Matrix Rank Calculation

Given a matrix ARR of dimensions N * M, your task is to determine the rank of the matrix ARR.

Explanation:

The rank of a matrix is defined as:

(a) The maximum number of linearly independent column vectors in the matrix, or
(b) The maximum number of linearly independent row vectors in the matrix.
Both definitions are equivalent.

Linear independence is defined as follows:

In vector space theory, a set of vectors is considered linearly dependent if there is a nontrivial linear combination of the vectors that equates to the zero vector. If no such linear combination exists, then the vectors are linearly independent.

Input:

The first line contains a single integer ‘T’ denoting the number of test cases.
Each test case consists of:
- The first line contains two space-separated integers, ‘N’ and ‘M’, representing the number of rows and the number of columns respectively.
- The next ‘N’ lines each contain ‘M’ integers that represent the matrix elements.

Output:

For each test case, return the rank of the matrix.

Example:

Input:
2
3 3
1 2 3
4 5 6
7 8 9
2 2
1 2
3 4
Output:
2
2

Constraints:

• 1 <= T <= 10
• 1 <= N, M <= 500
• -10^4 <= ARR[i][j] <= 10^4

Where ARR[i][j] denotes the matrix element at the j^th column in the i^th row of ARR.

Time Limit: 1 sec

Note:

You are not required to print anything; it has already been taken care of. Just implement the given function and return the answer.