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)

points_count, lines_count = gets.chomp.split(" ").map(&:to_i)
points = (1..points_count).to_a
lines = []
lines_count.times do
  lines << gets.chomp.split(" ").map(&:to_i)
end

valid_count = 0
(2..points_count).to_a.permutation do |path|
  used_lines = []
  valid = true
  [1, path].flatten.each_cons(2) do |from, to|
    # p [from, to], lines.include?([from,to]) if path == [3, 4, 5, 6, 7, 2]

    if (!lines.include?([from, to]) && !lines.include?([to, from])) ||
      used_lines.include?([from, to]) || used_lines.include?([to, from])
      valid = false
      break
    end

    used_lines << [from, to]
  end

  valid_count += 1 if valid
end

puts valid_count