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
	n,m,i,a,b:Longint;
	used:array[1..8]of Boolean;
	c:array[1..8]of Longint;
	G:array[1..8,1..7]of Longint;
function f(u,cnt:Longint):Longint;
var i,ret:Longint;
begin
	if cnt=n then begin
		f:=1;
		exit;
	end;
	ret:=0;
	for i:=1 to c[u] do begin
		if not used[G[u,i]]then begin
			used[G[u,i]]:=True;
			inc(ret,f(G[u,i],cnt+1));
			used[G[u,i]]:=False;
		end;
	end;
	f:=ret;
end;
begin
	read(n,m);
	for i:=1 to m do begin
		read(a,b);
		inc(c[a]);
		inc(c[b]);
		G[a,c[a]]:=b;
		G[b,c[b]]:=a;
	end;
	used[1]:=True;
	writeln(f(1,1));
end.