Explain how to implement doubly linked lists using only one pointer value x.np per item instead of the usual two (next and prev). Assume that all pointer values can be interpreted as k-bit integers, and define x.np to be x.np = x.next XOR x.preν, the k-bit "exclusive-or" of x.next and x.prev. (The value NIL is represented by 0.) Be sure to describe what information you need to access the head of the list. Show how to implement the SEARCH, INSERT, and DELETE operations on such a list. Also show how to reverse such a list in O(1) time.