3. (10 pts) Suppose we perform a sequence of stack operations (specifi- cally, PUSH, POP, and a new operation COPY) on a stack whose size never exceeds k. After every k operations, we make a copy of the entire stack for backup purposes. Show that the cost of n stack op- erations, including copying the stack, is O(n) by assigning suitable amortized costs to the three stack operations. Hint: Use the accounting method and assume that CoPY is called u tomatically every k operations; t cannot be called at any other time