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)

pub fn read1<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
    let s = read1::<String>();
    s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
}

fn dfs(i: usize, g: usize, edge: &Vec<Vec<usize>>, group: &mut Vec<usize>) -> bool {
    let g_inv = g ^ 1;
    group[i] = g_inv;

    for &j in edge[i].iter() {
        if group[j] == 2 {
            if !dfs(j, g_inv, edge, group) {
                return false;
            }
        } else if group[j] == g_inv { return false; }
    }

    true
}

fn main() {
    let nm = readn::<usize>(" ");
    let n = nm[0];
    let m = nm[1];

    let mut edge = vec![Vec::new(); n];
    for _ in 0..m {
        let ab = readn::<usize>(" ");
        edge[ab[0] - 1].push(ab[1] - 1);
        edge[ab[1] - 1].push(ab[0] - 1);
    }

    let mut group = vec![2; n];
    let mut flg = true;
    for i in 0..n {
        if group[i] == 2 {
            if !dfs(i, 0, &edge, &mut group) {
                flg = false;
                break;
            }
        }
    }

    let ans;
    if flg {
        let g1 = group.iter().sum::<usize>();
        let g2 = n - g1;
        ans = g1 * g2 - m;
    } else {
        ans = n * (n - 1) / 2 - m;
    }

    println!("{}", ans);
}