Given a undirected graph with n vertices and m edges. Your task is count the number of distinct pairs (u, v) that there is exist a path with length exactly 2 from u to v. Another mean, with each pair (u, v), we could find a vertex t that we have an edge (u, t) and (t, v). The input set may be contains multiple edge between any vertex and not consider to connected.

Input

- First line: n, m (1 <= n, m <= 10^5).

- m following line: u, v (1 <= u, v <= n).

Output

The number of distinct pairs.

Example

Input:
5 4
2 1
1 5
3 1
4 3

Output:
4

Note: we have (1, 4), (2, 3), (2, 5), (3, 5)