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.

The first line of the input data contains a non-empty string, consisting of Latin letters and digits. The length of the string does not exceed 5 \cdot 106. The string is case-sensitive.

Output the only number - the sum of the polindrome degrees of all the string's prefixes.