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 Ruby (2.3.3) (judge verdict: Accepted)

$cnt=0

def solve(adj,n,m)
	perm(0,1,0,adj,n,m)
	puts $cnt
end

def perm(i,u,c,adj,n,m)
	if i<n-1
		for x in 0..n-1
			if ((u>>x)&1)==0
				nu=u+(1<<x)
				if adj[c][x]==1
					perm(i+1,nu,x,adj,n,m)
				end
			end
		end
	else
		$cnt+=1
	end
end

if __FILE__==$0
	
	rl_i=lambda{|str,dl|str.strip.split(dl).map(&:to_i)}
	
	dl=" "
	num=rl_i[gets,dl]
	adj=Array.new(num[0]){Array.new(num[1]){0}}
	num[1].times do |i|
		v=rl_i[gets,dl]
		adj[v[0]-1][v[1]-1]=1
		adj[v[1]-1][v[0]-1]=1
	end
	solve(adj,num[0],num[1])
end