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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

import itertools

n,m=map(int,input().split())

if n ==2:
    print(1)
    exit()

arr=[[_] for _ in range(n)]

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

#print("arr",arr)

route=list(itertools.permutations(range(1,n)))
#print("route",route) 
ans=0
for i in route:
    chk0=False
    chk=True
    if i[0] in arr[0]:
        #print(i)
        for j in range(1,n-1):
            if i[j] in arr[i[j-1]]:
                chk0=True
                #print(i[j],arr[j])
                pass
            else:
                chk=False
    if chk==True and chk0==True:
        #print(i)
        ans+=1

print(ans)