Problem:
Score : 500 points

Problem Statement

Rng has a connected undirected graph with N vertices.
Currently, there are M edges in the graph, and the i-th edge connects Vertices A_i and B_i.

Rng will add new edges to the graph by repeating the following operation:

Operation: Choose u and v (u \neq v) such that Vertex v can be reached by traversing exactly three edges from Vertex u, and add an edge connecting Vertices u and v. It is not allowed to add an edge if there is already an edge connecting Vertices u and v.

Find the maximum possible number of edges that can be added.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N

The graph has no self-loops or multiple edges.

The graph is connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find the maximum possible number of edges that can be added.

Sample Input 1

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 1

4

If we add edges as shown below, four edges can be added, and no more.

Sample Input 2

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

Sample Output 2

5

Five edges can be added, for example, as follows:

Add an edge connecting Vertex 5 and Vertex 3.

Add an edge connecting Vertex 5 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 1.

Add an edge connecting Vertex 4 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 3.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
class Program{
	static void Main(){
		int[] s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		int ans=0;
		List<int>[] li=new List<int>[s[0]+1];
		int[,] h=new int[s[0]+1,3];
		List<int[]> qu=new List<int[]>();
		for(int i=1;i<=s[0];i++){li[i]=new List<int>();}
		for(int i=0;i<s[1];i++){
			int[] q=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			li[q[0]].Add(q[1]);
			li[q[1]].Add(q[0]);
		}
		for(int i=1;i<=s[0];i++){
			h[i,0]=i;
			h[i,2]=0;
			for(int j=0;j<li[i].Count;j++){
				h[li[i][j],0]=i;
				h[li[i][j],1]=1;
				h[li[i][j],2]=0;
				qu.Add(new int[]{li[i][j],1});
			}
			while(qu.Count>0){
				if(qu[0][1]==3){
					li[i].Add(qu[0][0]);
					li[qu[0][0]].Add(i);
					ans++;
				}
				else{
					for(int j=0;j<li[qu[0][0]].Count;j++){
						if(li[qu[0][0]][j]!=i&&(qu[0][1]!=2||h[li[qu[0][0]][j],0]!=i||h[li[qu[0][0]][j],1]!=1)&&(h[li[qu[0][0]][j],0]!=i||(h[li[qu[0][0]][j],1]!=qu[0][1]+1&&h[li[qu[0][0]][j],2]!=qu[0][1]+1))){
							if(h[li[qu[0][0]][j],0]==i){h[li[qu[0][0]][j],2]=qu[0][1]+1;}
							else{
								h[li[qu[0][0]][j],0]=i;
								h[li[qu[0][0]][j],1]=qu[0][1]+1;
								h[li[qu[0][0]][j],2]=0;
							}
							qu.Add(new int[]{li[qu[0][0]][j],qu[0][1]+1});
						}
					}
				}
				qu.RemoveAt(0);
			}
		}
		Console.WriteLine(ans);
	}
}