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 ll long long
#define INF 100000000000
#define mod 1000000007
#define pll pair<long,long>
#define se second
#define fi first
#define pb push_back
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;

typedef tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>ordered_set;
typedef tree<pll,null_type,less<pll>,rb_tree_tag,tree_order_statistics_node_update>pllordered_set;


int main()
{
			ios_base::sync_with_stdio(false);
			cin.tie(NULL);
			ll n,m;
			cin>>n>>m;
			map<pair<ll,ll>,ll> edge;
			for(ll i=0;i<m;i++)
			{
				ll u,v;
				cin>>u>>v;
				edge[{u,v}]=1;
				edge[{v,u}]=1;
			}
			vector<ll> v1;
			for(ll i=1;i<=n;i++)
			{
				v1.pb(i);
			}
			ll cnt=0;
			do
			{
				ll c1=1;
				for(ll i=1;i<=n;i++)
				{
					if(edge[{v1[i],v1[i-1]}]==1)
						c1++;
				}
				if(c1==n)
					cnt++;
			}while(next_permutation(v1.begin()+1,v1.end()));
			cout<<cnt;
			
			
			
}