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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

#define mod 1e9+7
#define ll long long int
#define epsilon 1e-7

ll min(ll x, ll y){
    if(x < y)return x;
    else return y;
}
int ans = 0;
int next(int start, int n, int y[n], int x[n][n]){
    int count = 0;
    int cc = 0;
    for(int i = 1;i < n;i++){
        if(x[start][i]==1 && y[i] == 0){
            count++;
            if(y[i]==0)cc++;
            y[i] = 1;
            ans += next(i, n, y, x);
            y[i] = 0;
        }
    }
    if(count == 0 && cc != 0)return 0;
    else if(count == 0)return 1;
    return ans;
}

int main(void){
    int n, m;
    scanf("%d %d", &n, &m);
    int a[m], b[m];
    for(int i = 0;i < m;i++)scanf("%d %d", &a[i], &b[i]);
    int x[n][n];
    for(int i = 0;i < n;i++){
        for(int j = 0;j < n;j++){
            x[i][j] = 0;
        }
    }
    for(int i = 0;i < m;i++){
        x[a[i]][b[i]] = 1;
        x[b[i]][a[i]] = 1;
    }
    int y[n];
    y[0] = 1;
    for(int i = 1;i < n;i++){
        y[i] = 0;
    }
    printf("%d\n", next(0, n, y, x));
    return 0;
}