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>
#include <string.h>

typedef struct {
	int a;
	int b;
} pass_t;

static int Count;

static void route(pass_t *pass, int M, int N, char history[8], int target);

int main(int argc, char *argv[])
{
	int i, N, M;
	pass_t pass[28];
	char history[8] = {0};

	scanf("%d %d", &N, &M);
	for ( i = 0; i < M; i++ ){
		scanf("%d %d", &pass[i].a, &pass[i].b);
	}
	route(pass, M, N, history, 1);
	printf("%d\n", Count);
	return 0;
}

static void route(pass_t *pass, int M, int N, char history[8], int target)
{
	char h[8];
	int i;

	if ( history[ target - 1 ]  == 1 ){
		return;
	}
	memcpy(h, history, 8);
	h[ target - 1] = 1;

	for ( i = 0; i < N; i++ ){
		if ( h[i] != 1 ){
			break;
		}
	}
	if ( i == N ){
		Count++;
	}

	for ( i = 0; i < M; i++ ){
		if ( pass[i].a == target ){
			route(pass, M, N, h, pass[i].b);
		} else if (pass[i].b == target ){
			route(pass, M, N, h, pass[i].a);
		}
	}
}