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# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;

namespace AtCoder
{
	public class ProblemA
	{
		private static int mask;

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

			mask = (1 << n) - 1;

			HashSet<int>[] connections = new HashSet<int>[n];

			for (int i = 0; i < m; i++)
			{
				line = Console.ReadLine().Split(' ');
				int a = int.Parse(line[0]) - 1;
				int b = int.Parse(line[1]) - 1;

				if (connections[a] == null)
					connections[a] = new HashSet<int>();

				connections[a].Add(b);

				if (connections[b] == null)
					connections[b] = new HashSet<int>();

				connections[b].Add(a);
			}

			int ans = Hop(0, 0, connections);

			Console.WriteLine(ans);
		}

		private static int Hop(int node, int bit, HashSet<int>[] connections)
		{
			bit |= 1 << (node + 1);

			if ((bit & mask) == mask)
				return 1;

			HashSet<int> hashSet = connections[node];

			if (hashSet == null)
				return 0;

			int ans = 0;

			foreach (var item in hashSet)
			{
				// 訪問済みなら飛ばす
				if ((bit & (1 << (item + 1))) == 1)
					continue;

				ans += Hop(item, bit, connections);
			}

			return ans;
		}
	}
}