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