where does $tmessages come from? You can just use Mail::IMAPClient's unseen method:

my @unread = $imap->unseen or warn "Could not find unseen msgs: $@\n";
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Also from the docs:

        foreach my $f ($imap->folders) {
                print   "The $f folder has ",
                        $imap->unseen_count($f)||0, 
                        " unseen messages.\n";          
        }
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I don't know if these are more efficient runtime-wise, but certainly make the code cleaner..