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 C++ (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<vector>
using namespace std;
typedef long long llong;

static const int MAX = 10;
int M[MAX][MAX];
int dp[1<<MAX][MAX];
int n, m;

int main(){
    cin >> n >> m;

    for (int i = 0; i < n; i++){
        for (int j = 0; j < n; j++) M[i][j] = 0;
    }

    int x, y;
    for (int i = 0; i < m; i++){
        cin >> x >> y;
        x--; y--;
        M[x][y] = 1;
        M[y][x] = 1;
    }

    dp[1][0] = 1;

    int cnt;
    int sub;
    for (int i = 0; i < (1<<n); i++){
        for (int j = 0; j < n; j++){
            if (!(i & (1<<j))) continue;

            sub = i ^ (1<<j);
            for (int k = 0; k < n; k++){
                if (M[j][k] == 1) dp[i][j] += dp[sub][k];
            }
        }
    }

    int ans = 0;
    for (int i = 0; i < n; i++){
        ans += dp[(1<<n) - 1][i];
    }
    cout << ans << endl;
    return 0;
}