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>
using namespace std;
typedef long long ll;
const static ll INF = 1e15;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
// __uint128_t
const ll MOD = 1e9+7;

int main(){
    ll N; cin >> N;
    unordered_map<ll, ll> M;
    for(ll x = 1; x <= N; x++){
        for(ll y = 1; y <= N; y++){
            ll temp = 1+x*x+y*y+x*y+y+x;
            if(temp > N) break;
            for(ll z = 1; z <= N; z++){
                ll n = x*x + y*y + z*z + x*y + y*z + z*x;
                if(n > N) break;
                M[n]++;
            }
        }
    }
    for(int i = 1; i <= N; i++) cout << M[i] << endl;
}