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;

    const int N = 10010;

    int n;
    int ans[N];

    int main()
    {
        cin >> n;
        int ceil = sqrt(n);
        for(int x = 1; x <= ceil; x++)
            for(int y = 1; y <= ceil; y++)
                for(int z = 1; z <= ceil; z++)
                {
                    int tmp = x * x + y * y + z * z + x * y + x * z + y * z;
                    if(tmp < N)
                        ans[tmp]++;
                }
            
        for(int i = 1; i <= n; i++)
            cout << ans[i] << endl;

        return 0;
    }