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>

int count = 0;

void dfs(int ver, int v[][10], int seen[], int n, int m){
	int end = 1;
	for(int i=0; i < n; i++) {
		if(!seen[i] && i != ver)
			end = 0;
	}
	if(end) {
		count++;
		return;
	}

	seen[ver] = 1;
	for(int i=0; v[ver][i]; i++) {
		if(seen[v[ver][i]-1])
			continue;
		dfs(v[ver][i]-1, v, seen, n, m);
	}
	seen[ver] = 0;
}

int main(void){
	int n, m, a, b, idx[10] = {0};
	int v[10][10] = {{0}};
	int seen[10] = {0};

	scanf("%d%d", &n, &m);
	for(int i=0; i < m; i++) {
		scanf("%d%d", &a, &b);
		a--; b--;
		v[a][idx[a]++] = b+1;
		v[b][idx[b]++] = a+1;
	}

	dfs(0, v, seen, n, m);
	printf("%d", count);

	return 0;
}