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 Ruby (2.3.3) (judge verdict: Runtime Error)

n, m = gets.chomp.split(" ").map(&:to_i)
node = Struct.new("Node", :to)
@g = Array.new(n+1){node.new([])}
@color = Array.new(n+1, 0)
m.times do
  a, b = gets.chomp.split(" ").map(&:to_i)
  @g[a].to << b
end
# 二部グラフ判定
def dfs(v, c)
  @color[v] = c
  @g[v].to.size.times do |i|
    if @color[@g[v].to[i]] == c
      return false
    end
    if @color[@g[v].to[i]] == 0 && !dfs(@g[v].to[i], -c)
      return false
    end
  end
  return true
end

1.upto(n) do |i|
  if @color[i] == 0
    if !dfs(i, 1)
      puts n * (n-1) / 2 - m
      exit
    end
  end
end
b = @color.count(1)
w = n - b
puts b * w - m