I'm trying to solve this problem 103708A - Anya's gifts, in more detail, we need to do this.

Given an array $$$A$$$ of length $$$n$$$ ($$$n \leq 10^5$$$, $$$a_i < 2^{50}$$$), divide it into two subsequences $$$X$$$ and $$$Y$$$ such that $$$(x_1 \oplus ... \oplus x_{|X|}) + (y_1 \oplus ... \oplus y_{|Y|})$$$ is maximum. Print the maximum $$$xor\text{_}sum(X) + xor\text{_}sum(Y)$$$.

It is obvious that for each $$$2^p$$$, if the ammount of elements $$$a_i$$$ such that $$$a_i \text{ and } 2^p = 2^p$$$ is odd, the answer will always have its $$$p$$$-th bit on. I don't know how to handle the case where it's even.

Any help would be appreciated. Thanks!