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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

process.stdin.resume();
process.stdin.setEncoding('utf8');
// Your code here!

const gcdArr = function(arr) {
  let gcdres = gcd(arr[0], arr[1])
  for (let i=2; i<arr.length; i++) {
    gcdres = gcd(gcdres, arr[i])
  }
  return gcdres
}

function gcd_impl(n,m) {
        for( let i = 0; i < 10; ++i ) {
                let t = n - m;
                let q = m > t;
                n = q ? m : t;
                m = q ? t : m;
                if( m == 0 ) { return n; }
        }
        return gcd_impl( m, n % m );
}

function gcd( n, m ) {
        return n > m ? gcd_impl( n, m ) : gcd_impl( m, n );
}

const Main = (p)=>{
	// 1行目がinput[0], 2行目がinput[1], …に入る
	p = p.split("\n");
	let N = parseInt(p[0])//p.split(" ").map(Number);
	let S = p[1].split("").map(e=>{
	    if(e=="R")return 1;
	    if(e=="G")return 2;
	    if(e=="B")return 4;
	});
	//console.log(S);return;
	
	//文字列から10進数に変換するときはparseIntを使います
	
	let s=0;
	for(let i=1;i<=N;i++){
	    for(let j=i+1;j<=N;j++){
    	    for(let k=j+1;k<=N;k++){
    	        if(S[i-1]+S[j-1]+S[k-1]==7){
    	            if(j-i!=k-j)
    	               s++;
    	        }
    	    }   
    	}
	}
	console.log(s);
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));