A riddle for you lot

F(string s, string b) returns the number of appearances of b as a substring of s times len(b).

Given an arbitrary string s, find a palindrome b for which F(s, b) is maximal in time O(n log n) where n = len(s)


Example: For the string "aaa"
F("aaa", "a") = 3*1 = 3
F("aaa", "aa") = 2*2 = 4
F("aaa", "aaa") = 1*3 = 3

Hence the solution is "aa"