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: Wrong Answer)

import java.util.Scanner;
import java.util.TreeMap;


public class Main {
//	final static int MOD = 1000000007;

	public static long ans = 0;

	public static void main(String[] args) {

//		int ans = 0;
		Scanner sc = new Scanner(System.in);
		boolean f = false;

//		long a = sc.nextLong();

		int n = sc.nextInt();
		long a = 1;
		long b = 1;
		long c = 1;
		TreeMap<Long,Long> map = new TreeMap<Long, Long>();

		//-------------------------------------------------------------------------------------

		for(long i = 1; i <= n; i++) {
			map.put(i, (long)0);
		}


		while(true) {
			long calc = 0;
			calc = a * a + b * b + c * c + a * c + a * b + b * c;
//			System.err.println(a + " " + b+ " " + c+ " " + calc);

			if(a == b && a == c) {
				if(a > 0 && b > 0 && c > 0) ans = 1;
			} else {
				if(a > 0 && b > 0 && c > 0) ans = 3;
			}

			if(a == b && a == c) {
				a++;
				b = 1;
				c = 1;
			} else if(a > b && b == c) {
				b++;
			} else if(b > c) {
				c++;
			}

			if(calc <= n) {
				long tmp = ans;
				tmp += map.get(calc);
				map.put(calc, tmp);
			}

			if(a > 400)
				break;

		}

		for(int i = 1; i <= n; i++) {
			System.out.println(map.get((long)i));
		}

		//-------------------------------------------------------------------------------------

//		if(f) {
//			System.out.println("Yes");
//		} else {
//			System.out.println("No");
//		}

//		System.out.println(ans);

		sc.close();
	}



}