#!perl -w
use strict;
sub choose {
  my ($str, $n) = @_;
  my @result;
  choose1(\@result, "", $str, $n, 0);
  return @result;
}

sub choose1 {
  my ($parray, $this, $str, $n, $x) = @_;
  if ($n == 0) {
    push @{$parray}, $this;
    return;
  }
  return if $x + $n > length($str);
  choose1($parray, $this . substr($str, $x, 1), $str, $n - 1, $x+1);
  choose1($parray, $this, $str, $n, $x+1);
}

my %edges;
my %nodes;
my %collinear;
for (qw(ab acfi adgj ae bcde bfhj bi ej eghi ij)) {
  $nodes{$_} = 1     for choose($_, 1);
  $edges{$_} = 1     for choose($_, 2);
  $collinear{$_} = 1 for choose($_, 3);
}
my $allnodes = join "", sort keys %nodes;

for my $triple (grep {!$collinear{$_}} choose($allnodes, 3)) {
  print "$triple\n" if 3 == grep { $edges{$_} } choose($triple, 2);
}
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