Circular ID Registry

In a secure facility, rotating security IDs are used. Two ID strings are considered 'equivalent' if one can be obtained by cyclically shifting the other (e.g., 'abc', 'bca', and 'cab' are equivalent). Given a list of observed IDs, count how many unique security entities are represented. Input Format: - Line 1: An integer N, the number of IDs. - Next N lines: Each line contains a string ID. Output Format: - A single integer representing the number of unique entities. Example: Input: 3 abc bca xyz Output: 2