Peter has an $n \times m$ matrix $M$. Let $S(a,b)$ be the sum of the weight all $a \times b$ submatrices of $M$. The weight of matrix is the sum of the value of all the saddle points in the matrix. A saddle point of a matrix is an element which is both the only largest element in its column and the only smallest element in its row. Help Peter find out all the value of $S(a,b)$.
Note: the definition of saddle point in this problem may be different with the definition you knew before.
Input
There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:
The first contains two integers $n$ and $m$ $(1 \le n, m \le 1000)$ -- the dimensions of the matrix.
The next $n$ lines each contain $m$ non-negative integers separated by spaces describing rows of matrix $M$ (each element of $M$ is no greater than $10^6$).
Output
For each test case, output an integer $W = (\displaystyle\sum_{a=1}^{n}\sum_{b=1}^{m}{a \cdot b \cdot S(a,b)}) \text{ mod } 2^{32}$.
