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 <string.h>
#include <math.h>
#include <ctype.h>
#include <limits.h>	
#define inf (INT_MAX-1)
#define INF 9223372036854775807
#define sq(n) ((n)*(n))
#define rep(i,n) for(i=0;i<n;i++)
#define rev(i,n) for(i=n-1;i>=0;i--)
#define sort(a,n) qsort(a,n,sizeof(TYPE),cmp)
#define sort_r(a,n) qsort(a,n,sizeof(TYPE),cmp_r);
#define chsort(s,n) qsort(s,n,sizeof(char),cmp)
#define chsort_r(s,n) qsort(s,n,sizeof(char),char_cmp_r);
#define TYPE long long
#define MEMSET(a) memset(a,0,sizeof(a))
const int mod=(int)1e09+7;

int in(void){
	int i;scanf("%d",&i);
	return i;
}
long long llin(void){
	long long i;scanf("%lld",&i);
	return i;
}
double din(void){
	double i;scanf("%lf",&i);
	return i;
}
void chin(char s[]){
	scanf("%s",s);
}
void print(int a){
	printf("%d\n",a);
}
void llprint(long long a){
	printf("%lld\n",a);
}
void dprint(double a){
	printf("%.10f\n",a);
}
void print2(int a,int b){
	printf("%d %d\n",a,b);
}
long long max(long long a,long long b){
	return a>b?a:b;
}
long long min(long long a,long long b){
	return a<b?a:b;
}
long long llabs(long long a){
	return a>0?a:-a;
}
double dmax(double a,double b){
	return a>b?a:b;
}
int cmp(const void *a,const void *b){
	return *(TYPE *)a-*(TYPE *)b;
}
int cmp_r(const void *a,const void *b){
	return *(TYPE *)b-*(TYPE *)a;
}
int char_cmp(const void *a,const void *b){
	return strcmp((char *)a,(char *)b);
}
int char_cmp_r(const void *a,const void *b){
	return strcmp((char *)b,(char *)a);
}
void swap(int *a,int *b){
	int t=*a;
	*a=*b;
	*b=t;
}
long long gcd(long long x,long long y){
	return x%y?gcd(y,x%y):y;
}
long long lcm(long long x,long long y){
	return x/gcd(x,y)*y;
}
struct list{
	int a;
	struct list *prev;
	struct list *next;
};
struct list *head,*tail;
struct list *make(int a){
	struct list *p;
	p=malloc(sizeof(struct list));
	p->a=a;
	p->prev=NULL;
	p->next=NULL;
	return p;
}

int g[8][8];
int mark[8];
int n;

int dfs(int i){
	int j,ret=0;
	mark[i]=1;
	rep(j,n)
		if(!mark[j])break;
	if(j==n)return 1;
	rep(j,n){
		if(g[i][j]&&!mark[j]){
			ret+=dfs(j);
			mark[j]=0;
		}
	}
	return ret;
}

int main(void){
	int m,i,a,b;
	n=in();
	m=in();
	rep(i,n){
		a=in();
		b=in();
		a--;
		b--;
		g[a][b]=g[b][a]=1;
	}
	print(dfs(0));
	return 0;
}