You are given an undirected, complete graph $G$ that contains $N$ vertices. Each edge is colored in either white or black. You are required to determine the number of triplets $(i,j,k)$ $(1 \le i < j < k \le N)$ of vertices such that the edges $(i,j), (j,k), (i,k)$ are of the same color.

There are $M$ white edges and $\frac{N(N-1)}{2} - M$ black edges.

Input format

• First line: Two integers - $N$ and $M$ $(3 \le N \le 10^5, 1 \le M \le 3 \cdot 10^5)$
• $(i + 1)^{th}$ line: Two integers - $u_i$ and $v_i$ $(1 \le u_i, v_i \le N)$ denoting that the edge $(u_i, v_i)$ is white in color

Note: The conditions$(u_i,v_i) \neq (u_j, v_j)$ and $(u_i,v_i) \neq (v_j,u_j)$ are satisfied for all $1 \le i < j \le M$.

Output format

Print an integer that denotes the number of triples that satisfy the mentioned condition.

Additional information

• For $20$ points: $N \le 200$ is satisfied
• For additional $20$ points: $N \le 2000$ is satisfied
• Original constraints for remaining points