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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

	public class Main {

		public static void main(String[] args) {
			// AISing_C
			Scanner sc = new Scanner(System.in);

			int N = sc.nextInt();
			int x=0, y=0, z=0;
			int kai = 0;
			int cnt = 0;

			double maxVal = Math.sqrt(N);

			for(int k=1; k <= N; k++) {
				cnt = 0;
				for(x=1; x < maxVal; x++) {
					for(y=1; y <= x; y++) {
						for(z=1; z <= y; z++) {
							kai = x*x + y*y + z*z + x*y + y*z + z*x;
							if(kai == k) {
								if(x==y && y==z) {
									cnt++;
								} else {
									cnt += 3;
								}
							}
						}
					}
				}
				System.out.println(cnt);
			}

    	    // Scannerクラスのインスタンスをクローズ
    		sc.close();
    	}

    }