Problem:
Score : 300 points

Problem Statement

You are given an undirected unweighted graph with N vertices and M edges that contains neither self-loops nor double edges.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

How many different paths start from vertex 1 and visit all the vertices exactly once?

Here, the endpoints of a path are considered visited.

For example, let us assume that the following undirected graph shown in Figure 1 is given.

Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

Figure 2: an example of a path that satisfies the condition

However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices.

Figure 3: an example of a path that does not satisfy the condition

Neither the following path shown in Figure 4, because it does not start from vertex 1.

Figure 4: another example of a path that does not satisfy the condition

Constraints

2≦N≦8

0≦M≦N(N-1)/2

1≦a_i<b_i≦N

The given graph contains neither self-loops nor double edges.

Input

The 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

Print the number of the different paths that start from vertex 1 and visit all the vertices exactly once.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 2

1

This test case is the same as the one described in the problem statement.

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

var ans,n,m,i,j,tot,u,v:longint;
    last,pre,other:array[0..100007] of longint;
	vis:array[0..100007] of boolean;
procedure insert(u,v:longint);
begin
  inc(tot);
  other[tot]:=v;
  pre[tot]:=last[u];
  last[u]:=tot;
end;
procedure dfs(x,u:longint);
var q,v:longint;
begin
  if (x=n) then inc(ans) else
  begin
    q:=last[u];
    while (q>0) do
	begin
	  v:=other[q];
	  if not(vis[v]) then
	  begin
	    vis[v]:=true;
	    dfs(x+1,v);
	    vis[v]:=false;
	  end;
	  q:=pre[q];
	end;
  end;
end;
begin
  readln(n,m);
  tot:=0;
  fillchar(last,sizeof(last),0);
  fillchar(pre,sizeof(pre),0);
  fillchar(other,sizeof(other),0);
  for i:=1 to m do
  begin
    readln(u,v);
    insert(u,v);
    insert(v,u);
  end;
  ans:=0;
  fillchar(vis,sizeof(vis),false);
  vis[1]:=true;
  dfs(1,1);
  writeln(ans);
end.