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: Time Limit Exceeded)

class Edge
  attr_accessor :s, :e, :c
#  attr_writer :c
  def initialize(s,e)
    @s = s
    @e = e
    @c = 0
  end
end

class Graph
  def initialize(graph)    #hはHash
#    @vs = vs    #Array:頂点（要素は Vertex）
    @es = {}    #Hash:枝（Vertex=>Array）:Arrayの要素はEdge
    graph.each do |hash|
      unless @es.has_key?(hash[:s])
        @es[hash[:s]] = []
      end
      @es[hash[:s]] << Edge.new(hash[:s],hash[:e])
    end
  end

  def add_edge(s,e)
    @es[s] << Edge.new(s,e)
    @es[e] << Edge.new(e,s)
  end

  def get_edges(v)
    @es[v]    #頂点vからのすべての枝（Array）を返す
  end

  #goalを見つければtrue, 見つけられなければfalseを返す
  def find(start)
    dfs(start, [], 0, 0)
  end

  def dfs(v, visited, score,node_count)
    vis = Marshal.load(Marshal.dump(visited))

    if visited.include?(v)
      return 0
    end

    if node_count == 3
#      puts "get_edges(#{v}) : #{get_edges(v)}"
      get_edges(v).each do |edge|
        if edge.s == v && edge.e == vis[0]
          return 0
        end
      end
#      puts "s:#{vis[0]} e:#{v}"
        return v
    end

    vis << v
#    puts "get_edges(#{v}) : #{get_edges(v)}"
    get_edges(v).each {|edge|
      ret = dfs(edge.e,vis,score,node_count+1)
      $score << ret
    }
    return 0
  end
end

n,m = gets.chomp.split(" ").map(&:to_i)

graph = []
m.times do
  input = gets.chomp.split.map(&:to_i)
  graph << {:s => input[0], :e => input[1]}
  graph << {:s => input[1], :e => input[0]}
end

g = Graph.new(graph)
#p g

ans = 0
n.times do |start|
  loop do
    $score = []
    g.find(start+1)
    $score.delete(0)
    $score.uniq!
    break if $score.empty?

    ans += $score.size
    $score.each do |node|
      g.add_edge(start+1,node)
    end
  end
end


puts ans