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;
using System.Threading.Tasks;

namespace atcoder
{
	class Program
	{
		static int In => int.Parse(Console.ReadLine());
		static int[] Ins => Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

		static void Main(string[] args)
		{
			var NM = Ins;
			var N = NM[0];
			var hash = new List<int>[N];
			for (int i = 0; i < N; i++) hash[i] = new List<int>();
			for(int i = 0;i< NM[1];i++)
			{
				var v = Ins;

				int s = Math.Min(v[0], v[1]) - 1;
				int t = Math.Max(v[0], v[1]) - 1;
				hash[s].Add(t);
				hash[t].Add(s);
			}
			int ans = 0;
			for (int i = 0; i < hash.Length; i++)
			{
				int index = 0;
				while (hash[i].Count > index)
				{
					var a = hash[i][index++];
					if (a == i) continue;
					int indexa = 0;
					while (hash[a].Count > indexa)
					{
						var b = hash[a][indexa++];
						if (b == i || b == a) continue;
						int indexb = 0;
						while (hash[b].Count > indexb)
						{
							var c = hash[b][indexb++];
							if (c == i || c == a || c == b) continue;
							if (hash[i].Contains(c)) continue;
							ans++;
							hash[i].Add(c);
							hash[c].Add(i);
						}
					}
				}
			}
			Console.WriteLine(ans);
			//Console.ReadLine();
		}
	}
}