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 Lua (LuaJIT 2.1.0) (judge verdict: Accepted)

N=io.read"*n"
io.read()
S=io.read()
local function count_char(s,c)
	local ret=0
	for _ in s:gmatch(c)do ret=ret+1 end
	return ret
end
c=count_char(S,"R")*count_char(S,"G")*count_char(S,"B")
for i=1,N do
	local I=S:sub(i,i)
	for d=1,(N-i)/2 do
		local J=S:sub(i+d,i+d)
		local K=S:sub(i+d+d,i+d+d)
		if(I~=J and J~=K and K~=I)then c=c-1 end
	end
end
print(c)