Problem: 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.

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Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

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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.

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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.

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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.

Examples

Input

3 3
1 2
1 3
2 3


Output

2


Input

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7


Output

1

Solution (in JAVA):

Solution:

import java.util.LinkedList;
import java.util.Scanner;
import java.util.Stack;

public class Main {

    static int cnt = 0;
    public static void main(String args[]) throws Exception
    {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M  = sc.nextInt();

        boolean map[][] = new boolean[N][N];

        for(int i=0;i<M;i++){
            int x = sc.nextInt();
            int y = sc.nextInt();
            map[x-1][y-1] = true;
            map[y-1][x-1] = true;
        }
        Stack<Integer> stack = new Stack<>();
        stack.push(0);
        dfsCount(map,stack);
        System.out.println(cnt);


        sc.close();
    }

    static void dfsCount(boolean [][] map , Stack<Integer> path ){
        int size = map.length;
        if (path.size()==size) {
            cnt++;
            return;
        }
        int peek = path.peek();
        for(int i =0;i<size;i++){
            if(map[peek][i]&&!path.contains(i)){
                Stack<Integer> sq = (Stack<Integer>)path.clone();
                sq.push(i);
                dfsCount(map,sq);
            }
        }
    }

}