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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			int[] nm = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			int n = nm[0];
			int m = nm[1];

			var to = new List<int>[n];
			for (int i = 0; i < n; i++) {
				to[i] = new List<int>();
			}

			for (int i = 0; i < m; i++) {
				int[] ab = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
				to[ab[0] - 1].Add(ab[1] - 1);
				to[ab[1] - 1].Add(ab[0] - 1);
			}

			var q = new Queue<Tuple<int, int>>();
			q.Enqueue(new Tuple<int, int>(0, 1));
			int ans = 0;
			int goal = ((int)Math.Pow(2, n)) - 1;
			while (q.Count > 0) {
				var cur = q.Dequeue();
				foreach (var next in to[cur.Item1]) {
					if ((cur.Item2 & (1 << next)) == 0) {
						q.Enqueue(new Tuple<int, int>(next, cur.Item2 | (1 << next)));
					}
				}

				if (cur.Item2 == goal) {
					++ans;
				}
			}

			Console.WriteLine(ans);
		}
	}
}