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;
using ll = long long;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define pb push_back
const int maxn = 10000;
const int INF32 = 1'050'000'000;
const long long INF64 = 4'000'000'000'000'000'000;
const int MOD7 = 1'000'000'007;
const int MOD9 = 1'000'000'009;

void ERROR(int num) { printf("ERROR%d!\n",num); }
ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }
int dx[8]={-1,0,1,0,1,1,-1,-1};
int dy[8]={0,-1,0,1,1,-1,1,-1};

int N, M;
vector<vector<int>> G;

int main(){
	cin >> N >> M;
	G.resize(N);
	rep(i,N) G[i].resize(M);
	rep(i,M){
		int a, b;
		cin >> a >> b;
		a--, b--;
		G[a][b] = G[b][a] = 1;
	}

	vector<int> array(N);
	rep(i,N) array[i] = i;

	int cnt = 0;
	do{
		if(array[0]!=0) break;
		int ok = 1;
		for(int i = 0; i+1<N; i++){
			int from = array[i];
			int to = array[i+1];
			if(G[from][to]==0) ok = 0;
		}
		if(ok) cnt++;
	}while(next_permutation(array.begin(), array.end()));

	cout << cnt << endl;
}