$[10$ points$]$ Simulation problem.

$($i$)$ Simulate a stack using queue$($s$).$ That is$,$ show how to implement Push and Pop functions of stack using Enqueue and Dequeue methods of queue$($s$).$

$($ii$)$ Simulate a queue using stack$($s$).$ That is$,$ show how to implement Enqueue and Dequeue functions of queue using Push and Pop methods of stack$($s$).$