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)

def calc(N, S):
    id = {'R': 0, 'G': 1, 'B': 2}
    rgb = [[0, 0, 0] for _ in range(N)]
    rgb[0][id[S[0]]] = 1
    for i in range(1, N):
        for j in [0, 1, 2]:
            rgb[i][j] = rgb[i - 1][j]
            if j == id[S[i]]:
                rgb[i][j] += 1
    result = 0
    for i in range(N - 1, -1, -1):
        X = S[i]
        YZ = (['G', 'B'] if X == 'R' else ['R', 'B'] if X == 'G' else ['R', 'G'])
        j = i - 1
        while j > -1:
            if S[j] in YZ:
                result += rgb[j][3 - id[X] - id[S[j]]]
                if 2 * j - i > -1 and not S[2 * j - i] in [X, S[j]]:
                    result -=1
            j -= 1
    return result


N = int(input())
S = input()
print(calc(N, S))