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)


#define _USE_MATH_DEFINES
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>  
#include <stdbool.h>   
#define inf (INT_MAX-1)
#define INF 9223372036854775807;
#define PI 3.14159265358979323846;
#define EPS 1e-10
#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 ll long long
#define MEMSET(a) memset(a,0,sizeof(a))
#define MEMSET_U(a) memset(a,-1,sizeof(a))
#define bool    _Bool
const int mod = (int)1e09 + 7;

//#define DEBUG1
//#define DEBUG2
//#define DEBUGF
#define DUMMY

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); }
int Max(int a, int b) { if (a > b) { return a; }return b; }
int Min(int a, int b) { if (a < b) { return a; }return b; }
long long llmax(long long a, long long b) { return a > b ? a : b; }
long long llmin(long long a, long long b) { return a < b ? a : b; }
double dmax(double a, double b) { return a > b ? a : b; }
double dmin(double a, double b) { return a < b ? a : b; }
//long long llmax(long long a, long long b) { return a > b ? a : b; }
//long long llmin(long long a, long long b) { return a < b ? a : b; }
//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; }

int N, M;
int visited[10];
int connected[10][10];
int ans;

void dfs(int, int);

int main() {
	scanf("%d %d", &N, &M);
	int i;

	for (i = 0; i < M; i++) {
		int a, b;
		scanf("%d %d", &a, &b);
		connected[a][b] = 1;
		connected[b][a] = 1;
	}
	dfs(1, 1);
	printf("%d\n", ans);


#ifdef DEBUGF
	getch();
#endif
	return 0;
}

void dfs(int now, int depth) {
	if (depth >= N) {
		ans++;
		return;
	}

	visited[now] = 1;

	for (int i = 1; i <= N; i++) {
		if (connected[now][i] == 1 && visited[i] == 0) {
			visited[i] = 1;
			dfs(i, depth + 1);
			visited[i] = 0;
		}
	}
}