01 Matrix

Given an m x 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 parameter: An integer m

Second parameter: An integer n

Third parameter: A matrix mat

Output Format

Return a matrix

Example 1

Input: m = 3, n = 3
mat = 
0 0 0
0 1 0
0 0 0

Output: 
0 0 0
0 1 0
0 0 0

Example 2

Input: m = 3, n = 3
mat = 
0 0 0
0 1 0
1 1 1

Output: 
0 0 0
0 1 0
1 2 1

Constraints

• 1 <= m, n <= 10^4
• 1 <= m * n <= 10^4
• mat[i][j] is either 0 or 1.
• There is at least one 0 in mat.
• Expected Time Complexity - O(m x n)
• Expected Space Complexity - O(m x n)