Implement rotated array binary search with duplicates

Given an integer array nums that is a non-decreasing array rotated an unknown number of times. Duplicates may exist. Implement a function that returns a pair: (rotation_count, leftmost_index_of_target) where rotation_count is the index of the rotation point and leftmost_index_of_target is the smallest index i such that nums[i] == target or -1 if absent. Definitions and constraints: - Rotation point is the smallest index r such that nums[r] < nums[(r-1+n)%n]. If no such r exists (array already sorted or all equal), rotation_count = 0. - Time: O(log n) expected; discuss and handle worst-case O(n) when duplicates make direction ambiguous. - Space: O(1). - Edge cases: all elements equal; target duplicated across the rotation boundary; n=1; empty array. - Example: nums = [4,5,5,6,6,1,2,3,3], target=3 → rotation_count=5, leftmost_index_of_target=7. - Provide: (a) algorithm idea; (b) correctness argument; (c) complexity; (d) thorough unit tests covering edge cases.