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Problems

# Bitmap

Time limit 2 seconds
Memory limit 128 MiB

Rectangular bitmap of size n \times m is given. 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 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|

For each pixel find the distance to the nearest white pixel.

## Input data

The number of test cases t is given in the first line, then t test cases follow. First line of each test case contains pair of integer numbers n, m~(1 \le n \le 1000, 1 \le m \le 1000). In each of the following n lines of the test case 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 \le i \le n, 1 \le j \le m) there is 1 if, and only if the pixel (i, j) is white.

## Output data

In the i-th line for each test case 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.

## Examples

Input example #1
1
3 4
0001
0011
0110

Output example #1
3 2 1 0
2 1 0 0
1 0 0 1