Problem 1. (8 points) Suppose we have the following operations on a stack S. : PUSH, POP and MULTIPOP(k) where MULTIPOP(k) pops min(k, size(S)) elements from the stack where k > 0. Note the actual cost of these operations are respectively 1,1 and min(k, s) where s is size of the stack at the time the MULITPOP operation is called. We need to show that a sequence of n such operations takes O(n) time i.e. amortized cost of a single such operation is O(1) Define the potential function o as the number of elements in the stack and show that the amortized cost of i-th operation e;