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: Accepted)

#include<stdio.h>

int main() {
	int n;
	int result = 0;

	scanf("%d", &n);

	int b, c;
	int i_flag, j_flag, k_flag;
	for (int cor = 1; cor <= n; cor++)
	{
		result = 0;
		b = 0, c = 0;
		i_flag = 0, j_flag = 0, k_flag = 0;
		for (int i = 1; i_flag == 0; i++)
		{
			j_flag = 0;
			for (int j = 1; j_flag == 0; j++)
			{
				k_flag = 0;
				for (int k = 1; k_flag == 0; k++)
				{
					int cal = i * i + j * j + k * k + i * j + j * k + k * i;
					if (cal == cor) {
						if (i == j && j == k) {
							result += 1;
						}
						else if (i == j || i == k || j == k) {
							b++;
							if (b == 3) {
								result += 3;
								b = 0;
							}
						}
						else {
							c++;
							if (c == 6) {
								result += 6;
								c = 0;
							}
						}
					}
					else if (cal > cor) {
						k_flag = 1;
						if (k == 1) {
							j_flag = 1;
							if (j == 1) {
								i_flag = 1;
								printf("%d\n", result);
							}
						}
					}
				}
			}
		}
	}

	return 0;
}