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>
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define pb push_back
#define all(v) v.begin(),v.end()
#define sort_1(v) sort(v.begin(),v.end())
#define sort_2(v) sort(v.begin(),v.end(),greater<ll>())
#define reverse(v) reverse(v.begin(),v.end())
typedef long long ll;
typedef long double la;
using namespace std;

int main(){
	int n;
    cin >> n;
    map<ll, ll> m;
    rep(x,1,95){
        rep(y,1,95){
            rep(z,1,95){
                m[x*x+y*y+z*z+x*y+y*z+z*x]++;
            }
        }
    }
    rep(i,0,n){
        cout << m[i+1] << endl;
    }
}