Split Array Into Maximum Number of Subarrays

Partition the array into contiguous subarrays so that the sum of each subarray's bitwise AND is as small as possible, and among all such optimal partitions return the maximum number of subarrays. The core challenge is to exploit that subarray ANDs can only lose bits when extended (bitwise monotonicity) to decide cut points efficiently for n up to 1e5 and values up to 1e6.