we would like to show the amortized time of a union operation when unionby-weight on linked-lists is used is (logn). For that, we need to come up with a sequence of (n) operations for which the amortized cost per operation is (logn). 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 (nlogn).