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 fr(i,n) _back
#define pb	push_back
#define eb	emplace_back
#define mk	make_pair
#define fi	first
#define se	second
#define endl	'\n'

typedef long long ll;
typedef pair<int,int> ii;
typedef vector<ii> vii;
const int INF = 0x3f3f3f3f;
const double PI = acos(-1.0);
const int N = 300;

int n,m,gol;
ll dp[10][N];
vector<int> g[10];

ll solve(int u, int mask) {
    if(mask == gol) return 1;
    ll &r = dp[u][mask];
    if(~r) return r;
    r = 0;

    for(int v : g[u]) {
        if(mask & (1 << v)) continue;
        r += solve(v, mask | (1 << v));
    }

    return r;
}

int main() {
    ios_base::sync_with_stdio(false);
    memset(dp,-1,sizeof dp);
    cin >> n >> m;
    gol = pow(2,n)-1;

    while(m--) {
        int a,b; cin >> a >> b;
        a--; b--;
        g[a].pb(b);
        g[b].pb(a);
    }

    cout << solve(0,1) << endl;

    return 0;
}