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: Runtime Error)

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

namespace ABC54_C
{
    class Program
    {

        static int dfs(int v, int n, bool[] visited, bool[][] g)
        {
            bool all_visited = true;

            for (int i = 0; i < n; i++) if (!visited[i]) all_visited = false;
            if (all_visited) return 1;

            int ret = 0;
            for (int i = 0; i < n; i++)
            {
                if (g[v][i] == false) continue;
                if (visited[i]) continue;
                visited[i] = true;
                ret+= dfs(i, n, visited, g);
                visited[i] = false;
            }
            return ret;
        }

        static void Main(string[] args)
        {
            var s = Console.ReadLine().Split();
            int n = int.Parse(s[0]);
            int m = int.Parse(s[1]);
            var g = new bool[m][];
            for (int i = 0; i < m; i++)
            {
                g[i] = new bool[m];
            }
            for (int i = 0; i < m; i++)
            {
                var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
                g[a[0] - 1][a[1] - 1] = true;
                g[a[1] - 1][a[0] - 1] = true;
            }
            var visited = new bool[8];
            for (int i = 0; i < n; i++) visited[i] = false;
            visited[0] = true;

            Console.WriteLine(dfs(0, n, visited, g));


        }
    }
}