Suppose we have a perfect binary tree D whose every node contains an integer. We would like to count the number of internal nodes of the tree (that is, non-leaf nodes) whose integer number is equal to the sum of the integer numbers of their two subtrees. 

a) Given a perfect binary tree D with n leaves, you are asked to design and analyze a Divide-and-Conquer algorithm that computes and returns the number of internal nodes of the tree that satisfy the properties such as these are described above. Your algorithm should have time complexity O(n), where n is the number of leaves of D and is a power of 2. The description of your algorithm should be given in the form of the three phases Divide, Conquer and Combine as well as the terminal case should be explicitly given. For your convenience, the description of the algorithm in the three phases should be independent of the tree structure