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: Time Limit Exceeded)

import kotlin.math.absoluteValue

fun main(args: Array<String>) {
    val line = readLine()!!.trim()
    val n = line.toInt()
    val line2 = readLine()!!.trim()
    val s: String = line2
    val rs: MutableList<Int> = mutableListOf()
    val gs: MutableList<Int> = mutableListOf()
    val bs: MutableList<Int> = mutableListOf()

    s.take(n).mapIndexed {i, c ->
        if (c == 'R') {
            rs.add(i)
        }

        if (c == 'G') {
            gs.add(i)
        }

        if (c == 'B') {
            bs.add(i)
        }
    }


    var result: Long = 0L

    for (ri in rs) {
        for (gi in gs) {
            for (bi in bs) {
                if (diffDist(ri, gi, bi)) {
                    result += 1
                }
            }
        }
    }

    println("${result}")
}

fun diffDist(a: Int, b: Int, c: Int): Boolean {
    val d = (b - a).absoluteValue
    val e = (c - b).absoluteValue
    val f = (c - a).absoluteValue

    return d != e && e != f && d != f
}