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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.lang.StringBuilder
import java.util.*

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val s = sc.nextLine()
    val countR = Array(n + 1) { 0 }
    val countG = Array(n + 1) { 0 }
    val countB = Array(n + 1) { 0 }
    for (i in n - 1 downTo 0) {
        countR[i] = countR[i + 1]
        countG[i] = countG[i + 1]
        countB[i] = countB[i + 1]
        if (s[i] == 'R') {
            countR[i]++
        } else if (s[i] == 'G') {
            countG[i]++
        } else {
            countB[i]++
        }
    }
    var sum = 0L
    for (i in 0 until n) {
        for (j in i + 1 until n) {
            val k = j + 1
            val ng = 2 * j - i
            if (k >= n) break
            if (s[i] == s[j]) continue

            if (s[i] != 'R' && s[j] != 'R') {
                sum += countR[k]
                if (ng < n && s[ng] == 'R') sum--
            } else if (s[i] != 'G' && s[j] != 'G') {
                sum += countG[k]
                if (ng < n && s[ng] == 'G') sum--
            } else {
                sum += countB[k]
                if (ng < n && s[ng] == 'B') sum--
            }
        }
    }
    println(sum)
}

fun main(args: Array<String>) {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}