Given an array of non-negative integers, find the largest value that XOR-ing any two of them together can produce. Checking every pair directly works, but there's a faster path: build the answer one bit at a time, starting from the most significant bit. At each step, tentatively assume that bit can be set, then check whether any two values in the array — reduced to just the bits decided so far — actually XOR together to hit that target. Lock the bit in only when a real pair backs it up.