The Fifth Dimension

Beyond the mirror lies a civilization far more advanced than ours. Long ago its scientists discovered interstellar tunnels: hidden passages, coiled inside a fifth dimension, that directly connect certain pairs of stars. Each tunnel is two-way, no tunnel joins a star to itself, and at most one tunnel joins any given pair of stars.

For safety, the government inspects every interstellar route. A route is a sequence of distinct stars $s_0, s_1, \dots, s_k$ in which every consecutive pair $s_i, s_{i+1}$ is joined by a tunnel; the length of the route is the number of tunnels it uses, $k$. A route and its reverse are considered two different routes.

Routes of length $1, 2, 3$ and $4$ have already been inspected. Now the routes of length exactly $5$ — those passing through $6$ distinct stars via $5$ tunnels — must be counted. For each universe, determine how many such routes exist.

The first line contains an integer $d$ ($1 \le d \le 100$), the number of universes. The descriptions of the universes follow.

Each universe begins with a line containing two integers $n$ and $m$ ($1 \le n \le 200$; $0 \le m \le n(n-1)/2$), the number of stars and the number of tunnels. Each of the next $m$ lines contains two integers $u$ and $v$ ($1 \le u, v \le n$, $u \ne v$), meaning that stars $u$ and $v$ are joined by a tunnel. No tunnel joins a star to itself, and at most one tunnel joins any pair of stars. Tunnels are two-way.

For each universe, print on its own line the number of distinct routes of length exactly $5$.