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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        private static int Solve(int N, int M, Tuple<int, int>[] tuples)
        {
            var link1 = new HashSet<int>[N + 1];
            var link2 = new HashSet<int>[N + 1];
            for (int i = 1; i <= N; ++i)
            {
                link1[i] = new HashSet<int>();
                link2[i] = new HashSet<int>();
            }
            int count = 0;
            var queue = new Queue<Tuple<int, int>>(tuples);
            Func<int, int, bool> linked = (a, b) => (a == b || link1[a].Contains(b) || link1[b].Contains(a));
            while (queue.Count > 0)
            {
                var tuple = queue.Dequeue();
                int A = tuple.Item1;
                int B = tuple.Item2;
                if (!linked(A, B))
                {
                    foreach (var a in link1[A])
                    {
                        foreach (var b in link1[B])
                        {
                            if (!linked(a, b)) { queue.Enqueue(new Tuple<int, int>(a, b)); }
                        }
                    }
                    foreach (var a in link2[A]) { if (!linked(a, B)) { queue.Enqueue(new Tuple<int, int>(a, B)); } }
                    foreach (var b in link2[B]) { if (!linked(A, b)) { queue.Enqueue(new Tuple<int, int>(A, b)); } }
                    foreach (var a in link1[A]) { if (a != B) { link2[B].Add(a); } }
                    foreach (var b in link1[B]) { if (b != A) { link2[A].Add(b); } }
                    link1[A].Add(B);
                    link1[B].Add(A);
                    ++count;
                }
            }
            return count - M;
        }
        static void Main(string[] args)
        {
            int[] values1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int N = values1[0];
            int M = values1[1];
            var tuples = new Tuple<int, int>[M];
            for (int i = 0; i < M; ++i)
            {
                int[] values2 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                tuples[i] = new Tuple<int, int>(values2[0], values2[1]);
            }
            Console.WriteLine(Solve(N, M, tuples));
        }
    }
}