AT_abc455_e [ABC455E] Unbalanced ABC Substrings

You are given a string $ S $ of length $ N $ consisting of the three characters `A`, `B`, and `C`. There are $ \frac{N(N+1)}{2} $ non-empty substrings of $ S $ ; find how many of them satisfy the following condition: - The numbers of occurrences of `A`, `B`, and `C` are all distinct from each other. Count two substrings separately if they are taken from different positions in $ S $ , even if they are identical as strings. What is a substring? A **substring** of $ S $ is a string obtained by deleting zero or more characters from the beginning and zero or more characters from the end of $ S $ . For example, `AB` is a substring of `ABC`, but `AC` is not a substring of `ABC`.

The input is given from Standard Input in the following format: > $ N $ $ S $

Output the answer on a single line.

### Sample Explanation 1 Deleting $ 0 $ characters from the beginning and $ 3 $ characters from the end of $ S $ gives `AAB`, which satisfies the condition. Deleting $ 1 $ character from the beginning and $ 2 $ characters from the end of $ S $ gives `ABB`, which satisfies the condition. Deleting $ 2 $ characters from the beginning and $ 1 $ character from the end of $ S $ gives `BBC`, which satisfies the condition. Deleting $ 3 $ characters from the beginning and $ 0 $ characters from the end of $ S $ gives `BCC`, which satisfies the condition. No other substrings satisfy the condition. ### Sample Explanation 2 No substring satisfies the condition. ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ |S|=N $ - $ N $ is an integer. - $ S $ is a string consisting of the three characters `A`, `B`, and `C`.