Maximum Hamming Distances

Given an array, find the maximum Hamming distance between the array and any of its cyclic rotations — i.e., the largest number of indices i where A[i] != A[(i+shift) mod n] over all nonzero shifts. The challenge is to compute this efficiently for large n (avoid O(n^2) rotation comparisons) using string/array-matching techniques (concatenation + KMP/Z/rolling-hash) and careful handling of duplicates.