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 standard input,
• for each pixel, computes the distance to the nearest white pixel,
• writes the results to the standard output.

Input

The number of test cases t is in the first line of input, then t test cases follow separated by an empty line. In the first line of each test case 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 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), 1 ≤ i ≤ n, 1 ≤ j ≤ m, is '1' if, and only if the pixel (i, j) is white.

Output

In the i-th line for each test case, 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

Sample input:
1
3 4
0001
0011
0110

Sample output:
3 2 1 0
2 1 0 0
1 0 0 1