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 <bits/stdc++.h>
#define rep(i, a, b) for(int i = a; i < b; i++)
#define Rep(i, a, b) for(int i = a; i <= b; i++)
#define _GLIBCXX_DEBUG
#define Vl vector<ll>
#define Vs vector<string>
#define Vp vector<pair<ll, ll>>
#define P pair<ll, ll>
#define ll long long
#define ALL(v) (v).begin(),(v).end()
#define endl "\n"
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define co(x) cout << x << endl
#define coel cout << endl
#define pb push_back
#define sz(v) ((int)(v).size())
using namespace std;  
const double pi = acos(-1.0);
const ll MOD = 1e9 + 7;
const ll INF = 1LL << 60;


////////////////////////////////////////////////////////

bool g[10][10];

int main() {
    ll n, m; cin >> n >> m;
    rep(i, 0, m){
        ll a, b; cin >> a >> b;
        g[a][b] = 1;
        g[b][a] = 1;
    }
    Vl v = {};
    ll cnt = 0;
    Rep(i, 1, n) v.push_back(i);
    // Rep(i, 1, n){
    //     Rep(j, 1, n) cout << g[i][j] << " ";
    //     cout << endl;
    // }
    do{
        bool f = true;
        rep(i, 0, sz(v)-1){
            if(!g[v[i]][v[i+1]]) f = false;
        }
        if(f) cnt++;
    }while(next_permutation(v.begin()+1, v.end()));
    co(cnt);

    return 0;
}