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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
  flag:boolean;
  da,sl:int64;
  hs:array[1..2] of int64;
  x,y,n,u,m,i:longint;
  hd,nx,t,ys:array[0..200100] of longint;
  procedure jb(x,y:longint);
    begin
      u:=u+1;
      nx[u]:=hd[x];
      hd[x]:=u;
      t[u]:=y;
    end;
  function ss(q,sc:longint):boolean;
    var
      i:longint;
      cg:boolean;
    begin //writeln(' ',q,' ',sc);
      ys[q]:=sc;
      sl:=sl+1;
      hs[sc]:=hs[sc]+1;
      cg:=true;
      i:=hd[q];
      while i<>0 do
        begin
          //if (ys[t[i]]=0)and(ss(t[i],3-sc)=false) then cg:=false;
          if ys[t[i]]=0 then cg:=ss(t[i],3-sc) and cg;
          if ys[t[i]]=sc then
            begin
              cg:=false;
              flag:=false;
            end;//writeln(q,' ',t[i],' ',cg);
          i:=nx[i];
        end;//writeln(q,' ',cg);
      exit(cg);
    end;
begin
  readln(n,m);
  for i:=1 to m do
    begin
      readln(x,y);
      jb(x,y);
      jb(y,x);
    end;
  for i:=1 to n do
    if ys[i]=0 then
      begin
        hs[1]:=0;
        hs[2]:=0;
        sl:=0;
        flag:=true;
        if ss(i,1)<>flag then writeln('?');
        if flag then da:=da+hs[1]*hs[2]
        else da:=da+sl*(sl-1) div 2;
      end;
  writeln(da-m);
end.