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.*;
public class Main {

	public static void main(String[] args) {
		
Scanner sc=new Scanner(System.in);
int n=sc.nextInt();

for(int i=1;i<=n;i++) {
	int count=0;
	for(int j=1;j<Math.sqrt(i);j++) {
		for(int k=1;k<Math.sqrt(i);k++) {
			for(int l=1;l<Math.sqrt(i);l++) {
				if((j*j+k*k+l*l+j*k+k*l+l*j)==i) {
			count++;
				}
				
			}
		}
	
	}
	System.out.println(count+ " ");
}
	}

}