Let the following sequence of operations are performed on a stack. $[5$ Marks$]-$ PUSH $3,$ POP, PUSH $4,$ POP, PUSH $1,$ PUSH $23,$ PUSH $9,$ POP, PUSH $20,$ PUSH $50,$ POP, POP

$($i$)$ Find the minimum size of the stack that is required to perform the above operations.

$($ii$)$ What is the top element after all these operations.