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 C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <string.h>
#include <math.h>

int main(void){
  int n;
  scanf("%d", &n);
  int k, l, m;
  int x, y, z;
  int i;
  int f;
  for(i=1; i<n+1; i++){
    f=0;
    k=sqrt(n);
    for(x=1; x<k+1; x++){
      l=sqrt(n-x*x);
      for(y=1; y<l+1; y++){
        m=sqrt(n-x*x-y*y);
        for(z=1; z<m+1; z++){
          if(((x+y+z)*(x+y+z)-(x*y+y*z+z*x))==i){
            f++;
          }
        }
      }
    }
    printf("%d\n", f);
  }
  return 0;
}