Suppose that we have a stack whose size is not allowed to exceed K (for instance, if K 10, then we are not allowed to have more than 10 elements on the stack at any time).

If you try to Push an element onto a stack that is already full, then nothing happens.

Suppose that after every K operations, we automatically make a copy of the stack for back-up purposes. (Note the stack may or may not be full at this point.)

Suppose that Push and Pop each cost $1 (including if you try to Push an element onto an already-full stack).

Suppose that copying the stack costs SC, where C is the number of elements currently on the stack. Perform an amortized analysis of the running time of n operations.

State your answer in terms of the average cost per operation, in dollars (that is, do not use big-O notation).