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: Accepted)

#include <algorithm>
#include <climits>
#include <iostream>
#include <string>
#include <utility>
#include <vector>
#include <map>

using namespace std;
using ll = long long int;

template <class T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (auto i = v.begin(); i != v.end(); i++) {
    os << *i << " ";
  }
  return os;
}

ll gcd(ll a, ll b) {
  ll tmp;
  if ( b > a) {
    tmp = a;
    a = b;
    b = tmp;
  }
  while (a % b !=0) {
    tmp = b;
    b = a % b;
    a = tmp;
  }
  return b;
}

ll lcm(ll a, ll b) {
  return a * b / gcd(a, b);
}

int main(void) {
  int n, m;
  cin>>n>>m;
  int e[10][10];
  for(int i=0; i<10; i++) {
    for(int j=0; j<10; j++) {
      e[i][j] = 0;
    }
  }
  for(int i=0; i<m; i++) {
    int x, y;
    cin>>x>>y;
    e[x][y] = 1;
    e[y][x]= 1;
  }
  vector<int> v;
  for(int i=2; i<=n; i++) {
    v.push_back(i);
  }
  int cnt=0;
  do {
    int prev = 1;
    bool f = true;
    for(auto &it : v) {
      if(!e[prev][it]) {
	f = false;
	break;
      }
      prev = it;
    }
    if(f)
      cnt++;
  }while(next_permutation(v.begin(), v.end()));
  std::cout << cnt << std::endl;
  return 0;
}