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.*;
import java.io.*;


public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        PrintWriter pw = new PrintWriter(System.out);
        for(int i=1;i<=N;i++){
            int count = 0;
            for(int x=1;x*x<=N;x++){
                for(int y=x;y*y<=N-x*x;y++){
                    for(int z=y;z*z<=N-x*x-y*y;z++){
                        if(x*x+y*y+z*z+x*y+y*z+z*x==i){
                            if(x==y && y==z){
                                count++;
                            }else if(x!=y && y!=z && z!=x){
                                count += 6;
                            }
                            else{
                                count += 3;
                            }
                            
                        }
                    }
                }
            }    
            pw.println(count);
        }
        pw.flush();
    }
}