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: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>

/* define */
#define Yes(X) puts ( X ? "Yes" : "No")
#define YES(X) puts ( X ? "YES" : "NO")
#define FOR(i, a, b) for ( i = a; i < b ; i++)
#define REP(i, n) for ( i = 0; i < n ; i++)
#define max(a, b) (((a) > (b)) ? (a) : (b))
#define min(a, b) (((a) < (b)) ? (a) : (b))
#define max3(a, b, c) ((max((a), (b)) > (c)) ? max((a), (b)) : (c))
#define min3(a, b, c) ((min((a), (b)) < (c)) ? min((a), (b)) : (c))

/* const */
const int MOD = (int)1e9 + 7;

/* alias */
typedef long long ll;

/* function */
int cmp(const void *a, const void *b) {
	return *(int*)a - *(int*)b;
}
int cmp2(const void *a, const void *b) {
	return *(int*)b - *(int*)a;
}

/* main */
int i, j, k;

#define nmax  8
int n, m, a, b, x = 0, ver[nmax][nmax] = { 0 }, visited[nmax] = { 1 };


int visit(int x, int visited[nmax]) {
	int all_visited = 1;
	REP(i, n) if (visited[i] == 0) all_visited = 0;
	if (all_visited) {
		printf("\n");
		return 1;
	}
	int c = 0;
	REP(i, n) {
		if (visited[i] == 0 && ver[x][i] == 1) {
			visited[i] = 1;
			printf("%d", x);
			c += visit(i, visited);
			visited[i] = 0;
		}
	}
	return c;
}

int main() {
	scanf("%d%d", &n, &m);
	REP(i, m) {
		scanf("%d%d", &a, &b);
		ver[a - 1][b - 1] = 1;
		ver[b - 1][a - 1] = 1;
	}
	printf("%d\n", visit(x, visited));
	return 0;
}