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 �1i1, �1j1, �2i2, and �2j2, if �1−�1=�2−�2i1−j1=i2−j2, then ��1,�1=��2,�2Bi1,j1=Bi2,j2.
• For any indices �1i1, �1j1, �2i2, and �2j2, if �1−�1≠�2−�2i1−j1=i2−j2, then ��1,�1≠��2,�2Bi1,j1=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 $T$ ($1\le T\le 100$), which represents the number of test cases.

The first line of each test case contains two integers $n$ and $m$ ($1\le n,m\le 1000$), representing the number of rows and columns in the matrix $A$.

Each of the next $n$ lines contains $m$ space-separated integers ��,1,��,2,…,��,�Ai,1,Ai,2,…,Ai,m (1≤��,�≤�×�1≤Ai,j≤n×m), representing the elements of the matrix $A$ for that particular test case.

It is guaranteed that ∑�×�≤107∑n×m≤107 over all test cases.