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;

namespace AtCoder
{
    class Program
    {
        public class Graph
        {
            List<int> node = new List<int>();
        }
        static void Main(string[] args)
        {
            String line;

            line = Console.ReadLine();
            string[] tempLine = line.Split(' ');
            int n = int.Parse(tempLine[0]);
            int m = int.Parse(tempLine[1]);

            Dictionary<int, List<int>> graph = new Dictionary<int, List<int>>();
            for (int i = 0; i < n; i++)
            {
                graph.Add(i + 1, new List<int>());
            }

            for (int i=0; i < m; i++)
            {
                line = Console.ReadLine();
                string[] temp = line.Split(' ');
                int u = int.Parse(temp[0]);
                int v = int.Parse(temp[1]);

                graph[u].Add(v);
                graph[v].Add(u);
            }

            int result = 0;
            int count = (int)Math.Floor((float)n/2f);
            for(int i=n; i > count; i--)
            {
                Queue<int> q = new Queue<int>();
                q.Enqueue(i);
                for(int j=0; j<3;j++)
                {
                    Queue<int> tempQueue = new Queue<int>();
                    while(q.Count > 0)
                    {
                        tempQueue.Enqueue(q.Dequeue());
                    }
                    while(tempQueue.Count > 0)
                    {
                        int index = tempQueue.Dequeue();
                        for (int k = 0; k < graph[index].Count; k++)
                        {
                            q.Enqueue(graph[index][k]);
                        }
                    }
                }

                bool added = false;
                while(q.Count>0)
                {
                    var item = q.Dequeue();
                    if(!graph[i].Contains(item))
                    {
                        graph[i].Add(item);
                        graph[item].Add(i);
                        result++;
                    }
                }
                if(added)
                {
                    i = n+1;
                }
            }
            Console.WriteLine(result);
            //while ((line = Console.ReadLine()) != null) { }
        }
    }
}