sub find_best_partition {
  # We're going to try to find partitions that add up to each possible
  # number that can be added up to.
  my $old;
  my $new = {0 => [[], []]};

  for my $n (sort {$a <=> $b} @_) {
    $old = $new;
    $new = {};
    while (my ($key, $value) = each %$old) {
      my ($p1, $p2) = @$value;
      $new->{$key + $n} ||= [[$n, $p1], $p2];
      $new->{$key - $n} ||= [$p1, [$n, $p2]];
    }
  }

  my $best = each %$new;
  while (my $difference = each %$new) {
    if (abs($difference) < abs($best)) {
      $best = $difference;
    }
  }

  # We need to flatten our nested arrays.
  my ($p1, $p2) = @{ $new->{$best} };

  my @part_1;
  while (@$p1) {
    push @part_1, $p1->[0];
    $p1 = $p1->[1];
  }

  my @part_2;
  while (@$p2) {
    push @part_2, $p2->[0];
    $p2 = $p2->[1];
  }

  return (\@part_1, \@part_2);
}