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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <utility>
#include <vector>
#include <stack>
#include <set>

using namespace std;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef pair<int, int> PII;
typedef long long LL;
#define ALL(a) (a).begin(),(a).end()
#define PB push_back
#define MP make_pair
#define SORT(c) sort((c).begin(),(c).end())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define IFOR(v,it) for(VI::iterator it=(v).begin();it!=(v).end();++it)

int N, M;
int solve(vector<vector<bool> >& edge, bool visited[9], int start) {
  visited[start] = true;
  bool allVisited = true;
  int count = 0;
  FOR(i, 1, N+1) {
    if (!visited[i]) {
      allVisited = false;
      if (edge[start][i])
        count += solve(edge, visited, i);
    }
  }
  visited[start] = false;
  if (allVisited)
    return 1;
  return count;
}

int main() {
  cin >> N >> M;

  vector<vector<bool> > edge;
  REP(i, N+1) {
    vector<bool> v(N+1, false);
    edge.PB(v);
  }
  REP(i, N) {
    int a, b;
    cin >> a >> b;
    edge[a][b] = true;
    edge[b][a] = true;
  }
  bool visited[9];
  fill(visited, visited + 9, false);
  cout << solve(edge, visited, 1) << endl;

  return 0;
}