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)

import Base.parse
import Base.StringVector

parse(::Type{String},  str::AbstractString) = str

isdelim(x::UInt8, xs::Set{UInt8}) = x in xs

function myreaduntil(s::IO, delims::Set{UInt8})::Vector{UInt8}
    out = StringVector(0)
    c::UInt8 = 0x00
    while !eof(s)
        c = read(s, UInt8)
        if !isdelim(c, delims)
            break
        end
    end
    push!(out, c)
    if eof(s)
        return out
    end
    while !eof(s)
        c = read(s, UInt8)
        if isdelim(c, delims)
            break
        end
        push!(out, c)
    end
    return out
end

delimset = Set([0x0a, 0x20])

function readword(io::IO = stdin, delims = delimset)::String
    word = myreaduntil(io, delims)
    i = length(word)
    if i == 0 || word[i] != 0x0a
        return String(word)
    elseif i < 2 || word[i-1] != 0x0d
        return String(resize!(word,i-1))
    else
        return String(resize!(word,i-2))
    end
end

pread(ty) = parse(ty, readword())

reads(tys...)::Tuple{tys...} = Tuple{tys...}(pread(ty) for ty in tys)

readvec(tys::Tuple , len::Signed)::Vector{Tuple{tys...}} = @inbounds Tuple{tys...}[reads(tys...) for i in 1:len]

readvec(ty::Type, len::Signed)::Vector{ty} = @inbounds ty[pread(ty) for i in 1:len]

function readmat(ty::Type, s...)::Matrix{ty}
    v = Matrix{ty}(undef, s...)
    @inbounds for i = 1:s[1]
        v[i,:] = readvec(ty, s[2])
    end
    v
end

function othernum(i,j)
    ij = i+j
    3 - ij%3
end

function main()
    N, S = reads(Int, String)
    SI = map(x -> begin x == 'R' && return 1; x == 'G' && return 2; x == 'B' && return 3 end, collect(S))
    d = zeros(Int, 3, N)

    for j in 1:3
        d[j,1] = 0
    end
    d[SI[begin],1] = 1

    for i in 2:length(SI)
        for j in 1:3
            d[j,i] = d[j,i-1]
        end
        d[SI[i],i] += 1
    end

    if N <= 3
        println(0)
        return
    end

    c = 0
    for i in 1:length(SI)-2, j in i+1:length(SI)-1
        if SI[i] != SI[j]
            k = othernum(SI[i],SI[j])
            c += d[k,N] - d[k,j]
            c -= (2j-i<=N && SI[2j-i]==k) ? 1 : 0
        end
    end
    println(c)
end

main()