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: Runtime Error)

#include <stdio.h>
int main(void){
int a;
  int i,j;
  int x, y,z;
  int sum=0;
  int num[99];
  scanf("%d", &a);
  for (i=1; i<=a; i++){
    for (x=1; x<=3; x++){
      for (y=1; y<=3; y++){
        for (z=1; z<=3; z++){
          if (x*x+y*y+z*z+x*y+x*z+y*z==i){
            sum++;
          }
          num[i]=sum;
        }
      }
    } 
     sum=0;
  }
     for (j=1;j<=a;j++){
       printf("%d\n", num[j]);
     }
  return 0;
}