We are given an $n \times m$ monochrome bitmap, which contains at least one white pixel. We denote the pixel at the $i$-th row and $j$-th column as $(i, j)$, and define the distance between two points $p_1=(i_1, j_1)$ and $p_2=(i_2, j_2)$ as: $$d(p_1, p_2)=|i_1 - i_2| + |j_1 - j_2|$$

For each pixel, calculate the distance to the nearest white pixel.

Input

The first line contains two space-separated integers $n$ and $m$, where $1 \le n \le 182$ and $1 \le m \le 182$. The following $n$ lines each contain a string of length $m$ consisting of $0$s and $1$s. If the $j$-th character in the $i$-th line is "1", it means the pixel $(i, j)$ is white; otherwise, it is black.

Output

Output an $n \times m$ table of numbers, where the $j$-th number in the $i$-th row is $f(i, j)$, representing the distance from pixel $(i, j)$ to the nearest white pixel.

Examples

Input 1

3 4
0001
0011
0110

Output 1

3 2 1 0
2 1 0 0
1 0 0 1