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++ (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <string>
#include <vector>
#include <limits>
#include <algorithm>
#include <functional>
#include <utility>
#include <sstream>
#include <numeric>
#include <deque>
#include <iterator>

using namespace std;

#define repd(i,a,b) for (int i=(a);i<(b);++i)
#define rep(i,n) repd(i,0,n)
typedef long long ll;
typedef pair<int, int> P;

int n;
string s;
ll ans = 0;

void recursive_comb(int *indexes, int s, int rest, std::function<void(int *)> f) {
  if (rest == 0) {
    f(indexes);
  } else {
    if (s < 0) return;
    recursive_comb(indexes, s - 1, rest, f);
    indexes[rest - 1] = s;
    recursive_comb(indexes, s - 1, rest - 1, f);
  }
}

// nCkの組み合わせに対して処理を実行する
void foreach_comb(int n, int k, std::function<void(int *)> f) {
  int indexes[k];
  recursive_comb(indexes, n - 1, k, f);
}

int main(int argc, const char * argv[]) {
  cin >> n;
  cin >> s;

  foreach_comb(n, 3, [](int *indexes) {
    if(indexes[1]- indexes[0] != indexes[2] - indexes[1]){
      if(s[indexes[0]] != s[indexes[1]] && s[indexes[1]] != s[indexes[2]] && s[indexes[0]] != s[indexes[2]]) ans++;
    }
  });

  cout << ans << endl;
  return 0;
}