Triangles

Description:

Input:

The first line contains two space-separated integers n and m (1 ≤ n ≤ 10⁶, 0 ≤ m ≤ 10⁶) — the number of vertices in the initial complete graph and the number of edges in Alice's graph, correspondingly. Then m lines follow: the i-th line contains two space-separated integers a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i), — the numbers of the two vertices connected by the i-th edge in Alice's graph. It is guaranteed that Alice's graph contains no multiple edges and self-loops. It is guaranteed that the initial complete graph also contains no multiple edges and self-loops.

Consider the graph vertices to be indexed in some way from 1 to n.

Output:

Print a single number — the total number of cycles of length 3 in Alice and Bob's graphs together.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Sample Input:

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

Sample Output:

3

Sample Input:

5 3
1 2
2 3
1 3

Sample Output:

4

Note:

In the first sample Alice has 2 triangles: (1, 2, 3) and (2, 3, 4). Bob's graph has only 1 triangle : (1, 4, 5). That's why the two graphs in total contain 3 triangles.

In the second sample Alice's graph has only one triangle: (1, 2, 3). Bob's graph has three triangles: (1, 4, 5), (2, 4, 5) and (3, 4, 5). In this case the answer to the problem is 4.