Triples

Problem Statement

You are given an undirected graph with $n$ vertices and $m$ edges. Pondo would like you to determine the number of $3$-cycles in the graph. A $3$-cycle (triangle) is a cycle of length $3$ in the graph.

Input Statement

Your first line will contain two space-separated integers $n$ and $m$ (respectively).

Your next line $m$ lines will contain two space-separated integers each, $u$ and $v$, representing an edge between nodes $u$ and $v$.

Output Statement

You should output a single integer representing the number of $3$-cycles in the given graph.

Constraints

• $1 \leq n \leq 10^4$
• $1 \leq m \leq \min(10^4, \frac{n \cdot (n - 1)}{2})$
• $1 \leq u, v \leq n$
• all $u, v$ pairs are unique and $u \neq v$

Sample Cases

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

10

Explanation 1

Notice that all triples of nodes form $3$-cycles.

6 8
1 2
1 3
2 3
2 4
3 5
4 5
4 6
5 6

2

Explanation 2

There are only two $3$-cycles formed by $(1, 2, 3)$ and $(4, 5, 6)$.