10. (15%) Consider a binary tree with height equal to H. The identification numbers of the vertices in the binary tree are given in the order of level-order traversal. Then each vertex is assigned a weight equal to the inverse of its identification number. The identification numbers and weights of the vertices in an example binary tree with H= 3 and 6 vertices are illustrated in the figure below.. identification number of vertices weights of vertices (1/1) (1/2) (1/3 6 (1/4) (1/5) (1/6) (a) (5%) How many vertices are there in a binary tree of height H? (H can be any positive integer.) (b) (10%) What is the lowest height of a binary tree whose sum of weights of all vertices is greater than 14.3? [Hint: In2 is roughly equal to 0.69.]