Given a matrix of dimension r*c where each cell in the matrix can have values 0, 1 or 2 which has the following meaning:
0 : Empty cell
1 : Cells have fresh oranges
2 : Cells have rotten oranges

So, we have to determine what is the minimum time required to all oranges. A rotten orange at index [i,j] can rot other fresh orange at indexes [i-1,j], [i+1,j], [i,j-1], [i,j+1] (up, down, left and right) in unit time. If it is impossible to rot every orange then simply return -1.

Input:
The first line of input contains an integer T denoting the number of test cases. Each test case contains two integers r and c, where r is the number of rows and c is the number of columns in the array a[]. Next line contains space separated r*c elements each in the array a[].

Output:
Print an integer which denotes the minimum time taken to rot all the oranges (-1 if it is impossible).

Constraints:
1 <= T <= 100
1 <= r <= 100
1 <= c <= 100
0 <= a[i] <= 2

Example:
Input:

2
3 5
2 1 0 2 1 1 0 1 2 1 1 0 0 2 1

3 5
2 1 0 2 1 0 0 1 2 1 1 0 0 2 1

Output:
2
-1

Explanation:
Testcase 1:

2 | 1 | 0 | 2 | 1
1 | 0 | 1 | 2 | 1
1 | 0 | 0 | 2 | 1

Oranges at positions {0,0}, {0, 3}, {1, 3} and {2, 3} will rot oranges at {0, 1}, {1, 0}, {0, 4}, {1, 2}, {1, 4}, {2, 4} during 1st unit time. And, during 2nd unit time, orange at {1, 0} got rotten and will rot orange at {2, 0}. Hence, total 2 unit of time is required to rot all oranges.
 

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Shashwat Jain
Author: shashwat jain


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