## 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
 egor091: 2020-06-19 16:45:24 AC in one go yash_999: 2020-06-16 10:03:06 can be done without multisource bfs using only bfs shortest path with a little optimization ran in 0.5 s although using multisource bfs ran in 0.03 s Last edit: 2020-06-16 10:24:13 gaur_gaur: 2020-05-31 08:44:05 simple mutisource bfs question :) joaoabrantes: 2020-05-28 14:52:57 Please take care after output each test, you need to read a empty line after every output, otherwise you gonna get RE prantoru: 2020-05-14 07:30:52 who still could't solve the problem, just goto geeksforgeeks and read the article about multisouce bfs and solve the problem.... :) prantoru: 2020-05-14 06:50:24 what is the maximum value of t....? -_- shuhbo: 2020-05-09 20:03:17 Simple logic. You can solve without bfs and dfs. abhishek_251: 2020-04-25 08:38:58 if you're using multisource bfs keep in mind don't use pair,map etc. theres high chances that you will get TLE. And also no need of visited{true} array. aman5898: 2020-04-10 15:49:53 Ac in one go :p Simple multisource bfs with dijkstra. khauf007: 2020-04-10 11:41:28 I am getting TLE repeatedly using multisource bfs i am not able to figure out the problem

 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