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 {
	
	static int triplets(int x){
	    int cnt = 0;
	    for(int i = 1; i <= (int)(1e2); i++){
	        for(int j = 1; j <= (int)(1e2); j++){
	            for(int k = 1; k <= (int)(1e2); k++){
	                if(i * i + j * j + k * k + i * j + j * k + k * i > x)break;
	                if(i * i + j * j + k * k + i * j + j * k + k * i == x)cnt++;
	            }
	        }
	    }
	    return cnt;
	}
	 
	 

	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		
		int n = stdIn.nextInt();
		 
		    for(int i = 1; i <= n; i++){
		        System.out.println(triplets(i));
		 
		    }
		 
		 
		
	}

}