sub prop3
{
    my $str = shift;
    my $level = shift || 0;
    return $str unless $level;  # 3rd update
    my @str = split(/[()]/, $str);
    splice @str, 0, $level;
    my $out = join('(', @str);
    $out .= ')' x ( @str - 1 );
    return $out;
}