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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
/*
    Problem URL : http://abc054.contest.atcoder.jp/tasks/abc054_c

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

ini_set('error_reporting', E_ALL & ~E_NOTICE);
ini_set('memory_limit', '-1');

$v = array();
$ans = 0;

fscanf(STDIN, "%d %d", $N, $M);

for ($i = 0; $i < $M; $i++) {
    fscanf(STDIN, "%d %d", $a, $b);
    $v[$a][$b] = 1;
    $v[$b][$a] = 1;
}

// var_dump($v);
// exit;

$arr = array("1");
$base = "1";

for ($i = 0; $i < $N-1; $i++) {
    $newArr = array();
    foreach ($arr as $tmp) {
        $last = substr($tmp, strlen($tmp) - 1);
        // echo "last:{$last}\n";
        // var_dump($v[$last]);
        foreach ($v[$last] as $nex => $dummy) {
            if (!in_array($nex, str_split($tmp))) {
                $newArr[] = $tmp . $nex;
            }
        }
    }
    $arr = $newArr;
}
// var_dump($arr);

foreach ($arr as $x) {
    $arrx = str_split($x);
    $sum = array();
    for ($i = 0; $i < $N; $i++) {
        $sum[$arrx[$i]]++;
    }
    // echo max($sum) . PHP_EOL;
    if (max($sum) == 1) {
        $ans++;
    }
}
echo $ans . PHP_EOL;