alphabrackets

Problem Description

An valid alphabracket string consists of a series of upper and lowercase letters, and must be in the form of:

• an empty string,
• A#a where A represents an uppercase letter, a represents a lowercase version of the same letter, and # represents a valid alphabracket string, or
• #@, where # and @ are two valid alphabracket strings.

For example, BAaCcb is a valid alphabracket string while ABab is not.

Given a string S consisting of only uppercase and lowercase letters, determine how many non-empty substrings of S are valid alphabracket strings.

Input

The first and only line of input will contain one string, S.

Output

The output should contain one integer, the number of non-empty substrings of S which are valid alphabracket strings.

Limits

Subtask 1 (16%): 1 ≤ length of string ≤ 300.

Subtask 2 (18%): 1 ≤ length of string ≤ 2000.

Subtask 3 (14%): 1 ≤ length of string ≤ 100000, the string will only consist of 'A' and 'a', and all 'A's will come before any 'a'.

Subtask 4 (23%): 1 ≤ length of string ≤ 100000, the string will only consist of 'A' and 'a'.

Subtask 5 (13%): 1 ≤ length of string ≤ 100000.

Subtask 6 (16%): 1 ≤ length of string ≤ 2000000.

Subtask 7 (0%): Sample Testcases.

Sample Input 1

BAaCcb

Sample Output 1

4

Sample Input 2

ABab

Sample Output 2

0

Sample Input 3

aAaAa

Sample Output 3

3