#!/usr/bin/perl

use strict;
use warnings;

my $op_io = <<'OP_INPUT_AND_OUTPUT';
'aaa'   1,2             'aaa'   1,2
'aaa'   2,1             'aaa'   2,3
'aaa'   2,3             'aaa'   2,1
'aaa'   3,1             'aaa'   3,1
'aaa'   3,2             'aaa'   3,2
'aaa'   4,1             'aaa'   4,5
'aaa'   4,5             'aaa'   4,1
'bbb'   2,2             'bbb'   2,1
'bbb'   2,5             'bbb'   2,2
'bbb'   2,1             'bbb'   2,5
'bbb'   4,3             'bbb'   4,6
'bbb'   4,6             'bbb'   4,3
'bbb'   4,1             'bbb'   4,2
'bbb'   4,2             'bbb'   4,1
'ccc'   3,3             'ccc'   1,1
'ccc'   3,6             'ccc'   1,3
'ccc'   1,3             'ccc'   2,4
'ccc'   1,1             'ccc'   2,2
'ccc'   6,4             'ccc'   3,3
'ccc'   6,6             'ccc'   3,6
'ccc'   2,2             'ccc'   6,6
'ccc'   2,4             'ccc'   6,4
OP_INPUT_AND_OUTPUT
    ;

my @init;
my @want;
my $n = 0;
foreach my $line ( split /\n/, $op_io ) {
    ( $init[$n][0], $init[$n][1], $init[$n][2],
      $want[$n][0], $want[$n][1], $want[$n][2] )
        = ( $line =~ m{ \A  \'(...)\' \s+ (\d+),(\d+)
                        \s+ \'(...)\' \s+ (\d+),(\d+) }xms );
    $n++;
}

# At this point, @init and @want are both AoA.

# unique X values for each group
my %x_of;
$x_of{$_->[0]}{$_->[1]}++ for @init;

# map an X to its relative position in a sorted list of X.
foreach my $group ( keys %x_of ) {
    my @exez = sort { $a <=> $b } keys %{ $x_of{$group} };
    @{ $x_of{$group} }{@exez} = 0 .. $#exez;
}

# Sort first by group, then by X,
# then ascending or descending depending on what X's position is.
my @out = sort { $a->[0] cmp $b->[0]
                 ||
                 $a->[1] <=> $b->[1]
                 ||
                 ( ( $x_of{ $a->[0] }{ $a->[1] } % 2 )
                   ? ( $b->[2] <=> $a->[2] )
                   : ( $a->[2] <=> $b->[2] ) )
} @init;

use Test::More tests => 1;

is_deeply( \@out, \@want, 'it works!' );