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)

#include<stdio.h>

int main(void){
	int a,b,c,d,e,f,g,i,n,m,w[16][16]={0},r=0;
	scanf("%d%d",&n,&m);
	for(i = 1;i <= m;i++){scanf("%d%d",&a,&b);w[a][b] = 1;w[b][a] = 1;}
	if(n == 8){
	for(a = 2;a <= 8;a++){
	for(b = 2;b <= 8;b++){if(b == a){continue;}
	for(c = 2;c <= 8;c++){if(c == a || c == b){continue;}
	for(d = 2;d <= 8;d++){if(d == a || d == b || d == c){continue;}
	for(e = 2;e <= 8;e++){if(e == a || e == b || e == c || e == d){continue;}
	for(f = 2;f <= 8;f++){if(f == a || f == b || f == c || f == d || f == e){continue;}
	for(g = 2;g <= 8;g++){if(g == a || g == b || g == c || g == d || g == e || g == f){continue;}
	if(w[1][a] && w[a][b] && w[b][c] && w[c][d] && w[d][e] && w[e][f] && w[f][g]){r++;}
	}
	}
	}
	}
	}
	}
	}
	}
	if(n == 7){
	for(a = 2;a <= 7;a++){
	for(b = 2;b <= 7;b++){if(b == a){continue;}
	for(c = 2;c <= 7;c++){if(c == a || c == b){continue;}
	for(d = 2;d <= 7;d++){if(d == a || d == b || d == c){continue;}
	for(e = 2;e <= 7;e++){if(e == a || e == b || e == c || e == d){continue;}
	for(f = 2;f <= 7;f++){if(f == a || f == b || f == c || f == d || f == e){continue;}
	if(w[1][a] && w[a][b] && w[b][c] && w[c][d] && w[d][e] && w[e][f]){r++;}
	}
	}
	}
	}
	}
	}
	}
	if(n == 6){
	for(a = 2;a <= 6;a++){
	for(b = 2;b <= 6;b++){if(b == a){continue;}
	for(c = 2;c <= 6;c++){if(c == a || c == b){continue;}
	for(d = 2;d <= 6;d++){if(d == a || d == b || d == c){continue;}
	for(e = 2;e <= 6;e++){if(e == a || e == b || e == c || e == d){continue;}
	if(w[1][a] && w[a][b] && w[b][c] && w[c][d] && w[d][e]){r++;}
	}
	}
	}
	}
	}
	}
	if(n == 5){
	for(a = 2;a <= 5;a++){
	for(b = 2;b <= 5;b++){if(b == a){continue;}
	for(c = 2;c <= 5;c++){if(c == a || c == b){continue;}
	for(d = 2;d <= 5;d++){if(d == a || d == b || d == c){continue;}
	if(w[1][a] && w[a][b] && w[b][c] && w[c][d]){r++;}
	}
	}
	}
	}
	}
	if(n == 4){
	for(a = 2;a <= 4;a++){
	for(b = 2;b <= 4;b++){if(b == a){continue;}
	for(c = 2;c <= 4;c++){if(c == a || c == b){continue;}
	if(w[1][a] && w[a][b] && w[b][c]){r++;}
	}
	}
	}
	}
	if(n == 3){
	for(a = 2;a <= 3;a++){
	for(b = 2;b <= 3;b++){if(b == a){continue;}
	if(w[1][a] && w[a][b]){r++;}
	}
	}
	}
	if(n == 2){
	for(a = 2;a <= 2;a++){
	if(w[1][a] && w[a][b]){r++;}
	}
	}
	printf("%d\n",r);
	return 0;
}