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.*;

public class Main{
	public static void main(String[] args){
      	Scanner sc = new Scanner(System.in);
    	int n = Integer.parseInt(sc.next());
      	int count = 0,jc = 1,jk = 1,kc = 1;
      	for(int cnt = 0;cnt < n;cnt++){
        	for(int i = 1;i * jc * jk < cnt;i++){
            	for(int j = 1;i * j * kc < cnt;j++){
                	for(int k = 1;i * j * k < cnt;k++){
                    	if(i * j * k == n){
                        	count++;
                        }
                    }
                }
            }
          	System.out.println(count);
          	count = 0;
        }
    }
}