#!/usr/bin/env perl

use strict;
use warnings;
use List::Util qw(minstr sum);
# bitstring; positions 0..11 correspond to vertical walls; 12..23 to horizontal;
my @old = "000000000000000000000000";

#   00  01  02
# 12  13  14  15
#   03  04  05
# 16  17  18  19
#   06  07  08
# 20  21  22  23
#   09  10  11

# 0..8 represent the nine internal corner points; 9 represents the outer wall
my @points = (
    # vertical walls 0..11
    [0, 9], [1, 9], [2, 9],
    [0, 3], [1, 4], [2, 5],
    [3, 6], [4, 7], [5, 8],
    [6, 9], [7, 9], [8, 9],
    # horizontal walls 12..23
    [0, 9], [0, 1], [1, 2], [2, 9],
    [3, 9], [3, 4], [4, 5], [5, 9],
    [6, 9], [6, 7], [7, 8], [8, 9]
);

my %symmetries = (
    id   => [0..23],
    rot1 => [qw(15 19 23 14 18 22 13 17 21 12 16 20 2 5 8 11 1 4 7 10 0 3 6 9)],
    rot2 => [qw(11 10 9 8 7 6 5 4 3 2 1 0 23 22 21 20 19 18 17 16 15 14 13 12)],
    rot3 => [qw(20 16 12 21 17 13 22 18 14 23 19 15 9 6 3 0 10 7 4 1 11 8 5 2)],
    flip => [qw(9 10 11 6 7 8 3 4 5 0 1 2 20 21 22 23 16 17 18 19 12 13 14 15)],
    frt1 => [qw(12 16 20 13 17 21 14 18 22 15 19 23 0 3 6 9 1 4 7 10 2 5 8 11)],
    frt2 => [qw(2 1 0 5 4 3 8 7 6 11 10 9 15 14 13 12 19 18 17 16 23 22 21 20)],
    frt3 => [qw(23 19 15 22 18 14 21 17 13 20 16 12 11 8 5 2 10 7 4 1 9 6 3 0)],
)
;

sub p { my ($s, $n) = @_; return substr($s, $n, 1) }
sub ch { my ($s, $n) = @_; return substr($s, 0, $n) . "1" . substr($s, $n + 1) }

for (1..9) {
    my %new;
    for my $s (@old) {
        my @active = (0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
        for my $n (0..23) {
            next unless p($s, $n);
            $active[$points [$n][0]] = 1;
            $active[$points [$n][1]] = 1;
        }
        for my $n (0..23) {
            next if p($s, $n);
            my @x = @{$points[$n]};
            if ($active[$x[0]] != $active[$x[1]]) {
                my @w = split //, ch($s, $n);
                my $min = minstr map { join '', @w[@{$symmetries{$_}}] } keys %symmetries;
                $new{$min}++;
            }
        }
    }

    @old = keys %new;
    warn scalar @old;
}

for (sort @old) {
     print substr($_, 0, 24), "\n";
}