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<math.h>

int func();

int main(void)
{
    int N, i;

    scanf("%d",&N);

    for(i=1; i<=N; i++) {
        printf("%d\n",func(i));
    }


    return 0;
}

int func(int n)
{
    int i, j, k, count=0;

    for(i=1; i<sqrt(n); i++) {
        for(j=1; j<=sqrt(n); j++) {
            for(k=1; k<=sqrt(n); k++) {
                if((i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i) == n) {
                    count++;
                }
            }
        }
    }

    return count;
}