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)

n,m = gets.split(" ").map{|v|
	v.to_i
}

$nbr = []
for i in 0..n-1
	$nbr[i] = []
end

#接続関係を配列に直す
m.times do
	a,b = gets.split(" ").map{|v|
		v.to_i
	}
	$nbr[a-1] << b-1
	$nbr[b-1] << a-1
end

def CountPath(cur, prevs, n)	
	if prevs.length == n-1
		return 1
	end

	sum = 0
	for v in $nbr[cur]
#		if v is not in prevs
		if !(prevs.include?(v))
			prevs << cur
			sum = sum + CountPath(v, prevs, n)
			prevs.delete_at(-1)

		end
	end
	
	return sum
end

if $nbr[0].length == 0
	# 頂点1からの辺がない
	puts 0
	exit
end

puts CountPath(0, [], n)