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: Wrong Answer)

function Main(input){
    const N = Number(input);
    let fn = new Array(N).fill(0);
    console.log(fn)
    for(let x=1; x**2<=N; x++){
        for(let y=1; y**2<=N; y++){
            if(x+y > N) break;
            for(let z=1; z**2<=N; z++){
                const i = x**2 + y**2 + z**2 + x*y + y*z + z*x;
                if(i >N) break;
                fn[i-1]++
            }
        }
    }
    return fn.join('\n');
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));