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 L = sc.nextInt();
        int anc = 0;
        int count = 0;
        int x=1,y=1,z=1;
        for(int N = 1;N <= L;N++){
            outsid:for(x = 1;x <= 99;x++){
                if(x+y > 110){
                    break outsid;
                }
                for(y = 1;y <= 99;y++){
                    if(x+y > 110){
                        break outsid;
                    }
                    for(z = 1;z <= 99;z++){
                        if(N == x*x + y*y + z*z + x*y + y*z + z*x){
                            count++;
                        }
                    }
                }
            }
            System.out.println(count);
            count = 0;
        }
    }
}