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.

输入描述:

The first line contains a non-empty string t(1 ≤ t ≤ 105). String t only consists of lowercase English letters.

输出描述:

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.

备注:

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.