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: Accepted)

#include"bits/stdc++.h"

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define REP(i, n) for (int i = 1; i <= (int)(n); i++)
#define all(v) v.begin(), v.end()
using namespace std;
using ll = long long;
using pi = pair<int, int>;
const ll INF = 1LL << 60;

int main() {
	vector<int>a(100), b, c;
	int n;
	cin >> n;
	int sum;
	map<int, int>mp;
	iota(all(a), 1);
	b = c = a;
	for (auto aa : a)for (auto bb : b)for (auto cc : c) {
		sum = aa * aa + bb * bb + cc * cc + aa * bb + aa * cc + bb * cc;
		mp[sum]++;
	}
	for (int i = 1; i <= n; i++) {
		cout << mp[i] << endl;
	}
	//for (auto m : mp)cout << m.first << ":" << m.second << endl;
}