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)

// XYZ Triplets
function Main(input) {
	try {
		input = input.split("\n");
		const n = input[0]


		const L = 105

		const set = {}
		let k;
		for (let x = 1; x < L; x++) {
			for (let y = 1; y < L; y++) {
				for (let z = 1; z < L; z++) {
					k = x * x + y * y + z * z + x * y + y * z + z * x
					set[k] = set[k] ? set[k] + 1 : 1
				}
			}
		}


		for (let i = 1; i < n; i++) {
			console.log(set[i] || 0)

		}
	} catch (error) {
		console.error(error)
	}

}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));