Given a binary tree consisting exactly of n vertices and rooted at vertex 1. Each vertex V of this tree has a value value[v] assigned to it.
The greatness of a vertex i = (value[i] x 1) + (value[par[i]] x 2) + (value[par[par[i]] x 3) + (value[par[par[par[i]]] x 4) + ... until you reach the root i.e par[par[.....par[i]...]] is the root
where par[i] represents the parent of vertex i.
Given a value array where value[i] (1-based indexing) corresponds to the value assigned to the ith vertex. The greatness of an entire tree is defined as the maximum of greatness of any of its vertices. Find the maximum greatness of the tree.
e.g. Consider the above tree where the number inside the node represents the value of the node.
The greatness of vertex with value 4 will be : (value x 1) + (par[4] x 2) + (par[par[4]] x 3).
The greatness of vertex with value 4 will be : (4 x 1) + (2 x 2) + (1 x 3) => 11.
Similarly greatness of vertex 6 will be : (6 x 1) + (3 x 2) + (2 x 3) + (1 x 4) => 22.