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

int n,m,a[30],b[30],count=0,ans=0;
bool visited[8];

int dfs(v){
    visited[v]=true;
    count++;
    if (count==n){
        ans++;
    }
    for (int i=0; i<m; i++){
        if (a[i]==v){
            int v2=b[i];
            if (visited [v2]==true){
            continue;
            }
            dfs(v2);
            visited[v2]=false;
            count--;
        } else if (b[i]==v){
            int v2=a[i];
            if (visited [v2]==true){
            continue;
            }
            dfs(v2);
            visited[v2]=false;
            count--;
        }
    }
    return 0;
}


int main(void){
    scanf("%d%d",&n,&m);
    for (int i=0; i<n; i++){
        visited[i]=false;
    }
    for (int i=0; i<m; i++){
        scanf("%d%d",&a[i],&b[i]);
    }
    
    dfs(1);
    printf ("%d\n",ans);
	return 0 ;
}