Look at the word and phrases below, rearrange them to form meaningful sentences in your answer sheet. (4) a) a clever/an/prisoner/planned/escape/once
Question
Look at the word and phrases below, rearrange them to form meaningful sentences in your answer sheet. (4) a) a clever/an/prisoner/planned/escape/once
Solution
"Once, a clever prisoner planned an escape."
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A prison is represented as an 𝑁×𝑀N×M grid containing 0's and 1's, where 0 denotes a prisoner and 1 denotes a guard.In one move, a prisoner can move one step left, right, up, or down. Formally, from cell (𝑥,𝑦)(x,y), a prisoner can move to any of the four cells (𝑥−1,𝑦),(𝑥+1,𝑦),(𝑥,𝑦−1),(𝑥,𝑦+1)(x−1,y),(x+1,y),(x,y−1),(x,y+1).A prisoner can escape if he reaches outside the prison: formally, if he reaches any cell (𝑥,𝑦)(x,y) such that 𝑥=0x=0 or 𝑦=0y=0 or 𝑥>𝑁x>N or 𝑦>𝑀y>M.Let the escape time of a prisoner be the minimum number of guards he needs to cross before he is able to escape the prison.What is the maximum escape time of any prisoner?Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝑀M — the dimensions of the prison.The next 𝑁N lines each contain a binary string of length 𝑀M, representing the structure of the prison.Output FormatFor each test case, output on a new line the maximum escape time of any prisoner.Constraints1≤𝑇≤10001≤T≤10001≤𝑁≤3⋅1051≤N≤3⋅10 5 1≤𝑀≤3⋅1051≤M≤3⋅10 5 Each character of grid is either 0 or 1.The sum of 𝑁⋅𝑀N⋅M over all test cases won't exceed 3⋅1053⋅10 5 .
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