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>
 
int main(void) {
    int N,i,x,y,z,j,k,flag,n,max;
    max=1;
    flag=0;
    scanf("%d" ,&N);
    for (n=1; n<=N; n++) {
        for (i=1;i<=100; i++) {
            x=i;
            if (flag>=1 && max==x) {
                break;
            }
          if(n<=x){
            break;
          }
            for (j=1;j<=100 ; j++) {
                y=j;
              if(n<=y){
            break;
          }
                for (k=1;k<=100 ; k++) {
                    z=k;
                  if(n<=z){
            break;
          }
                    if (n == x*x + y*y + z*z + x*y + y*z + z*x){
                        flag++;
                    }
                    if (max<=z) {
                        max=z;
                    }
                }
            }
        }
        printf("%d\n" ,flag);
        flag=0;
    }
    return 0;
}