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.chomp.split.map(&:to_i)

$graph = Array.new(n).map{Array.new(n,false)}
# 隣接行列を使う
m.times do
  a, b = gets.chomp.split.map(&:to_i)
  $graph[a-1][b-1] = true
  $graph[b-1][a-1] = true
end


# 深さ優先探索1回ごとにリセットされる
visited = Array.new(n, false)
visited[0] = true


def dfs(v, n, visited)
  all_visited = true

  # p visited

  # ループして全部に訪問したかを確認する
  n.times do |i|
    all_visited = false if visited[i] == false
  end

  return 1 if all_visited == true

  ret = 0
  n.times do |i|
    next if $graph[v][i] == false
    next if visited[i] == true
    # p i

    visited[i] = true
    ret += dfs(i, n, visited)
    visited[i] = false

  end

  return ret
end

# p $graph
# p visited

ans = dfs(0, n, visited)

p ans