Joseph recently received some strings as his birthday gift from Chris. He is interested in the similarity between those strings. He thinks that two strings a and b are considered J-similar to each other in one of these two cases: 1. a is equal to b. 2. he can cut a into two substrings a1; a2 of the same length, and cut b in the same way, then one of following is correct: (a) a1 is J-similar to b1, and a2 is J-similar to b2. (b) a2 is J-similar to b1, and a1 is J-similar to b2. Caution: the second case is not applied to strings of odd length. He ask you to help him sort this out. Please prove that only strings having the same length can be J-similar to each other, then design an algorithm to determine if two strings are J-similar within O(nlogn) time (where n is the length of strings).