", \"the dpst of ooe oeach is rehgih than th`t of eno apple.\", \"egt tspd of ooe hcaeq is higher than t`ht of eno apple.\", \"eht tsqd of ooe peach si higher than t`ht of dnn apple.\", \"thd cost nf one peach is higher than taht nf one apple.\", \"tie cost of one peacg js higher than th`t nf one apple.\", \"the cost of ooe hcaep is higher than s`ht of noe apple.\", \"the soct og ooe peach is hifher than th`t of eno `pple.\", \"the cpst of ooe peach is higher than tth` of neo bpple.\", \"eht cspt of ooe peach is higher tnah t_it of eno apple.\", \"eht dtsp og poe peach is higher nhat t`ht of eno apple.\", \"the dpst of ooe oeach is rehgih naht th`t of eno apple.\", \"egt pstd of ooe hcaeq is higher than t`ht of eno apple.\", \"eht tsqd of eoo peach si higher than t`ht of dnn apple.\", \"thd cost nf one peach si higher than taht nf one apple.\", \"tie cost of one peacg jr higher than th`t nf one apple.\", \"the cost of ooe hcaep it higher than s`ht of noe apple.\", \"teh soct og ooe peach is hifher than th`t of eno `pple.\", \"the cpst of ooe peach is higher than tth` nf neo bpple.\", \"eht cspt of ooe peach is higher tnah t_it of eno bpple.\", \"eht dtsp og poe peach si higher nhat t`ht of eno apple.\", \"the tspd of ooe oeach is rehgih naht th`t of eno apple.\", \"egt pstd of ooe hcaeq is higher than s`ht of eno apple.\", \"eit tsqd of eoo peach si higher than t`ht of dnn apple.\", \"thd cost nf one peach si higher tham taht nf one apple.\", \"tie cost nf one peacg jr higher than th`t nf one apple.\", \"the cost of ooe hcaep jt higher than s`ht of noe apple.\", \"teh soct og ooe peach is hifher than th`t of one `pple.\", \"the cpst of ooe peach is rehgih than tth` nf neo bpple.\", \"eht crpt of ooe peach is higher tnah t_it of eno bpple.\", \"eit dtsp og poe peach si higher nhat t`ht of eno apple.\", \"the tspd of ooe oeach is rehfih naht th`t of eno apple.\", \"etg pstd of ooe hcaeq is higher than s`ht of eno apple.\", \"fit tsqd of eoo peach si higher than t`ht of dnn apple.\", \"thd cost nf one peach si higher tham taht nf one aople.\", \"tie cost nf one qeacg jr higher than th`t nf one apple.\", \"the cost of eoo hcaep jt higher than s`ht of noe apple.\", \"teh soct og eoo peach is hifher than th`t of one `pple.\", \"the cpst of ooe peach is rehgih thna tth` nf neo bpple.\", \"eht crpt nf ooe peach is higher tnah t_it of eno bpple.\", \"eit dtsp og poe peach si higher nhat t`ht of emo apple.\", \"etg pstd of ooe hcaeq is higher than s_ht of eno apple.\", \"fit tsqd of eoo peach si higher than t`ht nf dnn apple.\", \"thd cost nf eno peach si higher tham taht nf one aople.\", \"tie cosu nf one qeacg jr higher than th`t nf one apple.\", \"the cost of eoo hcaep jt higher than s`ht of noe `pple.\", \"teh soct og eoo peach ir hifher than th`t of one `pple.\", \"the cpst of oof peach is rehgih thna tth` nf neo bpple.\", \"eht crpt nf ooe peach ir higher tnah t_it of eno bpple.\", \"eit dtsp og poe peach si higher than t`ht of emo apple.\", \"etg pstd of ope hcaeq is higher than s_ht of eno apple.\", \"fit tsqd of eoo peach si higger than t`ht nf dnn apple.\", \"thd cost nf eno peach si higher thal taht nf one aople.\", \"tie cosu nf one qeacg jr higher than th`t nf eno apple.\", \"the cost of eoo hcaep tj higher than s`ht of noe `pple.\", \"teh soct go eoo peach ir hifher than th`t of one `pple.\", \"the cpst of oof peach js rehgih thna tth` nf neo bpple.\", \"eht crpt nf ooe peach ir higher tnah t_it of one bpple.\", \"etg pstd of ope hcaeq is hhgher than s_ht of eno apple.\", \"fit tsqd of eoo peach si higger than t`th nf dnn apple.\", \"thd cost fn eno peach si higher thal taht nf one aople.\", \"ite cosu nf one qeacg jr higher than th`t nf eno apple.\"], \"outputs\": [\"the cost of one apple is higher than that of one peach.\", \"the cost of one apple is higher than th`t of one peach.\\n\", \"the cost of ooe apple is higher than th`t of one peach.\\n\", \"the cost of ooe apple is higher than th`t of eno peach.\\n\", \"the cpst of ooe apple is higher than th`t of eno peach.\\n\", \"the cpst of ooe apple is higher than t`ht of eno peach.\\n\", \"eht cpst of ooe apple is higher than t`ht of eno peach.\\n\", \"eht dpst of ooe apple is higher than t`ht of eno peach.\\n\", \"the dpst of ooe apple is higher than t`ht of eno peach.\\n\", \"the tspd of ooe apple is higher than t`ht of eno peach.\\n\", \"eht tspd of ooe apple is higher than t`ht of eno peach.\\n\", \"eht tspd of ooe apple is higher than t`ht of enn peach.\\n\", \"the cost nf one apple is higher than that of one peach.\\n\", \"tie cost of one apple is higher than th`t of one peach.\\n\", \"the cost of ooe apple is higher than th`t of noe peach.\\n\", \"the cost of ooe apple is higher than th`t of eno `pple.\\n\", \"the cpst of ooe apple is higher than th`t of eno bpple.\\n\", \"the cpst of ooe apple is hiehgr than t`ht of eno peach.\\n\", \"eht cpst of ooe apple is higher than t`it of eno peach.\\n\", \"eht dpst of ooe apple is higher nhat t`ht of eno peach.\\n\", \"the dpst of ooe apple is rehgih than t`ht of eno peach.\\n\", \"eht tspd of ooe hcaep is higher than t`ht of eno peach.\\n\", \"eht tsqd of ooe apple is higher than t`ht of enn peach.\\n\", \"the cost nf one apple is higher than taht of one peach.\\n\", \"tie cost of one apple is higher than th`t nf one peach.\\n\", \"the cost of ooe apple is higher than t`ht of noe peach.\\n\", \"the soct of ooe apple is higher than th`t of eno `pple.\\n\", \"the cpst of ooe apple is higher than th`t of neo bpple.\\n\", \"eht cpst of ooe apple is higher tnah t`it of eno peach.\\n\", \"eht dpst of poe apple is higher nhat t`ht of eno peach.\\n\", \"the dpst of ooe apple is rehgih than th`t of eno peach.\\n\", \"egt tspd of ooe hcaep is higher than t`ht of eno peach.\\n\", \"eht tsqd of ooe apple si higher than t`ht of enn peach.\\n\", \"the cost nf one apple is higher than taht nf one peach.\\n\", \"tie cost of one peacg is higher than th`t nf one peach.\\n\", \"the cost of ooe apple is higher than s`ht of noe peach.\\n\", \"the soct og ooe apple is higher than th`t of eno `pple.\\n\", \"the cpst of ooe apple is higher than `htt of neo bpple.\\n\", \"eht cpst of ooe apple is higher tnah t_it of eno peach.\\n\", \"eht dtsp of poe apple is higher nhat t`ht of eno peach.\\n\", \"the dpst of ooe oeach is rehgih than th`t of eno peach.\\n\", \"egt tspd of ooe hcaeq is higher than t`ht of eno peach.\\n\", \"eht tsqd of ooe apple si higher than t`ht of dnn peach.\\n\", \"thd cost nf one apple is higher than taht nf one peach.\\n\", \"tie cost of one peacg js higher than th`t nf one peach.\\n\", \"the cost of ooe hcaep is higher than s`ht of noe peach.\\n\", \"the soct og ooe apple is hifher than th`t of eno `pple.\\n\", \"the cpst of ooe apple is higher than tth` of neo bpple.\\n\", \"eht cspt of ooe apple is higher tnah t_it of eno peach.\\n\", \"eht dtsp og poe apple is higher nhat t`ht of eno peach.\\n\", \"the dpst of ooe oeach is rehgih naht th`t of eno peach.\\n\", \"egt pstd of ooe hcaeq is higher than t`ht of eno peach.\\n\", \"eht tsqd of eoo apple si higher than t`ht of dnn peach.\\n\", \"thd cost nf one apple si higher than taht nf one peach.\\n\", \"tie cost of one peacg jr higher than th`t nf one peach.\\n\", \"the cost of ooe hcaep it higher than s`ht of noe peach.\\n\", \"teh soct og ooe apple is hifher than th`t of eno `pple.\\n\", \"the cpst of ooe apple is higher than tth` nf neo bpple.\\n\", \"eht cspt of ooe apple is higher tnah t_it of eno bpple.\\n\", \"eht dtsp og poe apple si higher nhat t`ht of eno peach.\\n\", \"the tspd of ooe oeach is rehgih naht th`t of eno peach.\\n\", \"egt pstd of ooe hcaeq is higher than s`ht of eno peach.\\n\", \"eit tsqd of eoo apple si higher than t`ht of dnn peach.\\n\", \"thd cost nf one apple si higher tham taht nf one peach.\\n\", \"tie cost nf one peacg jr higher than th`t nf one peach.\\n\", \"the cost of ooe hcaep jt higher than s`ht of noe peach.\\n\", \"teh soct og ooe apple is hifher than th`t of one `pple.\\n\", \"the cpst of ooe apple is rehgih than tth` nf neo bpple.\\n\", \"eht crpt of ooe apple is higher tnah t_it of eno bpple.\\n\", \"eit dtsp og poe apple si higher nhat t`ht of eno peach.\\n\", \"the tspd of ooe oeach is rehfih naht th`t of eno peach.\\n\", \"etg pstd of ooe hcaeq is higher than s`ht of eno peach.\\n\", \"fit tsqd of eoo apple si higher than t`ht of dnn peach.\\n\", \"thd cost nf one apple si higher tham taht nf one aople.\\n\", \"tie cost nf one qeacg jr higher than th`t nf one peach.\\n\", \"the cost of eoo hcaep jt higher than s`ht of noe peach.\\n\", \"teh soct og eoo apple is hifher than th`t of one `pple.\\n\", \"the cpst of ooe apple is rehgih thna tth` nf neo bpple.\\n\", \"eht crpt nf ooe apple is higher tnah t_it of eno bpple.\\n\", \"eit dtsp og poe apple si higher nhat t`ht of emo peach.\\n\", \"etg pstd of ooe hcaeq is higher than s_ht of eno peach.\\n\", \"fit tsqd of eoo apple si higher than t`ht nf dnn peach.\\n\", \"thd cost nf eno apple si higher tham taht nf one aople.\\n\", \"tie cosu nf one qeacg jr higher than th`t nf one peach.\\n\", \"the cost of eoo hcaep jt higher than s`ht of noe `pple.\\n\", \"teh soct og eoo apple ir hifher than th`t of one `pple.\\n\", \"the cpst of oof apple is rehgih thna tth` nf neo bpple.\\n\", \"eht crpt nf ooe apple ir higher tnah t_it of eno bpple.\\n\", \"eit dtsp og poe apple si higher than t`ht of emo peach.\\n\", \"etg pstd of ope hcaeq is higher than s_ht of eno peach.\\n\", \"fit tsqd of eoo apple si higger than t`ht nf dnn peach.\\n\", \"thd cost nf eno apple si higher thal taht nf one aople.\\n\", \"tie cosu nf one qeacg jr higher than th`t nf eno peach.\\n\", \"the cost of eoo hcaep tj higher than s`ht of noe `pple.\\n\", \"teh soct go eoo apple ir hifher than th`t of one `pple.\\n\", \"the cpst of oof apple js rehgih thna tth` nf neo bpple.\\n\", \"eht crpt nf ooe apple ir higher tnah t_it of one bpple.\\n\", \"etg pstd of ope hcaeq is hhgher than s_ht of eno peach.\\n\", \"fit tsqd of eoo apple si higger than t`th nf dnn peach.\\n\", \"thd cost fn eno apple si higher thal taht nf one aople.\\n\", \"ite cosu nf one qeacg jr higher than th`t nf eno peach.\\n\"]}", "source": "primeintellect"}
|
Fukushima Prefecture is also famous for producing fruits, and among them, peaches and apples boast one of the highest production volumes in Japan. By the way, when I made a print manuscript of an English pamphlet for sale, I mistakenly wrote the description about apples and the description about peaches in reverse.
You've been tasked with fixing apple and peach, but it's kind of annoying. Enter a single line of English text and create a program that outputs the English text with all the character strings apple in it replaced with peach and all the character strings peach replaced with apple.
Input
English text (including half-width alphanumeric characters, spaces, and symbols) is given on one line. The length of the string entered is 1000 or less.
Output
Outputs English sentences with the character strings apple and peach exchanged on one line.
Example
Input
the cost of one peach is higher than that of one apple.
Output
the cost of one apple is higher than that of one peach.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"5 5\\nOIOOI\\nOOIOI\", \"5 0\\nOIOOI\\nOOIOI\", \"5 5\\nOIOOI\\nIOIOO\", \"0 9\\nOIOOI\\nIOIOO\", \"0 0\\nOIOOI\\nOOIOI\", \"5 0\\nOIOOI\\nOOIPI\", \"5 9\\nOIOOI\\nIOIOO\", \"5 0\\nOIOOI\\nOOINI\", \"5 5\\nIOOIO\\nIOIOO\", \"5 1\\nOIOOI\\nOOIPI\", \"5 1\\nOIOOI\\nOOIPH\", \"5 0\\nOIOOI\\nOOIPH\", \"7 0\\nOIOOI\\nOOIPH\", \"7 0\\nOIOOI\\nHPIOO\", \"7 0\\nOJOOI\\nHPIOO\", \"3 0\\nOIOOI\\nOOIOI\", \"5 7\\nOIOOI\\nIOIOO\", \"5 0\\nOIOOI\\nOIOPI\", \"5 5\\nIIOOO\\nIOIOO\", \"5 1\\nOIOOI\\nOOJPI\", \"5 1\\nOIOOH\\nOOIPH\", \"5 0\\nOIOOI\\nOHIPO\", \"13 0\\nOIOOI\\nOOIPH\", \"7 0\\nOOOII\\nHPIOO\", \"7 0\\nOKOOI\\nHPIOO\", \"3 1\\nOIOOI\\nOOIOI\", \"0 1\\nOIOOI\\nOOIOI\", \"3 5\\nIIOOO\\nIOIOO\", \"5 0\\nOIOOI\\nOOJPI\", \"5 0\\nIOOIO\\nOHIPO\", \"23 0\\nOIOOI\\nOOIPH\", \"7 0\\nIIOOO\\nHPIOO\", \"3 1\\nIIOOO\\nIOIOO\", \"5 0\\nOIOOI\\nOOJIP\", \"5 0\\nHOOIO\\nOHIPO\", \"12 0\\nIIOOO\\nHPIOO\", \"1 1\\nIIOOO\\nIOIOO\", \"5 -1\\nHOOIO\\nOHIPO\", \"12 0\\nIHOOO\\nHPIOO\", \"6 -1\\nHOOIO\\nOHIPO\", \"16 0\\nIHOOO\\nHPIOO\", \"6 -1\\nHOOIO\\nOHIQO\", \"16 0\\nIHOOO\\nGPIOO\", \"12 -1\\nHOOIO\\nOHIQO\", \"11 0\\nIHOOO\\nGPIOO\", \"12 0\\nHOOIO\\nOHIQO\", \"9 0\\nOIOOI\\nOOIOI\", \"5 0\\nIOOIO\\nOOIPI\", \"5 -1\\nOIOOI\\nOOINI\", \"5 8\\nIOOIO\\nIOIOO\", \"3 0\\nOIOOI\\nOOIPH\", \"5 0\\nOIOOI\\nOOHPH\", \"4 0\\nOIOOI\\nHPIOO\", \"5 6\\nOIOOI\\nIOIOO\", \"5 -1\\nOIOOI\\nOIOPI\", \"0 9\\nOIOOI\\nIOIOP\", \"2 0\\nOIOOI\\nOOJPI\", \"7 0\\nOOOII\\nHPHOO\", \"7 0\\nOKOOI\\nHOIOP\", \"5 0\\nOOIOI\\nOOJPI\", \"5 -1\\nIOOIO\\nOHIPO\", \"23 0\\nOOIOI\\nOOIPH\", \"7 0\\nIIOOO\\nHPJOO\", \"0 1\\nIIOOO\\nIOIOO\", \"0 0\\nOIOOI\\nOOJIP\", \"7 -1\\nHOOIO\\nOHIPO\", \"6 0\\nIIOOO\\nHPIOO\", \"5 -1\\nHOOIO\\nOHIPN\", \"5 0\\nIHOOO\\nHPIOO\", \"1 -1\\nHOOIO\\nOHIPO\", \"16 0\\nIHOOO\\nIPHOO\", \"6 -1\\nHOOIP\\nOHIQO\", \"12 -1\\nHPOIO\\nOHIQO\", \"5 0\\nIOOIO\\nOOIPH\", \"10 -1\\nOIOOI\\nOOINI\", \"3 0\\nOIPOI\\nOOIPH\", \"5 1\\nOIOOI\\nOOHPH\", \"4 0\\nIOOIO\\nHPIOO\", \"5 11\\nOIOOI\\nIOIOO\", \"5 -1\\nOIOOI\\nOINPI\", \"0 9\\nOIOOI\\nIOIPO\", \"0 0\\nOIOOI\\nOOJPI\", \"7 0\\nOOOII\\nPHHOO\", \"7 -1\\nOKOOI\\nHOIOP\", \"5 0\\nOOIOI\\nOOJPH\", \"5 -1\\nIOOIO\\nOPIHO\", \"18 0\\nOOIOI\\nOOIPH\", \"12 0\\nIIOOO\\nHPJOO\", \"0 1\\nIIOON\\nIOIOO\", \"0 0\\nOIOOI\\nPIJOO\", \"7 -1\\nHIOOO\\nOHIPO\", \"6 0\\nIIOOO\\nPHIOO\", \"5 -2\\nHOOIO\\nOHIPN\", \"5 0\\nOOOHI\\nHPIOO\", \"0 -1\\nHOOIO\\nOHIPO\", \"20 0\\nIHOOO\\nIPHOO\", \"6 -1\\nHOOIP\\nOQIHO\", \"5 0\\nIOOIP\\nOOIPH\", \"10 -1\\nOOIOI\\nOOINI\", \"3 0\\nOIPOI\\nOPIOH\", \"5 1\\nOIOOI\\nONHPH\"], \"outputs\": [\"7\", \"1\\n\", \"7\\n\", \"3\\n\", \"0\\n\", \"1\\n\", \"7\\n\", \"1\\n\", \"7\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"7\\n\", \"1\\n\", \"7\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"7\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"7\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"7\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"7\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
Take the'IOI'train
A new railway has been laid in IOI. Trains running on railways in IOI are a combination of several vehicles, and there are two types of vehicles, I and O. Vehicles can only be connected to different types of vehicles. Also, because the train has a driver's seat, the cars at both ends of the train must be of type I. A train is represented by a character string in which characters indicating the type of vehicle are connected in order, and the length of the train is assumed to be the length of the character string. For example, if vehicles are connected in the order of IOIOI, a train with a length of 5 can be formed, and vehicle I is a train with a length of 1 alone. Trains cannot be formed by arranging vehicles in the order of OIOI or IOOI.
Some vehicles are stored in two garages. Vehicles are lined up in a row in each garage. When forming a train, take out the train from the garage and connect it in front of the garage. Only the vehicle closest to the entrance of the garage can be taken out of the garage, but the order of taking out the vehicle from which garage is arbitrary.
Before forming a train, you can take as many cars out of the garage as you like and move them to another waiting rail. Vehicles that have been moved to the standby rails cannot be used to organize trains in the future. Also, once the train formation is started, the vehicle cannot be moved from the garage to the standby rail until the formation is completed.
When organizing a train, it is not necessary to use up all the cars in the garage. That is, after the train formation is completed, unused cars may remain in the garage.
It is believed that there are so many people on the railroad in IOI, so I want to organize the longest possible train.
<image>
Figure: The train is being organized, and the vehicle in the garage cannot be moved to the standby rail at this time. This figure corresponds to I / O example 1.
Task
Create a program to find the maximum length of trains that can be organized given the information of the cars stored in the garage. The row of vehicles stored in each garage is represented by a string consisting of only two types of letters I and O, and the information in the two garages is represented by the string S of length M and the string T of length N, respectively. Given. Each letter represents one vehicle, the letter of which is the same as the type of vehicle. The first letter of the string represents the vehicle closest to the entrance to the garage, and the last letter represents the vehicle closest to the garage.
Limits
* 1 ≤ M ≤ 2000 Length of string S
* 1 ≤ N ≤ 2000 Length of string T
input
Read the following data from standard input.
* In the first line, M and N are written separated by blanks.
* The character string S is written on the second line.
* The character string T is written on the third line.
output
Output an integer representing the maximum train length that can be organized to the standard output on one line. If no train can be organized, output 0.
Input / output example
Input example 1
5 5
OIOOI
OOIOI
Output example 1
7
Let the garage represented by S be the garage S and the garage represented by T be the garage T. At this time, for example, the first vehicle from the garage S, the first two vehicles from the garage T are put out and put on standby, and then the garage S, the garage S, the garage T, the garage S, the garage S, the garage T, and the garage T are placed in this order. If you take out the vehicle, you can form a train IOIOIOI with a length of 7.
In addition, after the first vehicle from garage S and the first two vehicles from garage T are put out and put on standby, the order is garage T, garage T, garage S, garage S, garage T, garage S, and garage S. You can also organize a 7-length train by putting out a vehicle. Since it is not possible to form a train longer than this, 7 is output.
Input example 2
5 9
IIIII
IIIIIIIII
Output example 2
1
Note that train I, which consists of only one car, also meets the conditions for a train.
The question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.
Example
Input
5 5
OIOOI
OOIOI
Output
7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 0 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n6 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n4 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n23\\n1 -x\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +y\\n3 +y +z -x\\n0\", \"19\\n0 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 0 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -y -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n0 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -y -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +y +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 2 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 5 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 5 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n4 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +x -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 4 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 5 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +x +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 1 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 5 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n0 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +y 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 2 +x 1 +y +z 3 +z\\n 4 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n6 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 3 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n4 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +y\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 5 +y\\n4 +z\\n2 +z\\n19\\n1 +x 0 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 1 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n4 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 1 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +x -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 2 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +z -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n0 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n0 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 0 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 1 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 1 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 5 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n0 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 1 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +z -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n0 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +y 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n6 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n6 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 3 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 2 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 1 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 2 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +z -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 1 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +y 3 +z\\n0 +z -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +y 3 +z\\n0 +z -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n1 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 0 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +y +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +x -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 5 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +x +z\\n3 +y +z -x\\n0\", \"19\\n2 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 4 +y\\n3 +z\\n2 +z\\n19\\n1 +x 0 +y +z 5 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n2 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +x +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 5 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +z -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 2 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n4 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -x\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +y\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 2 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 1 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +z -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n6 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 1 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 0 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 1 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +z -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n0 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +y 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 1 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -y +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 2 +y +z 3 +z -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +x -z +x +y -z -x +z 1 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 0 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 5 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +x -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 5 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -y +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 1 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +x +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 4 +y\\n3 +z\\n2 +z\\n19\\n1 +x 0 +y +z 5 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n3 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +z -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +x -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 5 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -y +x\\n 0 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +y 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 1 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n2 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +x +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +y 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 2 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n6 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n2 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n0 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -y -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +y +y +x +z +y -x -y 1 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 1 +x 1 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 5 +z\\n 2 +z\\n19\\n 0 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 5 +z\\n3 +y -z +x +y -z -x +z 1 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 4 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 5 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +z +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 1 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 1 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n4 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n3 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 2 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 1 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n0 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n0 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -y\\n0 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 0 +z\\n3 +y\\n19\\n0 +x 1 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 0 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 6 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 0 +y +z 3 +y -z +x +y -z -x +z 1 +y\\n3 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n0 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n0 +y -z +x +y -z -x +z 2 +z\\n3 +y\\n19\\n1 +x 2 +y +z 3 +y -z +x +y -z -x +z 3 +y\\n4 +z\\n2 +z\\n19\\n1 +x 1 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n0 +y -z +x\\n1 +z +y +x +z +y -x -y 2 -z\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +z\\n 2 +y\\n19\\n 0 +x 0 +x +z 3 +y -z +x +y -z -x +z 2 +y\\n 3 +z\\n 2 +z\\n19\\n 1 +x 1 +y +z 3 +z\\n 3 +y -z +x +y -z -x +z 2 +y\\n 2 +z\\n18\\n 1 -y\\n 1 +y -z +x\\n 1 +z +y +x +z +y -x -y 2 -y\\n 2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 0 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n2 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n1 +z +x +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\", \"19\\n1 +x 1 +y +z 3 +z\\n3 +y -z +x +y -z -x +z 2 +z\\n2 +y\\n19\\n1 +x 1 +y +z 1 +y -z +x +y -z -x +z 2 +y\\n3 +z\\n2 +z\\n19\\n1 +x 0 +y +z 6 +z\\n3 +y -z +x +y -z -x +z 1 +y\\n2 +z\\n18\\n1 -y\\n1 +y -z +x\\n2 +z +y +x +z +y -x -y 2 -y\\n2 +z\\n3 +x +y +z\\n3 +y +z -x\\n0\"], \"outputs\": [\"SAME\\nSAME\\nDIFFERENT\", \"SAME\\nSAME\\nDIFFERENT\", \"DIFFERENT\\nSAME\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nSAME\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nSAME\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nSAME\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nSAME\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"SAME\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nSAME\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nSAME\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\", \"DIFFERENT\\nDIFFERENT\\nDIFFERENT\\n\"]}", "source": "primeintellect"}
|
Professor Tsukuba invented a mysterious jewelry box that can be opened with a special gold key whose shape is very strange. It is composed of gold bars joined at their ends. Each gold bar has the same length and is placed parallel to one of the three orthogonal axes in a three dimensional space, i.e., x-axis, y-axis and z-axis.
The locking mechanism of the jewelry box is truly mysterious, but the shape of the key is known. To identify the key of the jewelry box, he gave a way to describe its shape.
The description indicates a list of connected paths that completely defines the shape of the key: the gold bars of the key are arranged along the paths and joined at their ends. Except for the first path, each path must start from an end point of a gold bar on a previously defined path. Each path is represented by a sequence of elements, each of which is one of six symbols (+x, -x, +y, -y, +z and -z) or a positive integer. Each symbol indicates the direction from an end point to the other end point of a gold bar along the path. Since each gold bar is parallel to one of the three orthogonal axes, the 6 symbols are enough to indicate the direction. Note that a description of a path has direction but the gold bars themselves have no direction.
An end point of a gold bar can have a label, which is a positive integer. The labeled point may be referred to as the beginnings of other paths. In a key description, the first occurrence of a positive integer defines a label of a point and each subsequent occurrence of the same positive integer indicates the beginning of a new path at the point.
An example of a key composed of 13 gold bars is depicted in Figure 1.
<image>
The following sequence of lines
19
1 +x 1 +y +z 3 +z
3 +y -z +x +y -z -x +z 2 +z
2 +y
is a description of the key in Figure 1. Note that newlines have the same role as space characters in the description, so that `"19 1 +x 1 +y +z 3 +z 3 +y -z +x +y -z -x +z 2 +z 2 +y"` has the same meaning.
The meaning of this description is quite simple. The first integer "19" means the number of the following elements in this description. Each element is one of the 6 symbols or a positive integer.
The integer "1" at the head of the second line is a label attached to the starting point of the first path. Without loss of generality, it can be assumed that the starting point of the first path is the origin, i.e., (0,0,0), and that the length of each gold bar is 1. The next element "+x" indicates that the first gold bar is parallel to the x-axis, so that the other end point of the gold bar is at (1,0,0). These two elements "1" and "+x" indicates the first path consisting of only one gold bar. The third element of the second line in the description is the positive integer "1", meaning that the point with the label "1", i.e., the origin (0,0,0) is the beginning of a new path. The following elements "+y", "+z", "3", and "+z" indicate the second path consisting of three gold bars. Note that this "3" is its first occurrence so that the point with coordinates (0,1,1) is labeled "3". The head of the third line "3" indicates the beginning of the third path and so on. Consequently, there are four paths by which the shape of the key in Figure 1 is completely defined.
Note that there are various descriptions of the same key since there are various sets of paths that cover the shape of the key. For example, the following sequence of lines
19
1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y
3 +z
2 +z
is another description of the key in Figure 1, since the gold bars are placed in the same way.
Furthermore, the key may be turned 90-degrees around x-axis, y-axis or z-axis several times and may be moved parallelly. Since any combinations of rotations and parallel moves don't change the shape of the key, a description of a rotated and moved key also represent the same shape of the original key. For example, a sequence
17
+y 1 +y -z +x
1 +z +y +x +z +y -x -y 2 -y
2 +z
is a description of a key in Figure 2 that represents the same key as in Figure 1. Indeed, they are congruent under a rotation around x-axis and a parallel move.
<image>
Your job is to write a program to judge whether or not the given two descriptions define the same key.
Note that paths may make a cycle. For example, `"4 +x +y -x -y"` and `"6 1 +x 1 +y +x -y"` are valid descriptions. However, two or more gold bars must not be placed at the same position. For example, key descriptions `"2 +x -x"` and `"7 1 +x 1 +y +x -y -x"` are invalid.
Input
An input data is a list of pairs of key descriptions followed by a zero that indicates the end of the input. For p pairs of key descriptions, the input is given in the following format.
key-description1-a
key-description1-b
key-description2-a
key-description2-b
...
key-descriptionp-a
key-descriptionp-b
0
Each key description (key-description) has the following format.
n` ` e1 ` ` e2 ` ` ... ` ` ek ` ` ... ` ` en
The positive integer n indicates the number of the following elements e1, ..., en . They are separated by one or more space characters and/or newlines. Each element ek is one of the six symbols (`+x`, `-x`, `+y`, `-y`, `+z` and `-z`) or a positive integer.
You can assume that each label is a positive integer that is less than 51, the number of elements in a single key description is less than 301, and the number of characters in a line is less than 80. You can also assume that the given key descriptions are valid and contain at least one gold bar.
Output
The number of output lines should be equal to that of pairs of key descriptions given in the input. In each line, you should output one of two words "SAME", when the two key descriptions represent the same key, and "DIFFERENT", when they are different. Note that the letters should be in upper case.
Examples
Input
19
1 +x 1 +y +z 3 +z
3 +y -z +x +y -z -x +z 2 +z
2 +y
19
1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y
3 +z
2 +z
19
1 +x 1 +y +z 3 +z
3 +y -z +x +y -z -x +z 2 +y
2 +z
18
1 -y
1 +y -z +x
1 +z +y +x +z +y -x -y 2 -y
2 +z
3 +x +y +z
3 +y +z -x
0
Output
SAME
SAME
DIFFERENT
Input
19
1 +x 1 +y +z 3 +z
3 +y -z +x +y -z -x +z 2 +z
2 +y
19
1 +x 1 +y +z 3 +y -z +x +y -z -x +z 2 +y
3 +z
2 +z
19
1 +x 1 +y +z 3 +z
3 +y -z +x +y -z -x +z 2 +y
2 +z
18
1 -y
1 +y -z +x
1 +z +y +x +z +y -x -y 2 -y
2 +z
3 +x +y +z
3 +y +z -x
0
Output
SAME
SAME
DIFFERENT
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1 1 1 2\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"3 1 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"1 0 1 0\\n3\\ndna: a b\\na: [AT]\\nb: [GC]\", \"1 0 1 2\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"1 1 1 2\\n1\\nk: [ASG] [ATG] [ATG] [C] [C]\", \"2 1 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 1 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 2 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"1 1 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 4 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"1 1 1 1\\n3\\nimv: at b b b\\nat: [ATG] b\\nb: [C]\", \"1 1 1 0\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"3 1 1 0\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 0 1 2\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"1 1 1 0\\n1\\nk: [ATG] [ATF] [ATG] [C] [C]\", \"0 0 0 2\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"0 0 0 4\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"2 0 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 2 1 1\\n3\\ninu: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 4 0 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 0 0 2\\n0\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"0 0 0 4\\n1\\nk: [ATG] [AGT] [ATG] [C] [C]\", \"0 0 0 2\\n0\\n:k [ATG] [ATG] [ATG] [C] [C]\", \"0 0 0 2\\n0\\n:l [ATG] [ATG] [ATG] [C] [C]\", \"0 0 -1 2\\n0\\n:l [ATG] [ATG] [ATG] [C] [C]\", \"0 0 -1 4\\n0\\n:l [ATG] [ATG] [ATG] [C] [C]\", \"0 0 -1 4\\n0\\n:l [ATG\\\\ [ATG] [ATG] [C] [C]\", \"0 0 -1 4\\n0\\n:l [ATG\\\\ [ATG] [BTG] [C] [C]\", \"0 0 -1 4\\n0\\n:l \\\\GTA[ [ATG] [BTG] [C] [C]\", \"1 0 1 2\\n1\\nk: [AGT] [ATG] [ATG] [C] [C]\", \"-1 2 1 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"1 1 1 1\\n0\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 1 1 2\\n1\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"1 1 1 0\\n1\\nk: [ATG] [ATF] [ATG] [C] [B]\", \"0 3 0 1\\n3\\ninv: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 1 0 2\\n0\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"0 0 0 2\\n0\\n:k [ATG] [ATG] ]GTA[ [C] [C]\", \"0 0 -1 2\\n0\\nl: [ATG] [ATG] [ATG] [C] [C]\", \"0 0 -1 4\\n0\\n:l [ATG] [A]GT [ATG] [C] [C]\", \"0 0 -1 4\\n0\\n:l [ATG\\\\ [ATG] [ATG] C[] [C]\", \"0 -1 -1 4\\n0\\n:l [ATG\\\\ [ATG] [BTG] [C] [C]\", \"0 0 -1 4\\n0\\n:l \\\\GTA[ [ATG] [BTG] ZC] [C]\", \"1 1 1 1\\n0\\ninv: at b b b\\nat: [ATG] b\\nb: [C\\\\\", \"1 0 1 0\\n1\\nk: [ATG] [ATF] [ATG] [C] [B]\", \"0 3 0 1\\n3\\nvni: at b b b\\nat: [ATG] b\\nb: [C]\", \"0 1 0 1\\n0\\nk: [ATG] [ATG] [ATG] [C] [C]\", \"0 0 0 2\\n0\\n:k [ATG] [ATG] [ATG] [C] ]C[\", \"0 1 -1 2\\n0\\nl: [ATG] [ATG] [ATG] [C] [C]\", \"0 0 -1 4\\n0\\n:l [ATG] [A]GT [ATG] [C\\\\ [C]\", \"0 0 -1 4\\n0\\n:l [ATG\\\\ [ATG^ [ATG] C[] [C]\", \"0 -1 -1 4\\n0\\n:l \\\\ATG\\\\ [ATG] [BTG] [C] [C]\", \"0 0 -1 4\\n0\\n:l \\\\GTA[ [ATG] [BTF] ZC] [C]\", \"1 1 1 1\\n0\\ninv: at b b b\\nta: [ATG] b\\nb: [C\\\\\", \"1 -1 1 0\\n1\\nk: [ATG] [ATF] [ATG] [C] [B]\", \"0 0 0 2\\n0\\n:k [ATG] [ATG] [ATG] [C] ][C\", \"0 1 -1 2\\n0\\nl: [ATG] [ATG] [ATG] [B] [C]\", \"0 0 -1 4\\n0\\n:l [ATG] [A]HT [ATG] [C\\\\ [C]\", \"0 0 -1 4\\n0\\n:l [ATG\\\\ [ATG^ [ATG] C\\\\] [C]\", \"0 -1 -1 4\\n0\\n:l \\\\ATG\\\\ [ATG] [BTG] \\\\C] [C]\", \"0 0 -1 4\\n0\\n:l \\\\GTA[ [ATG] [BTF] ZC] ZC]\", \"1 1 1 1\\n0\\ninv: at b b a\\nta: [ATG] b\\nb: [C\\\\\", \"0 0 0 2\\n0\\n:k [ATG] [ATG] [AUG] [C] ][C\", \"0 1 -1 2\\n0\\nl: [ATG] \\\\ATG] [ATG] [B] [C]\", \"0 0 -1 6\\n0\\n:l [ATG] [A]HT [ATG] [C\\\\ [C]\", \"0 0 -1 4\\n0\\n:l [ATG\\\\ [ATG^ [ATG] C\\\\^ [C]\", \"0 -1 -1 4\\n0\\nl: \\\\ATG\\\\ [ATG] [BTG] \\\\C] [C]\", \"0 0 -1 4\\n0\\n:l \\\\GTA[ [ATG] [BTF] ZC] ZC^\", \"1 1 1 1\\n0\\ninv: at c b a\\nta: [ATG] b\\nb: [C\\\\\", \"0 0 0 2\\n0\\n:k [ATG] [AT]G [AUG] [C] ][C\", \"0 1 -1 2\\n0\\nl: [A]GT \\\\ATG] [ATG] [B] [C]\", \"0 0 -1 6\\n0\\n:l [ATG] [A]HT [ATG] [B\\\\ [C]\", \"0 0 -2 4\\n0\\n:l [ATG\\\\ [ATG^ [ATG] C\\\\^ [C]\", \"0 -1 -1 4\\n0\\nl: \\\\ATG\\\\ [ATG] [BTG] \\\\C\\\\ [C]\", \"1 0 -1 4\\n0\\n:l \\\\GTA[ [ATG] [BTF] ZC] ZC^\", \"1 0 1 1\\n0\\ninv: at c b a\\nta: [ATG] b\\nb: [C\\\\\", \"0 1 -2 2\\n0\\nl: [A]GT \\\\ATG] [ATG] [B] [C]\", \"0 0 -1 6\\n0\\nl: [ATG] [A]HT [ATG] [B\\\\ [C]\", \"0 0 -2 4\\n0\\n:l [ATG\\\\ [ATG^ [AT]G C\\\\^ [C]\", \"0 -1 -1 4\\n0\\nl: \\\\ATG\\\\ [A]GT [BTG] \\\\C\\\\ [C]\", \"0 0 1 1\\n0\\ninv: at c b a\\nta: [ATG] b\\nb: [C\\\\\", \"0 1 -2 2\\n0\\nl: A[]GT \\\\ATG] [ATG] [B] [C]\", \"0 0 -1 6\\n0\\nl: ]GTA[ [A]HT [ATG] [B\\\\ [C]\", \"0 0 -2 4\\n0\\n:l [ATG\\\\ [ATG^ [AT]G C\\\\^ C[]\", \"0 0 2 1\\n0\\ninv: at c b a\\nta: [ATG] b\\nb: [C\\\\\", \"0 1 -2 2\\n0\\nl: TG][A \\\\ATG] [ATG] [B] [C]\", \"0 0 -1 6\\n0\\nk: ]GTA[ [A]HT [ATG] [B\\\\ [C]\", \"-1 0 -2 4\\n0\\n:l [ATG\\\\ [ATG^ [AT]G C\\\\^ C[]\", \"0 0 2 1\\n0\\ninv: at c b a\\nta: [ATG] b\\n:b [C\\\\\", \"0 1 -2 2\\n0\\nl: TG][A \\\\ATG] [ATG] [B] ]C[\", \"0 0 -1 12\\n0\\nk: ]GTA[ [A]HT [ATG] [B\\\\ [C]\", \"-1 0 -2 4\\n0\\n:l [ATG\\\\ [ATG^ G]TA[ C\\\\^ C[]\", \"0 0 2 1\\n0\\ninv: at c b `\\nta: [ATG] b\\n:b [C\\\\\", \"0 1 -2 0\\n0\\nl: TG][A \\\\ATG] [ATG] [B] ]C[\", \"-1 0 -2 4\\n0\\n:l [ATG\\\\ [ATG^ G]TA[ C[^ C[]\", \"0 0 2 0\\n0\\ninv: at c b `\\nta: [ATG] b\\n:b [C\\\\\", \"-1 0 -2 4\\n0\\n:l [ATG[ [ATG^ G]TA[ C[^ C[]\", \"0 0 2 0\\n0\\ninv: at c b `\\nta: [ATG] b\\n:b [\\\\C\", \"0 0 2 0\\n0\\ninv: as c b `\\nta: [ATG] b\\n:b [\\\\C\", \"0 0 2 0\\n0\\ninv: as c c `\\nta: [ATG] b\\n:b [\\\\C\", \"0 0 2 0\\n0\\ninv: as c c `\\nta: [ATG] b\\n:b [C\\\\\", \"0 -1 2 0\\n0\\ninv: as c c `\\nta: [ATG] b\\n:b [C\\\\\", \"0 -1 2 0\\n0\\ninv: as c c `\\nta: [ATG] b\\n:b [C]\", \"0 -1 2 0\\n0\\ninv: as d c `\\nta: [ATG] b\\n:b [C]\"], \"outputs\": [\"6\", \"0\", \"1\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
A gene is a string consisting of `A`,` T`, `G`,` C`. The genes in this world are strangely known to obey certain syntactic rules.
Syntax rules are given in the following form:
Non-terminal symbol 1: Symbol 1_1 Symbol 1_2 ... Symbol 1_n1
Non-terminal symbol 2: Symbol 2_1 Symbol 2_2 ... Symbol 2_n2
...
Non-terminal symbol m: symbol m_1 symbol m_2 ... symbol m_nm
The symbol is either a nonterminal symbol or a terminal symbol. Non-terminal symbols are represented by lowercase strings, and terminal symbols are some of the characters `A`,` T`, `G`,` C` surrounded by "` [` "and" `]` ". It is represented by a character string.
An example syntax rule looks like this:
dna: a a b b
a: [AT]
b: [GC]
"` Nonterminal symbol i: Symbol i_1 Symbol i_2 ... Symbol i_ni` "is called a rule for nonterminal symbol i, and there is exactly one rule for each nonterminal symbol that appears in the syntax rule.
A string s "` matches `" with the nonterminal i means that there is a substring {sj} of s such that s = s1 + s2 + ... + sni, and sj (1 ≤ j ≤ It means that ni) matches the symbol j in the rule.
When the string s "` matches `" with a terminal symbol, it means that the string consists of one character and that character is included in the string representing the terminal symbol.
A string that follows syntax rules means that it matches nonterminal symbol 1.
Rule i does not include the nonterminal symbol j (j ≤ i) in the symbol.
Given the syntax rules and the four integers Na, Nt, Ng, Nc. According to the syntax rules, find the remainder of the total number of genes that contain exactly Na for A, just Nt for T, just Ng for G, and just Nc for C, divided by 1,000,000,007.
Input
> Na Nt Ng Nc
> m
> Nonterminal 1: Symbol 11 Symbol 12 ... Symbol 1n1
> Non-terminal symbol 2: Symbol 21 Symbol 22 ... Symbol 2n2
> ...
> Non-terminal symbol m: symbol m1 symbol m2 ... symbol mnm
>
0 ≤ Na, Nt, Ng, Nc ≤ 50
1 ≤ m ≤ 50
1 ≤ ni ≤ 10
1 ≤ Length of the character string representing the symbol ≤ 20 (* Note that it is not the length of the character string that matches the symbol)
Output
The remainder of the total number divided by 1,000,000,007
Examples
Input
1 0 1 0
3
dna: a b
a: [AT]
b: [GC]
Output
1
Input
1 1 1 2
1
k: [ATG] [ATG] [ATG] [C] [C]
Output
6
Input
3 1 1 1
3
inv: at b b b
at: [ATG] b
b: [C]
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.