Help modifying recursive regex

[beeflobill]

A long time ago I worked really hard and wrote a piece of recursive regex code which I'm trying to modify now. It takes text with nested parentheses and returns a list with the "top" groups of parentheses.

Here is an example which shows what the regex does:
Input: "A (B C D)"
Output: "B C D"

Input: "A (B C D) (E F G)"
Output: "B C D", "E F G"

Input: "A B (C (D E) (F G)) (H I)"
Output: "C (D E) (F G)", "H I"

Even when I wrote the code I knew I would really, really want to keep the data that wasn't in parentheses too, but I couldn't figure out how to do it. Now I'm back on the problem.

Here is an example of what I am trying to get:
Input: "A (B C D)"
Output: "A", "B C D"

Input: "A (B C D) (E F G)"
Output: "A", "B C D", "E F G"

Input: "A B (C (D E) (F G)) (H I)"
Output: "A", "B", "C (D E) (F G)", "H I"

I still don't know how to do that. I've provided a test script demonstrating the subroutine that does what I'm describing. May I supplicate, how might I modify this to do what I need? Or, is there simply a better way to approach this problem? Thanks.

#!/usr/bin/perl -w
use strict;

sub strip_paren {
   my $input = $_[0];
   my $re;

   $re = qr/
        (?:
         \(
            (
              (?:
                [^()]+
                |
                (??{$re})
              )+
            )
         \)
       )
       |
       \(\)
       /x;

   my @output = $input =~ /$re/g;

   return @output;
}

sub print_crud {
   print shift, "\n";
   foreach my $line (@_) {
      print "  $line\n";
   }
   print "\n";
}

my $string = "A (B C D)";
print_crud($string, strip_paren($string));

$string = "A (B C D) (E F G)";
print_crud($string, strip_paren($string));

$string = "A B (C (D E) (F G)) (H I)";
print_crud($string, strip_paren($string));