How to make buckets of like data

[PRyanRay]

Hello, Monks!

I am attempting to "bucketize" binary lists. The basic idea is if I have a list like this:

my @array = (["A","B"],["C","D"],["A","C"],["E","F"],["F","G"]);

I would like to (using hases or arrays) bucket letters that are associated. In this example, I would like to have an object like this:

my @array1 = ([A,B,C,D],[E,F,G]);

I have not had much luck. I have some code that is close but it is very clumsy and cumbersome. Here is the "meat" of my code that is attempting to do this. The variables $req1 and $req2 are the letters in the above example, and, yes, I know it is not correct, that is why I am here:

#!usr/bin/perl
use strict;
use warnings;

my %buckets;

my @array2 = (["A","B"],["C","D"],["A","C"],["E","F"],["F","G"]);
my $count = 0;
foreach(@array2){
    my $req1 = $array2[$count][0];
    my $req2 = $array2[$count][1];
    my $j = 0;
    foreach my $key (keys %buckets){
        if($key =~ /$req1/i){
            $buckets{$key} .= $req2;
            $j++;
            last;
        }
        elsif($key =~ /$req2/i){
            $buckets{$key} .= $req1;
            $j++;
            last;
            }
        elsif($buckets{$key} =~ /$req1/i){
            $buckets{$key} .= $req2;
            $j++;
            last;
            }
        elsif($buckets{$key} =~ /$req2/i){
            $buckets{$key} .= $req1;
            $j++;
            last;
            }        
        }
        if($j == 0){$buckets{$req1} = $req2;}
    $count++;
    }
    
    foreach(keys %buckets){print $_,$buckets{$_},"\n";}

Am I missing something simple here? Any help would be appreciated.

The output from this is the following:

ABC

CD

EFG

See the problem is how to do the retroactive updating if a new hash entry was made.