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 PHP (5.6.30) (judge verdict: Accepted)

<?php
class main {
    var $arr = array();
    var $adv = array();
    var $step = array();
    var $cnt = 0;
    function run() {
        $line = trim(fgets(STDIN));
        $this->arr = explode(" ", $line);

        for ($i = 0;$i < $this->arr[1]; $i++) {
            $line = trim(fgets(STDIN));
            $tmp = explode(" ", $line);
            $this->adv[$tmp[0]][] = $tmp[1];
            $this->adv[$tmp[1]][] = $tmp[0];
        }

        foreach($this->adv[1] as $start) {
            $this->step[1] = 1;
            $this->next($start);
        }

        echo $this->cnt;
    }
    
    function next ($start) {
        $this->step[$start] = $start;
        if (count($this->step) == $this->arr[0]) {
            $this->cnt++;
            unset($this->step[$start]);
            return;
        }
        foreach($this->adv[$start] as $next) {
            if (!in_array($next, $this->step)) {
                $this->next($next);
                
            }
        }
        unset($this->step[$start]);
    }
}

$object = new main();
$object->run();