Given an m*n binary matrix mat, return the distance of the nearest 0 for each cell. The distance between two adjacent cells is 1.
Input Format
First line contains two integers n and m. Each of next n lines contain m numbers containing either 0 or 1.
Output Format
print a 2d matrix where each box contains distance to its nearest 0.
Constraints
1<= n <= 1000 1<= e <= n*(n-1)/2
Example
Input
3 3 0 0 0 0 1 1 1 1 1
Output
0 0 0 0 1 1 1 2 2