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 sys
import math
import heapq
mod=10**9+7
inf=float("inf")
from math import sqrt
from collections import deque
from collections import Counter
from math import ceil
input=lambda: sys.stdin.readline().strip()
sys.setrecursionlimit(11451419)
from decimal import Decimal #floatの高精度ver, 渡すのはstr型で
from functools import lru_cache
#メモ化再帰defの冒頭に毎回 @lru_cache(maxsize=10**10)
#引数にlistはだめ
#######ここまでテンプレ#######
#ソート、"a"+"b"、再帰ならPython3の方がいい
#######ここから天ぷら########

from itertools import permutations as per
n,m=map(int,input().split())
A=[[] for i in range(n)]
for i in range(m):
    a,b=map(int,input().split())
    a-=1 ;b-=1
    A[a].append(b)
    A[b].append(a)

ans=0
for bit in per([i for i in range(1,n)]):
    # print(bit)
    peanut=0
    bit=[0]+list(bit)
    for i in range(n-1):
        if not bit[i] in A[bit[i+1]]:
            peanut=1
            break
    else:
        ans+=1
    

print(ans)