Largest Repeated Substring Length

Given a non-empty string s, determine the length of the smallest substring t that, when repeated consecutively, forms s. Formally, find the smallest positive integer l such that s = t^(n/l), where n is the length of s and t is the prefix of s with length l. If no such t exists with l < n, then the answer is n. For example:

• If s = "abab", then t = "ab" and the answer is 2.
• If s = "aaaa", then t = "a" and the answer is 1.
• If s = "abcdef", no proper substring can be repeated to form s, so the answer is 6.

This problem can be mathematically represented as finding the smallest integer \(l\) (where \(1 \leq l \leq n\)) satisfying \(n \bmod l = 0\) and \(s = t^{(n/l)}\), with t being s's prefix of length \(l\). If there is no such \(l\) with \(l < n\), then output \(n\).

inputFormat

The input consists of a single line containing a non-empty string s (with \(1 \leq |s| \leq 10^5\)).

outputFormat

Output a single integer denoting the length of the smallest substring that can be repeated to form the string s.

abab

2