sub naive_shuffle_traverse {
  my $i = shift;
  my $j = shift;
  my $n = my @p = @_;
  @p[ $i, $j ] = @p[ $j, $i ] if defined $j; # swap
  if ( ++$i < $n ) {
    for my $j (0..$n-1) {
      naive_shuffle_traverse( $i, $j, $tally, @p );
    }
  }
  else {
    return;
  }
}