3468: Triangles
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
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≤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 ai, bi (1≤ai,bi≤n, ai≠bi), − 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 C++. It is advised to use the cin, cout streams or the %I64d specifier.
5 5
1 2
1 3
2 3
2 4
3 4
3
5 3
1 2
2 3
1 3
4
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.