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: Accepted)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
)

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func newReadString(ior io.Reader, sf bufio.SplitFunc) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+9)) // for Codeforces
	r.Split(sf)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}
func ReadInt2() (int, int) {
	return int(readInt64()), int(readInt64())
}
func ReadInt3() (int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64())
}
func ReadInt4() (int, int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64()), int(readInt64())
}

// ReadInt64 returns as integer as int64.
func ReadInt64() int64 {
	return readInt64()
}
func ReadInt64_2() (int64, int64) {
	return readInt64(), readInt64()
}
func ReadInt64_3() (int64, int64, int64) {
	return readInt64(), readInt64(), readInt64()
}
func ReadInt64_4() (int64, int64, int64, int64) {
	return readInt64(), readInt64(), readInt64(), readInt64()
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func ReadInt64Slice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt64()
	}
	return b
}

// ReadFloat64 returns an float64.
func ReadFloat64() float64 {
	return float64(readFloat64())
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(ReadString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadFloatSlice returns an float64 slice that has n float64.
func ReadFloat64Slice(n int) []float64 {
	b := make([]float64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadFloat64()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

// Strtoi is a wrapper of strconv.Atoi().
// If strconv.Atoi() returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// PrintIntsLine returns integers string delimited by a space.
func PrintIntsLine(A ...int) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.Itoa(A[i])
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintIntsLine returns integers string delimited by a space.
func PrintInts64Line(A ...int64) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.FormatInt(A[i], 10) // 64bit int version
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintfDebug is wrapper of fmt.Fprintf(os.Stderr, format, a...)
func PrintfDebug(format string, a ...interface{}) {
	fmt.Fprintf(os.Stderr, format, a...)
}

// PrintfBufStdout is function for output strings to buffered os.Stdout.
// You may have to call stdout.Flush() finally.
func PrintfBufStdout(format string, a ...interface{}) {
	fmt.Fprintf(stdout, format, a...)
}

/********** FAU standard libraries **********/

//fmt.Sprintf("%b\n", 255) 	// binary expression

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()
//a := ReadFloat64()
//A := ReadFloat64Slice(n)

//str := ZeroPaddingRuneSlice(num, 32)
//str := PrintIntsLine(X...)

/*
ASCII code

ASCII   10進数  ASCII   10進数  ASCII   10進数
!       33      "       34      #       35
$       36      %       37      &       38
'       39      (       40      )       41
*       42      +       43      ,       44
-       45      .       46      /       47
0       48      1       49      2       50
3       51      4       52      5       53
6       54      7       55      8       56
9       57      :       58      ;       59
<       60      =       61      >       62
?       63      @       64      A       65
B       66      C       67      D       68
E       69      F       70      G       71
H       72      I       73      J       74
K       75      L       76      M       77
N       78      O       79      P       80
Q       81      R       82      S       83
T       84      U       85      V       86
W       87      X       88      Y       89
Z       90      [       91      \       92
]       93      ^       94      _       95
`       96      a       97      b       98
c       99      d       100     e       101
f       102     g       103     h       104
i       105     j       106     k       107
l       108     m       109     n       110
o       111     p       112     q       113
r       114     s       115     t       116
u       117     v       118     w       119
x       120     y       121     z       122
{       123     |       124     }       125
~       126             127
*/

/*******************************************************************/

const (
	// General purpose
	MOD          = 1000000000 + 7
	ALPHABET_NUM = 26
	INF_INT64    = math.MaxInt64
	INF_BIT60    = 1 << 60
	INF_INT32    = math.MaxInt32
	INF_BIT30    = 1 << 30
	NIL          = -1

	// for dijkstra, prim, and so on
	WHITE = 0
	GRAY  = 1
	BLACK = 2
)

func init() {
	ReadString = newReadString(os.Stdin, bufio.ScanWords)
	stdout = bufio.NewWriter(os.Stdout)
}

var (
	n int
	S []rune

	R, G, B    []int
	RS, GS, BS []int
)

func main() {
	n = ReadInt()
	S = ReadRuneSlice()
	R, G, B = make([]int, n+1), make([]int, n+1), make([]int, n+1)
	RS, GS, BS = make([]int, n+1), make([]int, n+1), make([]int, n+1)

	if n <= 3 {
		fmt.Println(0)
		return
	}

	for i := 0; i < n; i++ {
		if S[i] == 'R' {
			R[i]++
		} else if S[i] == 'G' {
			G[i]++
		} else {
			B[i]++
		}
	}

	for i := 0; i < n; i++ {
		RS[i+1] = RS[i] + R[i]
		GS[i+1] = GS[i] + G[i]
		BS[i+1] = BS[i] + B[i]
	}

	ans := 0
	for i := 0; i < n; i++ {
		if S[i] == 'R' {
			befG, aftB := GS[i], BS[n]-BS[i+1]
			befB, aftG := BS[i], GS[n]-GS[i+1]
			sum := befG*aftB + befB*aftG

			for j := 1; ; j++ {
				if i-j < 0 || i+j >= n {
					break
				}

				before, after := S[i-j], S[i+j]
				if (before == 'G' && after == 'B') || (before == 'B' && after == 'G') {
					sum--
				}
			}

			ans += sum
		} else if S[i] == 'G' {
			befR, aftB := RS[i], BS[n]-BS[i+1]
			befB, aftR := BS[i], RS[n]-RS[i+1]
			sum := befR*aftB + befB*aftR

			for j := 1; ; j++ {
				if i-j < 0 || i+j >= n {
					break
				}

				before, after := S[i-j], S[i+j]
				if (before == 'R' && after == 'B') || (before == 'B' && after == 'R') {
					sum--
				}
			}

			ans += sum
		} else {
			// 'B'
			befR, aftG := RS[i], GS[n]-GS[i+1]
			befG, aftR := GS[i], RS[n]-RS[i+1]
			sum := befR*aftG + befG*aftR

			for j := 1; ; j++ {
				if i-j < 0 || i+j >= n {
					break
				}

				before, after := S[i-j], S[i+j]
				if (before == 'R' && after == 'G') || (before == 'G' && after == 'R') {
					sum--
				}
			}

			ans += sum
		}
	}

	fmt.Println(ans)
}

/*
- まずは全探索を検討しましょう
- MODは最後にとりましたか？
- 負のMODはちゃんと関数を使って処理していますか？
- ループを抜けた後も処理が必要じゃありませんか？
- 和・積・あまりを求められたらint64が必要ではありませんか？
- いきなりオーバーフローはしていませんか？
- MOD取る系はint64必須ですよ？
- 後ろ・逆・ゴールから考えましたか？
- 3者のうち真ん中に着目しましたか？
*/

/*******************************************************************/