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

function dfs($first, $last) {
    if (count($last) == 0) {
        return [$first];
    }

    $res = [];
    foreach ($last as $key => $val) {
        $next_f = $first;
        $next_l = $last;

        $next_f[] = $val;
        array_splice($next_l, $key, 1);
        $res = array_merge($res, dfs($next_f, $next_l));
    }

    return $res;
}

function next_permutation($end) {
    return dfs([1], range(2, $end));
}

fscanf(STDIN, "%d %d", $n, $m);
$passes = [];
for ($i = 0; $i < $m; ++$i) {
    $passes[] = explode(' ', trim(fgets(STDIN)));
}

$perms = next_permutation($n);
$count = 0;
foreach ($perms as $perm) {
    $flg = true;
    for ($i = 0; $i < $n - 1; ++$i) {
        $tmp = [
            $perm[$i],
            $perm[$i + 1],
        ];
        $tmp2 = [
            $perm[$i + 1],
            $perm[$i],
        ];

        foreach ($passes as $pass) {
            if (
                $pass == $tmp
                || $pass == $tmp2
            ) {
                continue 2;
            }
        }

        $flg = false;
        break;
    }

    if ($flg) {
        ++$count;
    }
}

echo $count;