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(100000000)

N,M = map(int,input().split())
graph = {i:[] for i in range(N)}
for _ in range(M):
    x,y = map(int,input().split())
    x -= 1
    y -= 1
    graph[x].append(y)
    graph[y].append(x)


def f(u,c):
    color[u] = c
    for v in graph[u]:
        if color[v] == 0: # まだ塗られていない場合
            if not f(v,-c):
                return False
        else:
            if color[v] == c: # 隣接している頂点が同色の場合 二部グラフではない
                return False
    return True 

flag = True
color = [0 for _ in range(N)]
for i in range(N):
    if color[i] == 0:
        if not f(i,1):
            flag = False
            break

if flag: # 二部グラフ
    ans = color.count(1)*color.count(-1) - M
else:
    ans = N*(N-1)//2 - M

print(int(ans))