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)

from sys import stdin
import sys

# A, B, C = [int(x) for x in stdin.readline().rstrip().split()]
# A,B = [int(x) for x in stdin.readline().rstrip().split()]
# U = input().split()
# A, B = [str(x) for x in stdin.readline().rstrip().split()]
N = int(input())
S = list(input())
r = []
g = []
b = []
for i in range(N):
    if S[i] == 'R':
        r.append(i+1)
    elif S[i] == 'G':
        g.append(i+1)
    else:
        b.append(i+1)
# print(r)
# print(g)
# print(b)
cnt = 0
for i in range(len(r)):
    for j in range(len(g)):
        for k in range(len(b)):
            x=min(r[i], g[j], b[k])
            y=max(r[i], g[j], b[k])
            if r[i] != x and r[i] != y:
                if r[i]-x != y-r[i]:
                    cnt += 1
            elif g[j] != x and g[j] != y:
                if g[j]-x != y-g[j]:
                    cnt += 1
            else:
                if b[k]-x != y-b[k]:
                    cnt += 1
print(cnt)