Triples with Bitwise AND Equal To Zero

Count the number of ordered triples (i, j, k) such that nums[i] & nums[j] & nums[k] == 0. With nums.length up to 1000 and values < 2^16, the challenge is to avoid O(n^3) brute force by using bitmask frequency precomputation (e.g., pairwise AND counts or SOS convolution over 2^16 masks) to aggregate valid triples efficiently.