## BITMAP - Bitmap

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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:

d(p1,p2)=|i1-i2|+|j1-j2|.

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
``` man: 2016-04-29 21:43:28 solved in execution time 3.69.. god knows how the top solution execution's time is 0.00 .. crazy.. Akshay Damle: 2016-04-28 23:13:55 Code ran in 1 go on my system w/o any debugging and then AC in 1 go :D Feels great! satoruu: 2016-04-27 17:44:09 AC using brute force!! 3.07 secs :) nonushikhar: 2016-03-24 23:04:40 very nice problem :) killjee_15: 2016-02-28 09:55:27 nice question to learn "MULTISOURCE BFS" Aqib Ahmed J: 2016-02-08 14:58:23 Took a while to realize how exactly but AC in one go :) 0.04s !! bunnycoder: 2016-01-29 22:09:37 Silly error ..... simple bfs traversal archit saxena: 2016-01-13 06:48:06 done with bfs using 0.03 sec but people might also try solving equation(try on paper and u will get easy graphical solution) mod(x1-x2)+mod(y1-y2)=z;and find the minimum value of z using binary search might work.if it works do comment dokz: 2016-01-08 14:23:29 Got WA at first, because of input. "then t test cases follow separated by an empty line". Note that there is a new line after every test case. utkarsh5: 2015-12-22 11:38:19 Can someone provide me some sample test cases, Im getting wrong answer even though my code produces correct answer for all the test cases Ive built so far?