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 <iostream>
#include <vector>
#include <queue>
#include <set>
#include <string>
#include <map>
#include <cmath>
#include <cstring>

#define fi first
#define se second
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define rrep(i,n) for (int i = 1; i < (n); ++i)
#define drep(i,n) for (int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define all(x) (x).begin(), (x).end()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define pb push_back
#define sz(x) (int)(x).size()
#define PQ(T) priority_queue<T, v(T), greater<T> >

//#define v(T) vector<T>
//#define vv(T) v(v(T))

using namespace std;
typedef long long ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
//typedef vector<int> vi;
//typedef vector<vi> vvi;
//typedef vector<ll> vl;
//typedef vector<P> vp;

const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;

const int mod = 1000000007;

int main() {
    int n, m;
    cin >> n >> m;
    vector<int> to[10];
    int a, b;
    rep(i,m) {
        cin >> a >> b;
        --a; --b;
        to[a].pb(b);
        to[b].pb(a);
    }

    vector<int> v(n-1);
    rep(i,n-1) v[i] = i+1;
    int ans = 0;
    do {
        int pre = 0;
        bool ok = true;
        for(auto i: v) {
            auto itr = find(all(to[pre]), i);
            if (itr == to[pre].end()) ok = false;
            pre = i;
        }
        if (ok) ++ans;
    } while(next_permutation(all(v)));
    cout << ans << endl;
    return 0;
}