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 ALL(obj) (obj).begin(), (obj).end()
#define REP(i, n) for(int i = 0;i < (n);++i)
#define REPLL(i, n) for(ll i = 0;i < (n);++i)

#define endl "\n"
#define pb push_back
#define MOD 1000000007LL
#define PI 3.1415926

typedef long long ll;

template <typename T> inline T GCD(T a,T b){T c;while(b!=0){c=a%b;a=b;b=c;}return a;}
template <typename T> inline T LCM(T a,T b){T c=GCD(a,b);a/=c;return a*b;}
template <typename T> inline T nCr(T a,T b){T i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
template <typename T> inline T nHr(T a,T b){return nCr(a+b-1,b);}
template <typename T> inline T POW(T a,T b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}

int n, m;
bool graph[8][8];
int dfs(int pos, bool visit[8]){
	bool allvisit = 1;
	REP(i, n){
		if(!visit[i]) allvisit = 0;
	}
	if(allvisit) return 1;

	int res = 0;
	REP(i, n){
		if(!graph[pos][i]) continue;
		if(visit[i]) continue;

		visit[i] = 1;
		res += dfs(i, visit);
		visit[i] = 0;
	}

	return res;
}
int main(void){
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin >> n >> m;
	int a, b;
	REP(i, m){
		cin >> a >> b;
		graph[a-1][b-1] = graph[b-1][a-1] = 1;
	}

	bool visited[8];
	REP(i, n) visited[i] = 0;
	visited[0] = 1;

	cout << dfs(0, visited) << endl;

	return 0;
}