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)

@ExperimentalStdlibApi
fun main(args: Array<String>) = abc162d()

@ExperimentalStdlibApi
fun abc162d() {
    val n = readLine()!!.toInt()
    val s = readLine()!!

    val csRed = s.scan(0) { acc, c -> acc + if (c == 'R') 1 else 0 }.toIntArray()
    val csGreen = s.scan(0) { acc, c -> acc + if (c == 'G') 1 else 0 }.toIntArray()
    val csBlue = s.scan(0) { acc, c -> acc + if (c == 'B') 1 else 0 }.toIntArray()

    val list = listOf(csRed, csGreen, csBlue)

    var answer = 0L

    for (i in 0 until n) {
        val c = s[i]
        val other = when (c) {
            'R' -> list - csRed
            'G' -> list - csGreen
            else -> list - csBlue
        }
        for (j in i + 1 until n) {
            val c2 = s[j]
            if (c2 == c) continue
            val remain = when (c2) {
                'R' -> other - csRed
                'G' -> other - csGreen
                else -> other - csBlue
            }[0]

            val jump = j + (j - i) + 1

            answer += remain.last() - remain[j] -
                    if (jump in remain.indices) remain[jump] - remain[jump - 1] else 0
        }
    }

    println(answer)
}