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>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
#define all(n) begin(n),end(n)
using ll = long long;
using P = pair<int,int>;

 //if((x*x + y*y + z*z + x*y + y*z + z*x)==n)
int comp(int x, int y, int z) {
    if(x==y && y==z) return 1;
    if(x==y || y==z) return 3;
    return 6;
}
int f(int i) {
    int res = 0;
    for(int x = 1; x*x<33334; ++x) {
        for(int y = x; y*y<33334; ++y) {
            for(int z = y; z*z < 33334; ++z) {
                if((x*x + y*y + z*z + x*y + y*z + z*x)==i){
                    res = comp(x, y, z);
                    return res;
                }
            }
        }
    }
    return 0;
}

int main() {
    int n;
    cin >> n;
    int ans = 0;
    for(int i = 1; i <= n; ++i) {
        if(i<6) { cout << 0 << endl; continue;}
        cout << f(i) << endl;
    }
    return 0;
}