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 (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(){
  int x,y,z,N,count = 0;
  scanf("%d", &N);

  for(int i = 0; i < N+1; i++){
 	 for(x = 1; x < 50; x++){
 	   for(y = 1; y < 50; y++){
 	     for(z = 1; z < 50; z++){
    	    if((x*x + y*y + z*z + x*y + y*z + x*z == i))
              count++;
           	if(z*z > i)
              break;
         }
         if(y*y > i)
              break;
       }
       if(x*x > i)
              break;
     }
  	printf("%d\n", count);
    count = 0;
  }
  return 0;
}