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 <iostream>
#include <math.h>
#include <vector>
#include <string>
using namespace std;
int main() {
	int N = 0;
	vector<long>v;
	scanf("%d", &N);
	int increament = 0;
	for (int i = 0; i < N; i++) {
		v.push_back(0);
	}

	for (int x = 1; x < N; x++) {
		for (int y = 1; y < N; y++) {
			for (int z = 1; z < N; z++) {
				if ((x * x + y * y + z * z + x * y + x * z + z * y) != 0 && ((x * x + y * y + z * z + x * y + x * z + z * y) < v.size())) {
					v[(x * x + y * y + z * z + x * y + x * z + z * y) - 1]++;
				}
			}
		}
	}
	
	for (int i = 0; i < v.size(); i++) {
		cout << v[i] << endl;
	}
	
	return 0;
}