Bitmap

You are given a rectangular bitmap of size $n \times m$. Each pixel of the bitmap is either white or black, and at least one pixel is white. The pixel in row $i$ and column $j$ is denoted $(i, j)$.

The distance between two pixels $p_1 = (i_1, j_1)$ and $p_2 = (i_2, j_2)$ is defined as

$d(p_1, p_2) = |i_1 - i_2| + |j_1 - j_2|.$

Write a program that, for every pixel, computes the distance to the nearest white pixel.

The first line contains two integers $n$ and $m$ separated by a single space ($1 \le n \le 182$, $1 \le m \le 182$).

Each of the following $n$ lines contains one string of length $m$ made of the characters 0 and 1, describing one row of the bitmap. In the string that describes row $i$ of the bitmap, the $j$-th character is 1 if and only if the pixel $(i, j)$ is white ($1 \le i \le n$, $1 \le j \le m$).

Print $n$ lines. The $i$-th line must contain $m$ integers $f(i, 1), \dots, f(i, m)$ separated by single spaces, where $f(i, j)$ is the distance from the pixel $(i, j)$ to the nearest white pixel.