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>
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=(ll)(b);i--)
#define ALL(x) (x).begin(),(x).end() 
#define SIZE(x) ((ll)(x).size())
#define MAX(x) *max_element(ALL(x))
#define MIN(x) *min_element(ALL(x))
#define INF 1000000000
using namespace std;
typedef long long ll;

int ans = 0;

void solv(int a, int b, int c, int n){
    int f = pow(a,2) + pow(b,2) + pow(c,2) + a*b + a*c + b*c;
    int na = a+1, nb = b+1, nc = c+1;
    //cout << a << " " << b << " " << c << " " << f << " ";
    if (f > n) return;
    if (f == n) {
        set<int> st{a, b, c};
        if (st.size() == 1) ans++;
        else if(st.size() == 2) ans += 3;
        else if(st.size() == 3) ans += 6;
        return;
    }
    if (f < n) {
        solv(na, b, c, n);
        solv(na, nb, c, n);
        solv(na, nb, nc, n);
    }
    return;
}

int main(){
    int N;
    cin >> N;

    FOR(i, 1, N){
        solv(1, 1, 1, i);
        cout << ans << endl;
        ans = 0;
    }
}