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;

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

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

    boolean[] visited = new boolean[N];
    visited[0] = true;
    System.out.println(dfs(N, graph, visited, 0));
  }

  private static int dfs(int N, int[][] graph, boolean[] visited, int id) {
    visited[id] = true;
    int numVisited = 0;
    for (int i = 0; i < N; i++) if (visited[i]) numVisited++;
    if (numVisited == N) {
      return 1;
    }
    int count = 0;
    for (int i = 0; i < N; i++) {
      if (graph[id][i] == 1 && !visited[i]) {
        visited[i] = true;
        count += dfs(N, graph, visited, i);
        visited[i] = false;
      }
    }
    return count;
  }
}