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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdbool.h>
int arr[9], N, M, ans;
bool flg[9], e[9][9];
void dfs(int x){
	if(x == N){
		bool t = true;
		for(int i=1; i<N; i++){
			t &= e[arr[i-1]][arr[i]];
		}
		ans += t;
		return;
	}
	for(int i=0; i<N; i++){
		if(!flg[i]){
			flg[i] = true;
			arr[x] = i;
			dfs(x + 1);
			flg[i] = false;
		}
	}
	return;
}
int main(){
	scanf("%d%d", &N, &M);
	while(M--){
		int a, b;
		scanf("%d%d", &a, &b);
		a--; b--;
		e[a][b] = true;
		e[b][a] = true;
	}
	flg[0] = true;
	arr[0] = 0;
	dfs(1);
	printf("%d\n", ans);
	return 0;
}