Do you insist that your sub-sub-directory name has three characters? If not, then

$s = $p1.$p2.$p3;
$s++;
$s =~ /(.*)(.{1})(.{1})/;
($p1,$p2,$p3) = ($1,$2,$3);
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Will generate an endless stream of path parts, with the added advantage you don't have to rewrite when you get to z/z/z because it goes straight on to aa/a/a.

§ George Sherston