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)

fun main(args: Array<String>) {
  val N = readInt()
  val S = readString()

  val memoL = Array(N) { Array(3) { 0 } }
  val memoR = Array(N) { Array(3) { 0 } }

  var cntR = 0
  var cntG = 0
  var cntB = 0
  for (i in 0 until N) {
    val c = S[i]
    if (c == 'R') cntR++
    if (c == 'G') cntG++
    if (c == 'B') cntB++
    memoL[i][0] = cntR
    memoL[i][1] = cntG
    memoL[i][2] = cntB
  }
  cntR = 0
  cntG = 0
  cntB = 0
  for (i in N - 1 downTo 0) {
    val c = S[i]
    if (c == 'R') cntR++
    if (c == 'G') cntG++
    if (c == 'B') cntB++
    memoR[i][0] = cntR
    memoR[i][1] = cntG
    memoR[i][2] = cntB
  }
//  println(memoL.joinToString { it.joinToString(":") })
//  println(memoR.joinToString { it.joinToString(":") })

  var cnt = 0L
  for (i in 0 until N) {
    val c = S[i]
    if (c == 'R') cnt += memoL[i][1] * memoR[i][2] + memoL[i][2] * memoR[i][1]
    if (c == 'G') cnt += memoL[i][0] * memoR[i][2] + memoL[i][2] * memoR[i][0]
    if (c == 'B') cnt += memoL[i][0] * memoR[i][1] + memoL[i][1] * memoR[i][0]
    for (j in 1..N) {
      val l = S.getOrNull(i - j) ?: break
      val r = S.getOrNull(i + j) ?: break
      if (l != c && c != r && l != r) cnt--
    }
  }
  println(cnt)
}

fun readString() = readLine()!!
fun readStrings() = readString().split(" ")
fun readInt() = readString().toInt()
fun readInts() = readStrings().map { it.toInt() }
fun readLong() = readString().toLong()
fun readLongs() = readStrings().map { it.toLong() }