Maximum XOR (Hard)

Vasylko has $N$ non-negative integers: a_1, a_2, \ldots, a_N. He and his friend Vitaliy, tired of the usual bitwise operations $AND$ and $OR$, decided to explore something new. Vasylko asked Vitaliy, the programmer, to compute the $XOR$ sum for every possible non-empty subsequence of these $N$ numbers. From the resulting 2^N-1 numbers, they want to find the maximum value.

Given the large number of integers Vasylko is dealing with this time, Vitaliy cannot solve the problem by brute force. Your task is to assist him, ensuring that Vasylko remains confident in the abilities of programmers.