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>
#define ll long long
using namespace std;
struct Edge {
	int s;
	int t;
	Edge(int s, int t) :s(s), t(t) {}
};

ll N, M;
ll ans = 0;

void dfs(ll n,ll x, vector<vector<Edge>> &G, vector<bool> used) {
	if (x == N - 1) { ans++; return; }
	used[n] = true;
	for (auto e : G[n]) {
		int next = e.t;
		if (!used[next]) {
			dfs(next, x + 1, G, used);
		}
	}
}

int main() {
	cin.tie(0); ios::sync_with_stdio(false);
	cin >> N >> M;
	vector<vector<Edge>> G(N);
	for (int i = 0; i < M;i++) {
		int a, b; cin >> a >> b;
		a--; b--;
		G[a].push_back(Edge(a, b));
		G[b].push_back(Edge(b, a));
	}
	vector<bool> used(N, false);
	dfs(0,0,G, used);
	cout << ans << endl;
}