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 (3.4.3) (judge verdict: Runtime Error)

N,M = map(int,input().split())
a = [0]*M
b = [0]*M
for i in range(M):
    a_, b_ = map(int,input().split())
    # 配列の添字としたいので-1
    a[i] = a_ -1
    b[i] = b_ -1

route = [0]*N  # 通過済
connect=[[0]*M for _ in range(M)]
def dfs(now, depth):
    # print("#"*depth,now, depth)
    # 通過済ならNG
    if route[now]: return 0
    # depth = Nなら達成
    if depth == N: return 1
    
    route[now] = 1
    ans = 0
    for i in range(N):
        if connect[now][i]:
            ans += dfs(i, depth+1)
    route[now] = 0
    return ans

for i in range(M):
    connect[a[i]][b[i]] = connect[b[i]][a[i]] = 1

# for xx in connect:
#     print(xx)
print(dfs(0,1))