Xenia and String Problem
Xenia the coder went to The Olympiad of Informatics and got a string problem. Unfortunately, Xenia isn't fabulous in string algorithms. Help her solve the problem.

String *s* is a sequence of characters *s*1*s*2... *s*|*s*|, where record |*s*| shows the length of the string. 

Substring *s*[*i*... *j*] of string *s* is string *s**i**s**i*<=+<=1... *s**j*.

String *s* is a Gray string, if it meets the conditions:
 -  the length of string |*s*| is odd; -  character  occurs exactly once in the string; -  either |*s*|<==<=1, or substrings  and  are the same and are Gray strings. 
For example, strings "abacaba", "xzx", "g" are Gray strings and strings "aaa", "xz", "abaxcbc" are not.

The beauty of string *p* is the sum of the squares of the lengths of all substrings of string *p* that are Gray strings. In other words, consider all pairs of values *i*,<=*j* (1<=≤<=*i*<=≤<=*j*<=≤<=|*p*|). If substring *p*[*i*... *j*] is a Gray string, you should add (*j*<=-<=*i*<=+<=1)2 to the beauty.

Xenia has got string *t* consisting of lowercase English letters. She is allowed to replace at most one letter of the string by any other English letter. The task is to get a string of maximum beauty.
The first line contains a non-empty string *t* (1<=≤<=|*t*|<=≤<=105). String *t* only consists of lowercase English letters.
Print the sought maximum beauty value Xenia can get.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
In the first test sample the given string can be transformed into string *p* = "zbz". Such string contains Gray strings as substrings *p*[1... 1], *p*[2... 2], *p*[3... 3] и *p*[1... 3]. In total, the beauty of string *p* gets equal to 1<sup class="upper-index">2</sup> + 1<sup class="upper-index">2</sup> + 1<sup class="upper-index">2</sup> + 3<sup class="upper-index">2</sup> = 12. You can't obtain a more beautiful string.

In the second test case it is not necessary to perform any operation. The initial string has the maximum possible beauty.