Explain how to implement two stacks in one array $A[1..n]$ in such a way that neither stack overflows unless the total number of elements in both stacks together is $n$. The

`PUSH`

and`POP`

operations should run in $\O(1)$ time.

The first stack starts at $1$ and grows up towards $n$, while the second starts form $n$ and grows down towards $1$. Stack overflow happens when an element is pushed when the two stack pointers are adjacent.