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 Python (3.4.3) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(10 ** 6)

def root(v):
    if v == par[v]:
        return v
    par[v] = root(par[v])
    return par[v]

def unite(u, v):
    u = root(u)
    v = root(v)
    if u == v:
        return
    if rank[u] < rank[v]:
        u, v = v, u
    par[v] = u
    if rank[u] == rank[v]:
        rank[u] += 1

def same(u, v):
    return root(u) == root(v)

N, M = map(int, input().split())
par = list(range(2 * N))
rank = [0] * (2 * N)
for _ in range(M):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    unite(a, b + N)
    unite(a + N, b)

if same(0, N):
    print(N * (N - 1) // 2 - M)
else:
    c = 0
    for i in range(N):
        c += same(0, i)
    print(c * (N - c) - M)