# Time:  O(n)
# Space: O(n)

class Solution(object):
    def findMaximumXOR(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        result = 0

        for i in reversed(xrange(32)):
            result <<= 1
            prefixes = set()
            for n in nums:
                prefixes.add(n >> i)
            for p in prefixes:
                if (result | 1) ^ p in prefixes:
                    result += 1
                    break

        return result