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 {
        static int threshold(int x,int y,int z){
            return x*x+y*y+z*z+x*y+x*z+y*z;
        }
        public static void main(String[]args){
            Scanner sc = new Scanner(System.in);
            int N= sc.nextInt();
            int f[]= new int[N];
            int sqN=(int)Math.sqrt(N);

            for(int n=1; n<N+1; n++) {
                for(int x=1; x<sqN+1; x++){
                    if(x*x>n){
                        break;
                    }
                    for(int y=1; y<sqN+1; y++){
                        if(x*x+y*y>n){
                            break;
                        }
            for(int z=1; z<sqN+1;z++){
                if(threshold(x,y,z)>n){
                    break;
                }else{
                    if(threshold(x,y,z)==n){
                        f[n-1]++;   
                    }
                }
            } 
                    }
                }
            }
              
            for(int i=0; i<N; i++){
                System.out.println(f[i]);
            }
        }
    }