In this problem, we would like to show the amortized time of a union operation when union by-weight on linked-lists is used is (log n). For that, we need to come up with a sequence of (n) operations for which the amortized cost per operation is (log n). We start with make-set(xi) for i {1, 2, . . . n} where n is a power of 2. Provide a consequent sequence of (n) union operations so that the total number of updated pointers for all operations is (n log n).