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.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
      	int N = sc.nextInt();
      
      	Integer a[] = new Integer[N+1];
        for (int i=1; i<=N; i++) {
            a[i] = 0;
        }
        for (int i=1; i<=N; i++) {
        	for(int x = 1; x<=42;x++){
            	for(int y = x; y<=60;y++){
                 	 for(int z = y; z<=100;z++){
                       if((x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (z * x) == i){
                         if(x == y && y == z){
                         a[i] += 1;
                         } else {
                           a[i] += 3;
                         }
                       }     
        		    }
            	}
            }
        }
      
      	for (int i=1; i<=N; i++) {
            System.out.println(a[i]);
        }
         
    }
}