A8721. Triangles

Alice and Bob don't play games anymore. Now they study properties of all sorts of graphs together. Alice invented the following task: she takes a complete undirected graph with $n$ vertices, chooses some $m$ edges and keeps them. Bob gets the  remaining edges.

Alice and Bob are fond of "triangles" in graphs, that is, cycles of length 3. That's why they wonder: what total number of triangles is there in the two graphs formed by Alice and Bob's edges, correspondingly?

The first line contains two space-separated integers $n$ and $m$ ( $1<=n<=10^{6},0<=m<=10^{6}$ ) — 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 $n$ .

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.

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.