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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
// const int INF = 2147483647;
// const ll INF = 9223372036854775807;
// const ll MOD = 1e9 + 7;

int main() {
	int N;
	cin >> N;

	vector<int> ans;

	for (int n=1; n<=N; n++) {
		int a = 0;
		for (int x=1; x*x<n; x++) {
			for (int y=x; x*x + y*y < n; y++) {
				for (int z=y; x*x + y*y + z*z < n; z++) {
					if (x*x + y*y + z*z + x*y + y*z + z*x == n) a++;
				}
			}
		}
		ans.push_back(a);
	}

	for (int a: ans) {
		cout << a << endl;
	}

	return 0;
}