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>
using namespace std;
#define fi first
#define se second
#define countof(array) (sizeof(array) / sizeof(array[0]))
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,n,s) for(int i = s; i < (n); ++i)
#define rsrep(i,n,s) for(int i = (n)-1; i >= s; --i)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define aall(a) (a), (a)+countof(a)//for array sorting
#define raall(a) (a), (a)+countof(a), greater<>()
#define show(x) cout<<#x<<" = "<<x<<endl;
#define vfind(v, a) find(all(v), a) != v.end()
#define yn(f) { if (f) puts("YES"); else puts("NO"); }
#define yns(f) { if (f) puts("Yes"); else puts("No"); }
#define show_ary(...) { cout<<#__VA_ARGS__<<" = "; for (const auto& x : (__VA_ARGS__)) { cout<<x<<" "; } cout<<endl; }
#define show_pair(...) cout<<#__VA_ARGS__<<" = "<<endl; for (const auto& x : (__VA_ARGS__)) { cout<<"  "<<x.fi<<" : "<<x.se<<endl; }
#define out_ary(...) { for (const auto& x : (__VA_ARGS__)) { cout<<x<<" "; } cout<<endl; }
#define argmax(v) distance((v).begin(), max_element(all(v)))
#define argmin(v) distance((v).begin(), min_element(all(v)))
#define vmax(v) *max_element(all(v))
#define vmin(v) *min_element(all(v))
typedef long long int ll;
typedef pair<int, int> P;
typedef vector<P> vpair;
typedef vector<int> vint;
typedef vector<ll> vll;
typedef vector<double> vdouble;
typedef vector<string> vstr;
typedef vector<bool> vbool;
typedef vector<vint> vvint;
typedef vector<vll> vvll;
typedef vector<vstr> vvstr;
typedef vector<vbool> vvbool;
const ll LINF = 2000000000000000000ll;
const int INF = 1000000100;
const ll MOD = 1e9+7;

int main() {
    int n, m;
    cin >> n >> m;
    vvbool e(n+1, vbool(n+1, false));
    rep(i, m) {
        int a, b;
        cin >> a >> b;
        e[a][b] = true;
        e[b][a] = true;
    }
    vint p(n);
    iota(all(p), 1);
    int ans = 0;
    do {
        if (p[0] != 1) break;
        rep(i, n-1) {
            if (!e[p[i]][p[i+1]]) break;
            if (i == n-2) ans++;
        }
    } while( next_permutation(all(p)) );

    cout << ans << endl;
    return 0;
}