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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program
{
    static int n;
    static int m;
    static int[] a;
    static int[] b;

    static void Main(string[] args)
    {
        var nm = Console.ReadLine().Split();
        n = int.Parse(nm[0]);
        m = int.Parse(nm[1]);

        a = new int[m];
        b = new int[m];
        for (int i = 0; i < m; i++)
        {
            var ab = Console.ReadLine().Split();
            a[i] = int.Parse(ab[0]);
            b[i] = int.Parse(ab[1]);
        }

        var v = new bool[n];
        v[0] = true;
        var ans = m1(1, v);
        Console.WriteLine(ans);
    }

    static int m1(int x, bool[] v)
    {
        var all = true;
        for (int i = 0; i < n; i++) all &= v[i];
        if (all) return 1;

        var ans = 0;
        for (int i = 0; i < m; i++)
        {
            if (a[i] == x && !v[b[i] - 1])
            {
                v[b[i] - 1] = true;
                ans += m1(b[i], v);
                v[b[i] - 1] = false;
            }
            else if (b[i] == x && !v[a[i] - 1])
            {
                v[a[i] - 1] = true;
                ans += m1(a[i], v);
                v[a[i] - 1] = false;
            }
        }
        return ans;
    }
}