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문제

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:

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.

입력

rst 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

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

힌트

출처

Olympiad > Polish Olympiad in Informatics > POI 1998/1999 > Stage 2 4번