Consider the following problem: You are given a pointer to the root r of a binary tree, where each vertex v has pointers v. lc and v. rc to the left and right child, and a value Val (v) >0. The value NIL represents a null pointer, showing that v has no child of that type. You wish to find the maximum total sum of vertices of a subset with the following constraints: If v is in the subset, then the following vertices cannot be in the subset: The parent of v
The children of v
The sibling of v (the other vertex that shares the same parent as v)

(You can assume that the tree is a full balanced binary tree with n vertices where n= 2^k -1) for some K>=1