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 sys
def p(*_a):
  _s=" ".join(map(str,_a))
  #print(_s)
  sys.stderr.write(_s+"\n")
#-------------------------------------------------------------------
N = int(input())
S = input()

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

from collections import defaultdict
Bd = defaultdict(lambda: -1)


for i in range(N):
	c = S[i]
	if c=='R': R.append(i)
	if c=='G': G.add(i)
	if c=='B': B.add(i)


p(R)
p(G)
p(B)

lenB = len(B)

ans=0
for i in R:
	for j in G:
		a = (i+j)/2
		b = (i*2-j)
		c = (j*2-i)
		
		x = lenB
		if (a in B): x -= 1
		if (b in B): x -= 1
		if (c in B): x -= 1
		
		ans += x

print(ans)