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: Wrong Answer)

#include<iostream>
#include<cstring>
#include<cmath>
#include<string>
#include<algorithm>
using namespace std;
typedef long long LL;
int main()
{
	int n;
	cin >> n;
	for (int i = 1;i <= n;i++)
	{
		int x, y, z;
		int flag = 0;
		x = y = z = 1;
		int cnt = x * x + y * y + z * z + x * y + y * z + z * x;
		if (i < cnt)
		{
			cout << 0 << endl;
			continue;
		}
		for (x = 1;(x * x < i) && flag == 0;x++)
			for (y = 1;(y * y < i) && flag == 0;y++)
				for (z = 1;(z * z < i) && flag == 0;z++)
				{
					cnt = x * x + y * y + z * z + x * y + y * z + z * x;
					if (cnt == i)
					{
						flag = 1;
						if (x == y && y == z)
							cout << 1 << endl;
						else if ((x == y && y != z) || (x == z && y != z) || (y == z && x != y))
							cout << 3 << endl;
						else
							cout << 6 << endl;
					}
					if (cnt > i)
						break;
				}
		if (flag == 0)
			cout << 0 << endl;
	}
	return 0;
}