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: Wrong Answer)

def f v, list, num, n
	ans = 0
	jd = true
	list.each do |ll|
		if ll == 0
			jd = false 
			break
		end
	end
	if jd 
		return 1 
	end
	n.times do |i|
		next if i == num 
		next if list[i] == 1
		if v[num][i] == 1 
			list[i] = 1 
			ans +=	f v.dup, list.dup, i, n
			list[i] = 0
		end
	end
	return ans
end


N,M = gets.split.map(&:to_i)

v = Array.new(N){Array.new(N){0}}

M.times do
	a = gets.split.map(&:to_i)
	v[a[0] - 1][a[1] - 1] = 1
end
list = Array.new(N){0}
list[0] = 1

ans = f v.dup, list.dup, 0, N

puts ans