Check if subcategory has subsubcategories

This code checks whether current post has any subcategory under the category 16 and echo the subcategory(if there is any). I would like to further check for any subsubcategory listed under the individual subcategory and echo it after subcategory. Which means I would like to echo subcategory followed by subsubcategory. Am struggling to do so. Would appreciate any help! Thanks in advance.

<?php foreach (get_the_category() as $cat){
if(cat_is_ancestor_of(16, $cat)){
 $parent = get_category($cat->category_parent);
 $parent_name = $parent->cat_name;
 echo $parent->cat_name . '<p>';
}}?>