Reachable Sequences

ZZX has a sequence $a$, which is a permutation of $1, 2, \ldots, n$. ZZX wants to modify this sequence. In one modification, he chooses a pair of integers $i$ and $j$ with $1 \le i < j \le n$ and $a_i > a_j$, then swaps $a_i$ and $a_j$.

If a permutation $b$ can be obtained from the initial sequence $a$ by performing some (possibly zero) modifications, then ZZX says $b$ is reachable from $a$.

JRY has $m$ sequences $a^{(1)}, a^{(2)}, \ldots, a^{(m)}$. Each of them is a permutation of $1, 2, \ldots, n$. He wants to know how many pairs $(i, j)$ with $1 \le i \le m$ and $1 \le j \le m$ satisfy that $a^{(i)}$ is reachable from $a^{(j)}$.

The first line contains an integer $T$. Then $T$ test cases follow. In each test case, the first line contains two integers $n$ and $m$. After that, $m$ lines follow. The $k$-th of them contains $n$ integers $a^{(k)}_1, a^{(k)}_2, \ldots, a^{(k)}_n$. Each $a^{(k)}$ is a permutation of $1, 2, \ldots, n$.

There are at most $1000$ small test cases and $1$ large test case. The small test cases satisfy $1 \le n \le 5$ and $1 \le m \le 500$. The large test case satisfies $1 \le n \le 9$ and $1 \le m \le 3 \cdot 10^5$.

For each test case, print the answer on a separate line.