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

typedef struct edge{
	int u,v;
} EDGE;

int search(int n,int visited[],int node[n][n],int position){
	int node_local[n][n];
	int visited_local[n];
	memcpy(node_local,node,sizeof(int)*n*n);
	memcpy(visited_local,visited,sizeof(int)*n);
	int i,j;
	int sum=0;
	visited_local[position]=1;
	
	/* puts("==========");
	printf("node:%d\n",position+1);
	for(i=0;i<n;i++){
		for(j=0;j<n;j++){
			printf("%d",node_local[i][j]);
		}puts("");
	}
	printf("visited node\n");
	for(i=0;i<n;i++){
		printf("%d",visited_local[i]);
	}puts("");
	puts("=========="); */
	
	visited_local[position]=1;
	for(i=0;i<n;i++){
		if(node_local[position][i]==1){
			node_local[position][i]=0;
			if(visited_local[i]==0){
				sum+=search(n,visited_local,node_local,i);
			}
		}
	}
	
	int allVisited=1;
	for(i=0;i<n;i++){
		if(visited_local[i]==0){
			allVisited=0;
			break;
		}
	}
	
	return sum+allVisited;
}

int main(){
	int n,m;
	scanf("%d %d",&n,&m);
	EDGE e[m];
	int node[n][n];
	int visited[n];
	int i,j;
	for(i=0;i<n;i++){
		visited[i]=0;
		for(j=0;j<n;j++){
			node[i][j]=0;
		}
	}
	
	for(i=0;i<m;i++){
		scanf("%d %d",&e[i].u,&e[i].v);
		e[i].u--;e[i].v--;
		node[e[i].u][e[i].v]=1;
		node[e[i].v][e[i].u]=1;
	}
	
	int position=0;
	printf("%d\n",search(n,visited,node,position));
	
	return 0;
}