Maintains a data structure that supports the following operations:

• inserts an element $$$x$$$ into the set $$$S$$$
• deletes an element $$$x$$$ from the set $$$S$$$
• queries the maximum value of xor for each pair of elements in the set ( $$$\max\limits_{i,j\in S}i\oplus j$$$ )

Can this problem be solved within $$$O(n^2)$$$ better time complexity?