Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

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

function Main(input){
    const N = Number(input);

    for(let i=1; i<=N; i++){
        let count = 0;
        for(let x=1; x<=N; x++){
            for(let y=1; y<=N; y++){
                if(x+y > N) break;
                for(let z=1; z<=N; z++){
                    if(x+y+z > N) break;
                    if(x**2 + y**2 + z**2 + x*y + y*z + z*x === i) {
                        // console.log(x,y,z)
                        count++
                    }; 
                }
            }
        }
        console.log(count);
    }
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));