## 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|.

### 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
```

hide comments
 kxingh: 2017-08-21 11:19:06 used brute force AC in 10th go anurag31: 2017-07-04 15:12:29 bottom up dp rocks....AC in 0.01 sec sipian: 2017-06-03 22:19:12 a good question botstar: 2017-05-29 22:43:09 got 15 TLEs....mistake == using iosbase and scnf together...fkcu...c++.. akash619j: 2017-05-29 09:20:25 Little tricky even after you know its bfs! s407189: 2017-04-03 12:01:56 it could use some more examples. Does it even test for more than one data set ? vengatesh15: 2017-03-27 12:35:45 AC in 1 go using BFS nilabja16180: 2017-02-19 16:51:59 Awesome 0 1 BFS implementation Last edit: 2017-02-19 16:52:09 scorpion_ajay: 2017-02-14 12:42:59 must try, learned a lot from this single problem :) manish_hacked: 2017-02-06 05:40:43 Very good question for learning bfs!! don't try brute force method ,try to solve by using bfs!!

 Added by: Piotr Ćowiec Date: 2004-09-13 Time limit: 4s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All Resource: 6th Polish Olympiad in Informatics, stage 2