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 Python (3.8.2) (judge verdict: Accepted)

import itertools

N,M = map(int, input().split())
g = [[0 for i in range(N)] for j in range(N)]

for i in range(M):
  a,b = map(int, input().split())
  g[a-1][b-1]=1
  g[b-1][a-1]=1

  
jr = list(itertools.permutations(range(2,N+1),N-1))
js = []

for i in jr:
  j = list(i)
  j.insert(0,1)
  js.append(j)

ans = 0
  
for i in range(len(js)):
  hantei = True
  for j in range(N-1):
    a = js[i][j]
    #print(a)
    b = js[i][j+1]
    #print(b)
    if g[a-1][b-1] == 0:
      hantei = False
  if hantei:
    ans += 1

print(ans)