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)

def solve(n, s):
    D = {"R": 0, "G": 0, "B": 0}
    for c in s:
        D[c] += 1
    ans = D["R"] * D["G"] * D["B"]
    for i in range(n):
        for j in range(i+1,(i+n+1)//2):
            k = 2*j - i
            if (s[i] != s[j]) and (s[j] != s[k]) and (s[k] != s[i]):
                ans -= 1
    return ans

n = int(input())
s = input()
print(solve(n, s))