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: Wrong Answer)

import itertools as it

n, m = map(int, input().split())
a = list(list(map(int, input().split())) for _ in range(m))

#print(a)

#無向グラフのルート作成（リスト）
for i in range(len(a)):
    a.append([a[i][1],a[i][0]])
#print(a)


#１を始点とするルートを全探索で作成
lis  = list(it.permutations(range(2, n + 1)))
#print(lis)
for i in range(len(lis)):
    lis[i] = (1,) + lis[i]
#print(lis)

#リストに変換
lis2 = []
for i in range(len(lis)):
    lis[i] = list(lis[i])
    lis2.append(lis[i])
#print(lis2)

#ルート探索
for i in range(len(lis2)):
    flag = 0
    for j in range(len(lis2[i]) - 1):
        for k in range(len(a)):
            if lis2[i][j : j + 2] == a[k]:
                flag += 1
                #print(lis[i][j : j + 2], a[k])
        #print(lis[i][j : j + 2])
print(flag)