CodeForces 788B--Weird journey

Posted 2020-09-08 Pic

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Description

Little boy Igor wants to become a traveller. At first, he decided to visit all the cities of his motherland — Uzhlyandia.

It is widely known that Uzhlyandia has n cities connected with m bidirectional roads. Also, there are no two roads in the country that connect the same pair of cities, but roads starting and ending in the same city can exist. Igor wants to plan his journey beforehand. Boy thinks a path is good if the path goes over m?-?2 roads twice, and over the other 2 exactly once. The good path can start and finish in any city of Uzhlyandia.

Now he wants to know how many different good paths are in Uzhlyandia. Two paths are considered different if the sets of roads the paths goes over exactly once differ. Help Igor — calculate the number of good paths.

Input

The first line contains two integers n, m(1?≤?n,?m?≤?10⁶) — the number of cities and roads in Uzhlyandia, respectively.

Each of the next m lines contains two integers u and v (1?≤?u,?v?≤?n) that mean that there is road between cities u and v.

It is guaranteed that no road will be given in the input twice. That also means that for every city there is no more than one road that connects the city to itself.

Output

Print out the only integer — the number of good paths in Uzhlyandia.

Sample Input

Input

5 4
1 2
1 3
1 4
1 5

Output

6

Input

5 3
1 2
2 3
4 5

Output

0

Input

2 2
1 1
1 2

Output

1

题意：

给定义一个可以有自环的n点m边的图，求其中有多少goodway。

goodway的定义为：经过m-2条边两次，经过剩下2条边1次

思路：

本题数据范围太大，tarjan之类的算法不适用，只能从图本身的性质入手

将题目中的每个边都复制一遍（每个边有一个重边）

题目即变成了：去掉其中两条边可以构成欧拉回路，有几种去法。

根据无向图欧拉回路的充要条件：所有顶点的度数都为偶数

可以得出两种情况使问题成立：

· 去掉相邻的两条边；

· 去掉的两条边中有一条为自环。