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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func out(x ...interface{}) {
	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

// min, max, asub, absなど基本関数
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func asub(a, b int) int {
	if a > b {
		return a - b
	}
	return b - a
}

func abs(a int) int {
	if a >= 0 {
		return a
	}
	return -a
}

func solve(N int, s []byte) {
	ans := 0
	for i := N - 1; i >= 0; i-- {
		for j := N - 1; j > i; j-- {
			if s[i] == s[j] {
				continue
			}
			for k := N - 1; k > j; k-- {
				if s[i] == s[k] || s[j] == s[k] {
					continue
				}
				if j-i != k-j {
					ans++
				}
			}
		}
	}
	out(ans)
}

func solve2(N int, s []byte) {
	ans := 0
	for i := 0; i < N; i++ {
		for j := i + 1; j < N; j++ {
			if s[i] == s[j] {
				continue
			}
			for k := j + 1; k < N; k++ {
				if s[i] == s[k] || s[j] == s[k] {
					continue
				}
				if j-i != k-j {
					ans++
				}
			}
		}
	}
	out(ans)
}

func main() {
	sc.Split(bufio.ScanWords)
	sc.Buffer([]byte{}, 1000000)

	N := getInt()
	s := getString()

	// N := 4000
	// s := make([]byte, N)
	// for i := 0; i < N; i++ {
	// 	switch i % 3 {
	// 	case 0:
	// 		s[i] = 'R'
	// 	case 1:
	// 		s[i] = 'G'
	// 	case 2:
	// 		s[i] = 'B'
	// 	}
	// }

	solve(N, []byte(s))

}