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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)


import java.util.Arrays;
import java.util.Scanner;

class Point{
	int x;
	int y;
	int z;
	Point(int a,int b,int c){
		this.x = a;
		this.y = b;
		this.z = c;
	}
}
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int M = sc.nextInt();

		int[][] S = new int[M][2];

		for(int i = 0 ; i < M ; i++){
			S[i][0] = sc.nextInt();
			S[i][1] = sc.nextInt();
		}

		sc.close();

		int n = (int)Math.pow(2, M);

		String ar = "%0" + M + "d";
		String aa;

		int[][] ans = new int[2][M];
		for(int i = 0 ; i < M ; i++){
			ans[0][i] = i+1;
		}

		int answer = 0;
		for(int i = 0 ; i < n ; i++){
			aa = String.format(ar,Integer.parseInt(Integer.toBinaryString(i)));
			//System.out.println(aa);
			for(int j = 0 ; j < M ; j++){
				if(aa.substring(j, j+1).equals("1")){
					ans[1][S[j][0]-1] ++ ;
					ans[1][S[j][1]-1] ++ ;
					//System.out.println(S[j][0] - 1);
				}
			}

			int count = 0 ;
			int onecount = 0;
			int twocount = 0;

			for(int k = 0 ; k < M ; k++){
				count += ans[1][k];
				if(ans[1][k] == 1){
					onecount++;
				}
				if(ans[1][k] == 2){
					twocount++;
				}
			}

			if(count != N*2-2 || onecount != 2 || twocount != N-2){
				for(int[]  x : ans){
					Arrays.fill(x, 0);
				}
			}
			else{
				/*
				System.out.println(aa);
				for(int l = 0 ; l < M ; l++){
					System.out.println(ans[1][l]);
				}
				*/
				answer++;
			}
		}
		System.out.println(answer);

	}

}