for my $witness (2..int((10**length($i) - 1) / $i)) {
            if ($i_sorted eq join '', sort split //, $i * $witness) {
                if (++$pairs == $count) {
                    ++$qualifying_integers;
                    next I;
                }
            }
        }
        # maximum witness can't be more than i's first digit
        for my $witness (2..substr $i, 0, 1) {
            if (!( $i % $witness ) && $i_sorted eq join '', sort split //, $i / $witness) {
                if (++$pairs == $count) {
                    ++$qualifying_integers;
                    next I;
                }
            }
        }