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

\(1 ≤ N, M ≤ 10^3 \)