Triangles

题意翻译

给定n（1<=n<=10^6）个点组成的完全图，现在从原图中拿走m（0<=m<=10^6）条边到另一个平面上，问一共还能组成多少个三角形。

题目描述

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?

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

3

输入样例 #2

5 3
1 2
2 3
1 3

输出样例 #2

4

说明

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.