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<string>
#include<iostream>
#include <algorithm>
#include<vector>
#include<functional>
#include <cstdlib>
#include <iomanip>
#include <cmath>
#include <numeric>
#include <math.h>
#include <map>
#define ll long long 
#define PI 3.14159265358979323846
#define INF 10000000000
#define rep(i,n) for(ll i=0;i<(ll)n;i++)
using namespace std;

int main() {
	ll N;
	cin >> N;
	for (ll i = 1; i < N + 1; i++) {
		ll con = 0;
		for(ll x=1;x<=45;x++) {
			for(ll y = 1; y <=45;y++) {
				for (ll z = 1; z <= 45; z++) {
					ll ans = pow(x, 2) + pow(y, 2) + pow(z, 2) + (x * y) + (x * z) + (y * z);
					if (ans == i) con++;
				}
			}
		}
		cout << con << endl;
	}
	return 0;
}