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 <iostream>
#include <map>
using namespace std;

map<long, int> sq;

int f(int n)
{
    int res=0;
    for(long x=1; x*x<n; ++x) {
        for(long y=1; y*y<n; ++y) {
            long d=(x+y)*(x+y)-4*(x*x+y*y+x*y-n);
            if (d<0) continue;
            if (!sq.count(d)) continue;
            d=sq[d];
            long a=d-x-y;
            if (a%2==0 and a/2>0) ++res;
        }
    }
    return res;
}

int main()
{
    int n; cin>>n;
    for(long i=1; i<10000; ++i) sq[i*i]=i;

    for(int i=1; i<=n; ++i)
        cout<<f(i)<<'\n';
}