Memento Mori

Professor Zhang has an $n \times m$ matrix where every element is 0. Professor Zhang changes $k$ elements of the matrix into 1s.

Given a permutation $p_1, p_2, p_3, p_4$ of $1, 2, 3, 4$, Professor Zhang wants to count the submatrices that satisfy all of the following:

• The submatrix contains exactly 4 ones.
• Let the positions of the ones in the submatrix be $(r_1, c_1), (r_2, c_2), (r_3, c_3), (r_4, c_4)$. Then $r_1 < r_2 < r_3 < r_4$, and $(p_i - p_j) \cdot (c_i - c_j) > 0$ for all $1 \le i < j \le 4$.
• The chosen submatrix contains no other submatrix that satisfies the two conditions above.

The first line contains an integer $T$, the number of test cases. Each test case starts with a line containing three integers $n$, $m$, and $k$ ($1 \le n, m, k \le 2000$), the size of the matrix and the number of ones. The next line contains four integers $p_1, p_2, p_3, p_4$, the permutation. Each of the next $k$ lines contains two integers $r_i$ and $c_i$ ($1 \le r_i \le n$, $1 \le c_i \le m$), the position of the $i$-th one. No two ones share the same position.

There are at most 250 test cases, and the total input size is at most 250 KiB.

For each test case, output a single integer: the number of submatrices that satisfy all the requirements.