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: Time Limit Exceeded)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int,int> pii;

typedef int _loop_int;
#define REP(i,n) for(_loop_int i=0;i<(_loop_int)(n);++i)
#define FOR(i,a,b) for(_loop_int i=(_loop_int)(a);i<(_loop_int)(b);++i)
#define FORR(i,a,b) for(_loop_int i=(_loop_int)(b)-1;i>=(_loop_int)(a);--i)

#define VIN(v) for(auto&elem_: (v) )cin>>elem_
#define VOUT(v, sep) for(_loop_int idx=0; idx<(_loop_int)v.size(); idx++) {cout<<v[idx]; if(idx<(_loop_int)v.size()-1) cout<<sep;} cout<<endl
#define ALL(a) (a).begin(),(a).end()

#define DEBUG(x) cout<<#x<<": "<<x<<endl
#define DEBUG2(x,y) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<endl
#define DEBUG_VEC(v) cout<<#v<<":";REP(debugidx,v.size())cout<<" "<<v[debugidx];cout<<endl
#define DEBUG_ARR(v,n) cout<<#v<<":";REP(debugidx,n)cout<<" "<<v[debugidx];cout<<endl

const ll MOD = 1000000007ll;
const int IINF = numeric_limits<int>::max()/2-1;
const ll LINF = numeric_limits<ll>::max()/2-1;

template<class T> inline bool chmin(T& a, const T b) { if (a>b) { a=b; return true; } return false; }
template<class T> inline bool chmax(T& a, const T b) { if (a<b) { a=b; return true; } return false; }



int main() {
    ios::sync_with_stdio(false); cin.tie(0);
    int n;
    cin>>n;

    FOR(i,1,n+1){
        int d = sqrt(i)+1;
        //int d = i;
        int ans = 0;

        FOR(x,1,d+1){
            FOR(y,1,d+1){
                FOR(z,1,d+1){
                    int tmp;
                    tmp = x*x + y*y + z*z + x*y + y*z + z*x;
                    if(tmp==i) ans++;
                }
            }
        }

        cout << ans << endl;
    }
    
    return 0;
}