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){
		Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        for(int i=1;i<=n;i++){
        	int ans=0;
        	for(int x=1;x<=(int)Math.pow(n, 0.5);x++){
        		for(int y=x;y<=(int)Math.pow(n, 0.5);y++){
        			for(int z=y;z<=(int)Math.pow(n, 0.5);z++){
        				if((x*x+y*y+z*z+x*y+y*z+z*x)==i){
        					if(x==y&&y==z){ans++;}
        					else if(x==y||y==z||z==x){ans=ans+3;}
        					else{ans=ans+6;}
        				}
        			}
        		}
        	}
        	System.out.println(""+ans);
        }
}
}