Parity Again

You are given a set $S$ and $Q$ queries. Initially, $S$ is empty. In each query: - You are given a positive integer $X$. - You should insert $X$ into $S$. - For each $y \in S$ before this query such that $y \neq X$, you should also insert $y \oplus X$ into $S$ ($\oplus$ denotes the XOR operation). - Then, you should find two values $E$ and $O$: the number of elements of $S$ with an even number of