There is given a rectangular bitmap of size n*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:

Task

Write a program which:

• reads the description of the bitmap from the text file BIT.IN,
• for each pixel, computes the distance to the nearest white pixel,
• writes the results to the text file BIT.OUT

Input

In the first line of the text file BIT.IN 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 file BIT.IN 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.

Output

In the i-th line of the output file BIT.OUT, 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.

Example

For the input file BIT.IN:

3 4
0001
0011
0110

the correct answer is the text file BIT.OUT: 

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

On the web site: http://www.mimuw.edu.pl/~msawicki/stereo.html you can find an applet Stereogram, which was the prototype for this problem.