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D - RGB Triplets

Score : $400$ points

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.

4
RRGB

1

Only the triplet $(1,~3,~4)$ satisfies both conditions. The triplet $(2,~3,~4)$ satisfies the first condition but not the second, so it does not count.

39
RBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB

1800