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: Accepted)

# import numpy as np
# import math
# import copy
# from collections import deque
import sys
input = sys.stdin.readline
# sys.setrecursionlimit(10000)


def main():
    N = int(input())
    S = input().rstrip()

    R = set([])
    G = set([])
    B = set([])

    for i in range(N):
        temp = S[i]
        if temp == 'R':
            R.add(i)
        elif temp == 'G':
            G.add(i)
        else:
            B.add(i)

    all = [R,G,B]

    M = [len(R),len(G),len(B)]
    res = M[0] * M[1] * M[2]
    index = M.index(max(M))

    most = all.pop(index)
    first = all[0]
    second = all[1]

    count = 0

    for f in first:
        for s in second:
            temp1 = s * 2 - f
            temp2 = f * 2 - s
            temp3 = (f + s) // 2
            if (True) & (temp1 in most):
                count += 1
            if (True) & (temp2 in most):
                count += 1
            if (s + f) % 2 == 0:
                if temp3 in most:
                    count += 1

    res -= count
    print(res)




main()