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;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Solver
        {
            public readonly int N;
            private bool[][] links;
            public Solver(int N, int[][] paths)
            {
                this.N = N;
                links = new bool[N][];
                for (int i = 0; i < N; ++i) { links[i] = new bool[N]; }
                foreach (int[] path in paths)
                {
                    int a = path[0] - 1;
                    int b = path[1] - 1;
                    links[a][b] = true;
                    links[b][a] = true;
                }
            }
            public int Solve(Stack<int> stack)
            {
                if (stack.Count == N) { return 1; }
                int i = stack.First();
                int sum = 0;
                for (int j = 1; j < N; ++j)
                {
                    if (!stack.Contains(j) && links[i][j])
                    {
                        stack.Push(j);
                        sum += Solve(stack);
                        stack.Pop();
                    }
                }
                return sum;
            }
        }
        static void Main(string[] args)
        {
            int[] V = ReadInts();
            int N = V[0];
            int M = V[1];
            int[][] paths = new int[M][];
            for (int i = 0; i < M; ++i) { paths[i] = ReadInts(); }
            var stack = new Stack<int>();
            stack.Push(0);
            Console.WriteLine(new Solver(N, paths).Solve(stack));
        }
    }
}