There is given a rectangular bitmap of size n x m. Each pixel of the bitmap is either white or black, but at least one is white. The pixel in i-th line and j-th column is called the pixel (i,j). The distance between two pixels p1=(i₁,j₁) and p2=(i₂,j₂) is defined as:</p>

d(p₁,p₂)=|i₁-i₂|+|j₁-j₂|.

Write a program which:

• reads the description of the bitmap from standard input,
• for each pixel, computes the distance to the nearest white pixel,
• writes the results to the standard output.

First line of the standard input there is a pair of integer numbers n, m separated by a single space, 1 ≤ n ≤ 182, 1 ≤ m ≤ 182. In each of the following n lines of the input exactly one zero-one word of length m, the description of one line of the bitmap, is written. On the j-th position in the line (i+1), 1 ≤ i ≤ n, 1 ≤ j ≤ m, is 1 if, and only if the pixel (i,j) is white.

출력 형식

In the i-th line of the standard output, 1 ≤ i ≤ n, there should be written m integers f(i,1),…,f(i,m) separated by single spaces, where f(i,j) is the distance from the pixel (i,j) to the nearest white pixel.

예제 입력

3 4
0001
0011
0110

예제 출력

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