CF7D Palindrome Degree

String $ s $ of length $ n $ is called $ k $ -palindrome, if it is a palindrome itself, and its prefix and suffix of length  are $ (k-1) $ -palindromes. By definition, any string (even empty) is 0-palindrome. Let's call the palindrome degree of string $ s $ such a maximum number $ k $ , for which $ s $ is $ k $ -palindrome. For example, "abaaba" has degree equals to $ 3 $ . You are given a string. Your task is to find the sum of the palindrome degrees of all its prefixes.

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