Trim trees are binary trees whose nodes are labelled with strings, such that Each leaf node has label "left", "right", or "back" If a node has one child, it has label x where where is the child's label. E.g. if the child has label "left" then the parent has "leftx". If a node has two children, it contains where and are the child labels. E.g. if the children have labels "right" and "back", then the parent has label "rightback". Let S(n) be the length of the label on node n. Let L(n) be the number of leaves in the subtree rooted at n. Use (strong) induction to prove that S(n)4L(n) if n is the root node of any Trim tree