Start by understanding the concept of **borders** in string matching (a border is a proper prefix that is also a suffix). How can borders help in analyzing repetition factors in strings?

Explore the **Knuth-Morris-Pratt (KMP) algorithm's failure function** (or LPS array) to identify borders efficiently. How can this be adapted to analyze repetition factors in O(n) time?

Consider **generalizing the border analysis** to handle multiple repetition factors. How can you modify the failure function to account for nested or overlapping repetitions while maintaining linear time complexity?