问题 I: Diagonal Fancy

Given a matrix A with n rows and m columns, your objective is to compute the total number of continuous sub-square matrices B that are diagonal fancy. A square matrix B is designated as diagonal fancy if it satisfies the subsequent criteria: • For any indices i1, j1, i2, and j2, if i1 − j1 = i2 − j2, then Bi1,j1 = Bi2,j2 . • For any indices i1, j1, i2, and j2, if i1 − j1 6= i2 − j2, then Bi1,j1 6= Bi2,j2 . Here, Bi,j signifies the element located at the i-th row and j-th column of matrix B. A continuous sub-square matrix from matrix A with n rows and n columns is defined as the matrix derived from A by selecting continuous n rows and continuous n columns.

Ensure to use cin/cout and disable synchronization with stdio to avoid unexpected TLE verdict. The input consists of multiple test cases. The first line of the input contains an integer T (1 ≤ T ≤ 100), which represents the number of test cases. The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 1000), representing the number of rows and columns in the matrix A. Each of the next n lines contains m space-separated integers Ai,1, Ai,2, . . . , Ai,m (1 ≤ Ai,j ≤ n × m), representing the elements of the matrix A for that particular test case. It is guaranteed that Pn × m ≤ 107 over all test cases.

For each test case, output a single integer in a single line, which represents the count of continuous sub-square matrices in matrix A that are diagonal fancy.

3
2 2
1 2
3 1
2 2
1 2
2 1
3 3
1 2 3
4 1 2
5 4 1

5
4
14

In the first test case, there are 5 diagonal fancy subsquares in total. They are listed in bold below. 1 2 1 2 1 2 1 2 1 2 3 1 3 1 3 1 3 1 3 1