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: Wrong Answer)

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


int main()
{
	int n;
	int g;
	int x;
	int count;
	int sum;

	scanf("%d", &n);

	for (int i = 0; i < n; i++) {
		g = i + 1;
		count = 0;
		x = 1;
		sum = pow(x, 2) + 1 + 1 + x + 1 + x;
		while (sum <= g) {
			if (sum == g) {
				if (x == 1)
					count++;
				else
					count += 3;
			}
			x++;
			sum = pow(x, 2) + 1 + 1 + x + 1 + x;
		}
		printf("%d\n", count);
	}

	return 0;
}