Xenia and String Problem
Description
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 s1s2... s|s|, where record |s| shows the length of the string.
Substring s[i... j] of string s is string sisi + 1... sj.
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.
Input
The first line contains a non-empty string t (1 ≤ |t| ≤ 105). String t only consists of lowercase English letters.
Output
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.
Samples
zzz
12
aba
12
abacaba
83
aaaaaa
15
Note
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 12 + 12 + 12 + 32 = 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.