sub swap_elements_by_idx {
    my ( $i, $j ) = @_;
    @actual_data[ $i, $j ] = @actual_data[ $j, $i ];
    @key_for{ $i, $j } = @key_for{ $j, $i }; # note this is a hash now
    @index_of{ @key_for[ $i, $j ] } = @index_of{ @key_for[ $j, $i ] };
}