(3) Consider a stack that is backed up regularly. We keep a count of the number of stack operations (limited to push and pop); every 100 such stack operations, we copy the stack into backup storage. (Copying a stack containing m elements takes (m) time.) You are given that the application is such that the stack size never exceeds 100. Assign amortized costs to each operation and show thereby that the cost of any sequence of n operations is O(n). (3) Consider a stack that is backed up regularly. We keep a count of the number of stack operations (limited to push and pop); every 100 such stack operations, we copy the stack into backup storage. (Copying a stack containing m elements takes (m) time.) You are given that the application is such that the stack size never exceeds 100. Assign amortized costs to each operation and show thereby that the cost of any sequence of n operations is O(n)