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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>
#include <numeric>
#include <cstdlib>
#include <queue>
#include <stack>
using namespace std;

typedef long long ll;
#define pb push_back

#define rep(i, n) for (int i=0;i<(n);++i)
#define rep2(i, s, n) for (int i=s;i<(n);++i)
#define INF (1e9+1e9)

class Edge{
public:
    int u, v, cost;
    Edge(int u, int v, int cost):
        u(u), v(v), cost(cost) {}
    bool operator < (const Edge& e) const {
        return cost != e.cost ? cost > e.cost : // for min-priority queue
            u != e.u ? u < e.u : v < e.v;
    }
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;


bool dfs(vector<vector<int > >& G, int u, vector<bool>& visited, int& count, int depth, int s) {
    visited[u] = true;

    int V = G.size();
    if (depth == 3 ) {
        if (G[u][s] == 0) {
            G[u][s]++; G[s][u]++; count++; return true;}
        else return false;
    }
    rep(v, V) {
        if (!visited[v] && G[u][v] == 1)
            if(dfs(G, v, visited, count, depth+1, s)) return true;
    }
    return false;
}

int main()
{
    int V,E; cin>>V>>E;
    vector<vector <int> > G(V, vector<int>(V,0));

    rep(i,E) {
        int u,v; cin>>u>>v;
        u--; v--;
        G[u][v] = 1;
        G[v][u] = 1;
    }

    int count = 0;
    while(1) {
        bool end = true;
        rep(i,V) {
            vector<bool> visited(V,false);
            if (dfs(G, i, visited, count, 0, i)) end = false;
        }
        if (end) { cout << count << endl; return 0;}
    }
    
}