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 s_is_i + 1... s_j.

String s is a Gray string, if it meets the conditions:

the length of string |s| is odd;
character $\text{[math]}$ occurs exactly once in the string;
either |s| = 1, or substrings $\text{[math]}$ and $\text{[math]}$ 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.

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.

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.

Xenia and String Problem

Examples