Problem:
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.

Sample Input 1

4
RRGB

Sample Output 1

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.

Sample Input 2

39
RBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB

Sample Output 2

1800

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

N = int(input())
S = input()
count = 0
for i, s_i in enumerate(S[:-2]):
    for j, s_j in enumerate(S[i + 1: -1]):
        if s_i == s_j:
            continue
        j += i + 1
        for k, s_k in enumerate(S[j + 1:]):
            k += j + 1
            if j - i != k - j:
                if s_i != s_k and s_j != s_k:
                    count += 1
print(count)