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 $2$ gets converted from $1$ to $2$. This operation must be performed 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

$1 ≤ N, M ≤ 10^3$