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 Rust (1.15.1) (judge verdict: Accepted)

use std::collections::VecDeque;
use std::io::*;
use std::str::FromStr;

fn main() {
    let (n, m): (usize, usize) = (read(), read());
    let mut graph: Vec<Vec<usize>> = vec![Vec::new(); n];
    for _ in 0..m {
        let (a, b) = (read::<usize>() - 1, read::<usize>() - 1);
        graph[a].push(b);
        graph[b].push(a);
    }
    let mut color: Vec<i32> = vec![0; n];
    let mut nibu = true;
    let mut que: VecDeque<usize> = VecDeque::new();
    que.push_back(0);
    color[0] = 1;
    while !que.is_empty() {
        let p = que.pop_front().unwrap();
        for i in &graph[p] {
            if color[*i] == 0 {
                color[*i] = 3 - color[p];
                que.push_back(*i);
            }
            if color[*i] == color[p] {
                nibu = false;
                break;
            }
        }
    }
    let mut sum = n * (n - 1) / 2;
    if nibu {
        let (mut c1, mut c2) = (0, 0);
        for i in 0..n {
            if color[i] == 1 {
                c1 += 1;
            } else {
                c2 += 1;
            }
        }
        sum -= c1 * (c1 - 1) / 2;
        sum -= c2 * (c2 - 1) / 2;
    }
    println!("{}", sum - m);
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}