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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define REP(i,s,n) for(int i=s; i<(n); ++i)
#define ALL(n) begin(n),end(n)
using ll = long long;
const ll INF = numeric_limits<long long>::max();


int main(){
    int N;
    string S;
    cin >> N >> S;

    int R_cnt = 0, G_cnt = 0, B_cnt = 0;
    REP(i, 0, N){
        if (S[i] == 'R')
            ++R_cnt;
        else if (S[i] == 'G')
            ++G_cnt;
        else 
            ++B_cnt;
    }

    ll sum = R_cnt * G_cnt * B_cnt;

    char i_str, j_str, k_str;
    REP(i, 0, N){
        i_str = S[i];
        for (int width = 1; i + width + width < N; ++width){
            j_str = S[i + width];
            k_str = S[i + width + width];
            if (i_str != j_str && i_str != k_str && j_str != k_str)
                --sum;
        }
    }
    cout << sum << endl;

    return 0;
}