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 INF 1001000100010001000
#define MOD 1000000007
#define EPS 1e-10
#define int long long
#define rep(i, N) for (int i = 0; i < N; i++)
#define Rep(i, N) for (int i = 1; i < N; i++)
#define For(i, a, b) for (int i = (a); i < (b); i++)
#define pb push_back
#define mp make_pair
#define i_i pair<int, int>
#define vi vector<int>
#define vvi vector<vi >
#define vb vector<bool>
#define vvb vector<vb >
#define vp vector< i_i >
#define all(a) (a).begin(), (a).end()
#define Int(x) int x; scanf("%lld", &x);
 
//int dxy[5] = {0, 1, 0, -1, 0};
// assign

string path;
vb used(8, false);
vvb graph(8, vb(8, false));
int n, m, ret = 0;

void mp();
int search();

signed main()
{
    cin >> n >> m;
    rep(i, m) {
        int a, b;
        cin >> a >> b;
        graph[a-1][b-1] = true;
        graph[b-1][a-1] = true;
    }
    used[0] = true;
    path.pb(0);
    mp();
    cout << ret << endl;

    return 0;
}

void mp()
{
    if (path.size() == n) {
        ret += search();
    } else {
        Rep(i, n) {
            if (!used[i]) {
                used[i] = true;
                path.pb(i);
                mp();
                used[i] = false;
                path.pop_back();
            }
        }
    }
}

int search()
{
    int state = path[0];
    Rep(i, n) {
        if (!graph[state][path[i]]) {
            return 0;
        } else {
            state = path[i];
        }
    }
    return 1;
}