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 "fmt"

func main() {
	var N int
	var S string

	fmt.Scan(&N, &S)
	R := make(map[int]struct{})
	G := make(map[int]struct{})
	B := make(map[int]struct{})

	for idx, c := range S {
		if c == 'R' {
			R[idx] = struct{}{}
		} else if c == 'G' {
			G[idx] = struct{}{}
		} else {
			B[idx] = struct{}{}
		}
	}

	ans := 0
	for r, _ := range R {
		for g, _ := range G {
			for b, _ := range B {
				i, j, k := po(r, g, b)
				if j-i != k-j {
					ans++
				}
			}
		}
	}
	fmt.Println(ans)
}

func po(a, b, c int) (i, j, k int) {
	if a < b && a < c {
		i = a
		if b < c {
			j = b
			k = c
		} else {
			j = c
			k = b
		}
	} else if b < a && b < c {
		i = b
		if a < c {
			j = a
			k = c
		} else {
			j = c
			k = a
		}
	} else {
		i = c
		if a < b {
			j = a
			k = b
		} else {
			j = b
			k = a
		}
	}
	return
}