Circular Signal Reconciliation

A series of deep-space satellites emit periodic signal patterns. Due to orbital timing, two satellites might be emitting the exact same periodic sequence, but starting at different points in the cycle. Given N signal strings, each representing one full cycle, determine how many unique signal patterns exist. Two signals are identical if one can be cyclically shifted to match the other. Input Format: - Line 1: An integer N, the number of signals. - Next N lines: Each line contains a string S representing a signal's cycle. Output Format: - A single integer representing the number of unique signal patterns. Example: Input: 3 ABCDE CDEAB VWXYZ Output: 2