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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		new Main().solve();
	}
	
	ArrayList<Integer>[]path;
	int n,m;
	int[]a;
	int[]b;
	void solve() {
		Scanner sc = new Scanner(System.in);
		n=sc.nextInt();
		m=sc.nextInt();
		a=new int[m];
		b=new int[m];
		path=new ArrayList[n];
		for(int i=0;i<n;i++) {
			path[i]=new ArrayList<Integer>();
		}
		for(int i=0;i<m;i++) {
			a[i]=sc.nextInt()-1;
			b[i]=sc.nextInt()-1;
			path[a[i]].add(b[i]);
			path[b[i]].add(a[i]);
		}
		visited=new boolean[n];
		for(int t=0;t<2;t++) {
			for(int i=0;i<n;i++) {
				Arrays.fill(visited, false);
				visited[i]=true;
				dfs(i,i,0);
			}
		}
		System.out.println(max);
	}
	
	int max=0;
	boolean[] visited;
	
	void dfs(int start,int x,int depth) {
		visited[x]=true;
		if(depth==3) {
			int judge=0;
			for(int j=0;j<path[start].size();j++) {
				if(path[start].get(j)==x)judge++;
			}
			if(judge==0) {
				max++;
				path[start].add(x);
				path[x].add(start);
			}
			visited[x]=false;
			return;
		}
		for(int j=0;j<path[x].size();j++) {
			if(!visited[path[x].get(j)])dfs(start, path[x].get(j), depth+1);
		}
		visited[x]=false;
		return;
	}
}