Suppose we are given a perfectly balanced binary tree T (a perfectly balanced binary tree is one in which every non-leaf has exactly two children, and every leaf is located at the same depth of the tree as every other leaf) in which every node is assigned a number. Give a divide and conquer algorithm which will rearrange the leaf nodes such that: The overall shape of the tree remains the same. The numbers associated with the leaf nodes appear in increasing sorted order from left to right. The number associated with every parent node is the sum of its two children. Provide a runtime analysis of your algorithm. As an example, the tree on the left would be rearranged to look like the tree on the right: 4 5 10 1 3 5 2 1 3 2 10 3 7 4