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 <iostream>
#include <vector>
#include <algorithm>
#include <iterator>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <string>
#include <cmath>
using namespace std;
#define MOD 1000000007
#define INF 1<<30
#define LINF (ll)1<<62
#define MAX 510000
#define rep(i,n) for(ll i=0; i<(n); i++)
#define REP(i,a,b) for(ll i=(a); i<(b); i++)
#define all(x) (x).begin(),(x).end()
#define uni(q) unique(all(q)),q.end()
using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<ll, ll> P;
typedef vector<pair<ll, ll>> vpl;

vvl G(10);
bool visit[10];
ll cnt = 0;
ll n,m;

void dfs(ll u){
    if(visit[u]) return;
    visit[u] = true;
    for(auto v : G[u]){
        if(visit[v]) continue;
        dfs(v);
    }
    bool flag = true;
    rep(i,n){
        if(!visit[i]){
            flag = false;
            break;
        }
    }
    if(flag) cnt++;
    visit[u] = false;
}

int main(){
	cin >> n >> m;
    rep(i,m){
        ll a,b; cin >> a >> b;
        a--;  b--;
        G[a].push_back(b);
        G[b].push_back(a);
    }
    dfs(0);
    cout << cnt << endl;
}