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: Accepted)

import java.util.Scanner;

/*
 * AtCoder Beginner Contest 054
 * 2017/02/11
 * C - One-stroke Path
 *
 * https://beta.atcoder.jp/contests/abc054/tasks/abc054_c
 * */
public class Main {

	static int[] a, b;
	static int N, M, ans;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();
		M = sc.nextInt();
		a = new int[M];
		b = new int[M];
		boolean[] flg = new boolean[N];

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

		int now = 0;
		flg[now] = true;
		dfs(now, flg);

		System.out.println(ans);
	}

	public static void dfs(int now, boolean[] flg) {
		for (int i = 0; i < M; i++) {
			if (a[i] == now && !flg[b[i]]) {
				flg[b[i]] = true;
				dfs(b[i], flg);
				flg[b[i]] = false;
			}
			if (b[i] == now && !flg[a[i]]) {
				flg[a[i]] = true;
				dfs(a[i], flg);
				flg[a[i]] = false;
			}
		}

		for ( int i = 0; i < N; i++) {
			if ( flg[i] == false) {
				return;
			}
		}
		ans++;
		return;
	}

}