#!/usr/bin/perl

$|=1;

# A block should have eight letters
# The letters come in pairs:
# One of ac   or   bb
# Two of dg   or   ef
# One of hj   or   ii

my %pairs = ('a' => 'c',
             'b' => 'b',
             'd' => 'g',
             'e' => 'f',
             'h' => 'j',
             'i' => 'i',
            );
for my $l (keys %pairs) { $pairs{$pairs{$l}} = $l } # LOD

my %good_pair = map {$_ => 1} qw(addh addi adeh adei aeeh aeei
                                 bddh bddi bdeh bdei beeh beei);

use decrement_count;

while (<>) {
  chomp;
  my ($block, $shapes) = split /: /;
  print "$block: ";
  my @shapes = split m{/}, $shapes;
  {
    my $sshapes = join '/', sort @shapes;
    if ($shapes ne $sshapes) {
      die "Shape list '$shapes' not sorted";
    }
  }
  my %triangle_count;
  my $triangle_count = 0;
  for my $char (split //, $shapes) {
    next if $char eq '/';
    $triangle_count{$char}++;
    $triangle_count++;
  }
  die "$triangle_count triangles" unless $triangle_count == 8;
  my @pairs;
  while (%triangle_count) {
    my ($key_1) = keys %triangle_count;
    my $val_1 = $pairs{$key_1};
    $key_1 = $val_1 if $key_1 gt $val_1;
    decrement_count(%triangle_count, $key_1);
    decrement_count(%triangle_count, $pairs{$key_1});
    push @pairs, $key_1;
  }
  my $pairs = join "", sort @pairs;
  die "Wrong pair set '$pairs'" unless $good_pair{$pairs};
  print "\n";
}