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 Julia (1.4.0) (judge verdict: Accepted)

parseInt(x)=parse(Int, x)
parseMap(x::Array{SubString{String},1})=map(parseInt, x)

function main()
	n = readline() |> parseInt
	s = readline() |> chomp
	t = zeros(Int,n)
	dp = zeros(Int,n)
	r = zeros(Int,n+1)
	g = zeros(Int,n+1)
	b = zeros(Int,n+1)
	for i in 1:n
		r[i+1]=r[i]
		g[i+1]=g[i]
		b[i+1]=b[i]
		if s[i]=='R'
			r[i+1]+=1
		elseif s[i]=='G'
			g[i+1]+=1
			t[i]=1
		else
			b[i+1]+=1
			t[i]=2
		end
	end
	for i in 1:n
		if s[i]=='R'
			dp[i]=g[i]*(b[n+1]-b[i+1])+b[i]*(g[n+1]-g[i+1])
			for j in 1:min(i-1,n-i)
				if t[i-j]!=t[i+j]&&t[i-j]!=t[i]&&t[i+j]!=t[i]
					dp[i]-=1
				end
			end
		elseif s[i]=='G'
			dp[i]=r[i]*(b[n+1]-b[i+1])+b[i]*(r[n+1]-r[i+1])
			for j in 1:min(i-1,n-i)
				if t[i-j]!=t[i+j]&&t[i-j]!=t[i]&&t[i+j]!=t[i]
					dp[i]-=1
				end
			end
		else
			dp[i]=r[i]*(g[n+1]-g[i+1])+g[i]*(r[n+1]-r[i+1])
			for j in 1:min(i-1,n-i)
				if t[i-j]!=t[i+j]&&t[i-j]!=t[i]&&t[i+j]!=t[i]
					dp[i]-=1
				end
			end
		end
	end
	println(sum(dp))
end

main()