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);
    
    //行数
    int n = sc.nextInt();
    //現在の行数
    int i = 1;
    while(i <= n){
      int ans = 0;
      for(int x = 1;x <= i;x++){
        for(int y = 1; y <= i;y++){
          for(int z = 1; z <= i;z++){
            int xsquare = (int)Math.pow(x,2);
            int ysquare = (int)Math.pow(y,2);
            int zsquare = (int)Math.pow(z,2);
            int ans1 = xsquare + ysquare + zsquare + x * y + y * z + z * x;

            //System.out.println(ans1);
            if(ans1 == i){
              ans++;
            }
          }
        }
      }
      i++;
      System.out.println(ans);
    }
  }
}