You are given a matrix of size \(N \times M\) that contains the digits 0, 1, or 2 only. All the cells that contain 1 and are adjacent to any cell that contains 2 will be converted from 1 to 2, simultaneously in 1 second. Write a program to find the minimum time to convert all the cells having value 1 to 2.
Input format
- First line: Two space-separated integers N and M
- Next N lines: M space-separated integers (denoting the matrix)
Output format
Print the minimum time to convert all the cells having value 1 to 2.
Constraints
\(1 ≤ N, M ≤ 10^3 \)
3 5 2 1 0 2 1 1 0 1 2 1 1 0 0 2 1
2
If you starts from the cell [1,4] or [3,4] and travels to [2,3] then the cost will be 2 which is maximum of all possible journeys.
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