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>

void go(_Bool* bridge, _Bool* via, int now, int N, int* path){
//	printf("now%d\n", now);           //現在の居場所
	int i;
	_Bool t = 0;
	_Bool via_Copy[N];
	for(i = 0; i < N; i ++){
		via_Copy[i] = via[i];
	}
	via_Copy[now] = 1;

	for(i = 0; i < N; i ++){
		
//		printf("%d", via[i]);
		
		if(via_Copy[i] == 0){
			t = 1;
//			printf("t = 1, %d\n", i);
			break;
		}
	}
//	printf("\n");
	
	if(t == 0){
		*path = *path + 1;
//		printf("Yes\n");
	}else{
				
		for(i = 0; i < N; i ++){
			if(bridge[now * N + i] == 1 && via[i] != 1){  // bridge[now][i]
				go(bridge, via_Copy, i, N, path);
			}
		}
	}
	
}

int main(){
	int N, M, a, b;
	int sc, i, j, k;
	int path = 0;
//	*path = 0;
	sc = scanf("%d %d", &N, &M);
	_Bool bridge[N][N];  // bridge[a][b] aからbに橋があれば１
	_Bool via[N];        // via[a]　通った島は1
	for(i = 0; i < N; i ++){
		for(j = 0; j < N; j ++){
			bridge[i][j] = 0;
		}
		via[i] = 0;
	}
	
	for(i = 0; i < M; i ++){
		sc = scanf("%d %d", &a, &b);
		bridge[a - 1][b - 1] = 1;
		bridge[b - 1][a - 1] = 1;
	}
	
	for(i = 0; i < N; i ++){
		for(j = 0; j < N; j ++){
//			printf("%d", bridge[i][j]);
		}
//		printf("\n");
	}
	
	go(&bridge[0][0], via, 0, N, &path);
	
	printf("%d\n", path);
	return 0;
}