Problem Statement

We have a string $S$ of length $N$ consisting of R, G, and B.

Find the number of triples $(i,~j,~k)~(1 \leq i < j < k \leq N)$ that satisfy both of the following conditions:

• $S_i \neq S_j$, $S_i \neq S_k$, and $S_j \neq S_k$.
• $j - i \neq k - j$.

Constraints

• $1 \leq N \leq 4000$
• $S$ is a string of length $N$ consisting of R, G, and B.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of triplets in question.