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 <iostream>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <cctype>
#include <cmath>
#include <vector>
#include <climits>
#include <queue>
#include <utility>
#include <iomanip>
#include <sstream> 
#define rep(i, n) for (long long i = 0; i < (long long)(n); i++)
using namespace std;
using ll = long long;
using Graph = vector<vector<int>>;
template<typename T1, typename T2>
inline void chmin(T1& a, T2 b) { if (a > b) a = b; }
template<typename T1, typename T2>
inline void chmax(T1& a, T2 b) { if (a < b) a = b; }
const ll MOD = 1000000006;
const ll INF = 1LL << 60;

ll a[10100] = {0};

int main()
{
    ll n;
    cin >> n;
    
    for (int i = 1; i <= 100; i++) {
        for (int j = 1; j <= 100; j++) {
            for (int k = 1; k <= 100; k++) {
                ll temp = i * i + j * j + k * k + i * j + j * k + k * i;
                if(temp <= 10000)
                    a[temp]++;
            }
        }
    }


    rep(i, n) {
        cout << a[i + 1] << endl;
    }
    



}