Anagrammatic Periodic Partition

A string S is 'Anagram-Periodic' with period L if S can be divided into segments of exactly length L such that every segment is an anagram of every other segment. Given a string S, find the smallest length L such that L divides the total length of S and S is Anagram-Periodic with period L. Input Format: A single string S. Output Format: An integer representing the smallest L. Example: Input: abccbaacb Output: 3 Explanation: Length 9. Possible L: 1, 3, 9. L=1 (a,b,c... no), L=3 (abc, cba, acb... yes, all are anagrams). L=3 is smallest.