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: Accepted)

#include<bits/stdc++.h>
typedef long long int ll;
using namespace std;
#define fastio ios_base::sync_with_stdio(false);cout.tie(0);cin.tie(0);

const ll mod=998244353 ;
const ll MAXN=1e6+5;
const ll inf=1e17;

int main()
{
    fastio;
    ll n;
    cin >> n;
    string s;
    cin >> s;
    set < ll > r, g, b;
    for(int i = 0; i < n; i++){
        if(s[i] == 'R') r.insert(i);
        else if(s[i] == 'G') g.insert(i);
        else if(s[i] == 'B') b.insert(i);
    }
    ll ans = 0;
    for(auto i : r){
        for(auto j : g){
            ll e = i, f = j;
            if(e > f) swap(e, f);
            ans += b.size();
            if(b.count(f + f - e)) ans--;
            if((e + f) % 2 == 0 && b.count((e + f) / 2)) ans--;
            if(b.count(e + e - f)) ans--;
        }
    }
    cout << ans << endl;
}