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: Time Limit Exceeded)

#include<stdio.h>
#include<math.h>
int main() {

	int N, i, count = 0, x, y, z;

	scanf("%d", &N);

	for (i = 1; i <= N; i++) {
		for (x = 1; x <= sqrt(i); x++) {
			for (y = 1; y <= i-(x * x ); y++) {
				for (z = 1; z <= i-(x * x + y * y + x * y); z++) {
					if (x * x + y * y + z * z + x * y + y * z + z * x == i)
						count++;
				}
			}
		}
		printf("%d\n", count);
		count = 0;
	}

	return 0;
}