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 n, m;
  int root = 0;
  int count = 1;
  int memo[9][9] = {0};
  int seen[9] = {0};

void dfs(int x, int y){

  if(seen[y] == 1){
    return;
  }

  seen[y]++;
  count ++;
  if(count == n) ++root;
  for(int i = 1; i <= n; ++i){
    if( (memo[y][i] == 1) && (i != x) ){
      dfs(y,i);
    }
  }
  count --;
  return;
}

int main(){

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

  seen[1] = 1;
  for(int vertex = 2; vertex <= n; ++vertex){
    if(memo[1][vertex] == 1){
      dfs(1,vertex);
      for(int i = 2; i <= n; ++i){
        seen[i] = 0;
      }
    }
  }

  printf("%d",root);
  return 0;

}