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C. Triangles

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAlice 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?

Input

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*.

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.

Examples

Input

5 5

1 2

1 3

2 3

2 4

3 4

Output

3

Input

5 3

1 2

2 3

1 3

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.

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