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#!/usr/bin/perl
use strict;
...
        #  The references are the array resulting from split, using []
        push(@strings, [split /\s/]) foreach (@smallarray);
}

#       The array of anonymous arrays now looks like this:
#
...
#                       'kkk',
#                       'lll'
#               ];

#  Print out the whole AoA contents
foreach my $arrayref (@strings) {
...
bbb
ccc