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>
int n,m,map[20][20],mark[20],sum;
void dfs(int x)
{
	int i,j=0;
	for(i=1;i<=n;i++)
	{
		if(mark[i]==1)
		j++;
	}
	if(j==n)
	{
		sum++;
		return;
	}
	for(i=2;i<=n;i++)
	{
		if(!mark[i]&&map[x][i]==1)
		{
			mark[i]=1;
			dfs(i);
			mark[i]=0;
		}
	}
}
int main(void)
{
	int a,b,i,j,k;
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		memset(map,0,sizeof(map));
		memset(mark,0,sizeof(mark));
	for(i=1;i<=m;i++)
	{
		scanf("%d%d",&a,&b);
		map[a][b]=map[b][a]=1;
	}
	mark[1]=1;
	sum=0;
	for(i=2;i<=m;i++)
	{
		if(!mark[i]&&map[1][i]==1)
		{
			mark[i]=1;
			dfs(i);
			mark[i]=0;
		}
	}
	printf("%d\n",sum);
	}
	return 0;
}