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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>

#define INF 1 << 29
#define REP(i,n) for(int i=0; i<(int)(n); i++)
#define FOR(i,k,n) for(int i=(k);i<(int)(n);i++)

using namespace std;

typedef pair<int,int> pii;
typedef long long int ll;

void gen_sosuu(int sosuu[]){
  REP(i,100010){
    sosuu[i] = true;
  }
  sosuu[0] = false;
  sosuu[1] = false;
  sosuu[2] = true;
  FOR(i,2,sqrt(100000)+1){
    if(sosuu[i] == false) continue;
    for(int j = 2; i*j<=100000;j++){
      //printf("%d %d %d\n",i*j,i,j);
      sosuu[i*j] =false;
    }
  }
}

int n,m;
int graph[8][8] = {0};
ll sum = 0;
bool visited[8] = {false};
void dfs(int now,bool visited[],int graph[8][8]){
  bool flag = true;
  REP(i,n){
    flag &= visited[i];
  }
  if(flag){
    sum++;
  }
  REP(i,n){
    if(graph[now][i] == 0) continue;
    bool tmp = visited[i];
    visited[i] = true;
    graph[now][i]--;
    graph[i][now]--;
    dfs(i,visited,graph);
    visited[i] = tmp;
    graph[now][i]++;
    graph[now][i]++;
  }
  return;
}

int main(){
  scanf("%d %d",&n,&m);
  REP(i,m){
    int a,b;
    scanf("%d %d",&a,&b);
    graph[a-1][b-1] = graph[b-1][a-1] = 1;
  }
  visited[0] = true;
  dfs(0,visited,graph);
  printf("%lld\n",sum);
}