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)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
    n=parseInt(readline())
    s=chomp(readline())
    cnt=[Vector{Int}() for i in 1:3]
    color=[0 for i in 1:n]
    for i in 1:n
        if s[i]=='R'
            push!(cnt[1],i)
            color[i]=1
        elseif s[i]=='G'
            push!(cnt[2],i)
            color[i]=2
        else
            push!(cnt[3],i)
            color[i]=3
        end
    end
    l=[length(cnt[i]) for i in 1:3]
    ans=0
    for i in 1:n
        for j in i+1:n
            if s[i]==s[j]
                continue
            end
            if (s[i]=='R' && s[j]=='G') || (s[j]=='R' && s[i]=='G')
                res=searchsortedfirst(cnt[3],j)
                if l[3]<res
                    continue
                end
                ans+=l[3]-res+1
                if cnt[3][res]<=j+j-i<=n &&  color[j+j-i]==3
                    ans-=1
                end
            elseif (s[i]=='R' && s[j]=='B') || (s[i]=='B' && s[j]=='R')
                res=searchsortedfirst(cnt[2],j)
                if l[2]<res
                    continue
                end
                ans+=l[2]-res+1
                if cnt[2][res]<=j+j-i<=n && color[j+j-i]==2
                    ans-=1
                end
            else
                res=searchsortedfirst(cnt[1],j)
                if l[1]<res
                    continue
                end
                ans+=l[1]-res+1
                if cnt[1][res]<=j+j-i<=n &&  color[j+j-i]==1
                    ans-=1
                end
            end
        end
    end
    println(ans)
end
main()