# Sub-Matrix with Sum Zero

Posted: 4 Jan, 2021

Difficulty: Moderate

#### Given a 2-dimensional matrix of size ‘N’ x ‘M’. Find the size of the largest sub-matrix whose sum is equal to 0. The size of a matrix is the product of rows and columns in it.

#### A sub-matrix is a matrix obtained from the given matrix by deletion of several (possibly, zero or all) rows/columns from the beginning and several (possibly, zero or all) rows/columns from the end.

#### For example :

#### If there is no sub-matrix with sum equal to 0, then return 0.

##### Input Format

```
The first line of input contains an integer 'T' representing the number of test cases. Then the test cases follow.
The first line of each test case contains two single-spaced integers 'N' and 'M', representing the number of rows and columns of the matrix, respectively.
The next 'N' lines contain 'M' single-spaced integers denoting matrix elements.
```

##### Output Format:

```
For each test case, in the first line, print an integer denoting the size of the largest sub-matrix with sum equal to 0.
The output of each test case is printed in a separate line.
```

##### Note:

```
You do not need to print anything, it has already been taken care of. Just implement the given function.
```

##### Constraints:

```
1 <= T <= 10
1 <= N, M <= 50
-10^5 <= data <= 10^5,
Where ‘data’ is the value of the elements of the matrix.
Time Limit: 1 sec
```