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>
#define rep(i,a,b) for(int i=a;i<b;i++)
using namespace std;
#define maxn 10000000

int n,cnt=0; 

int check(int x,int y,int z,int n)
{
	int flag=0;
	if(x*x+y*y+z*z+x*y+y*z+z*x==n)
		flag=1;
	return flag;
}
int book[6000003];
int main()
{
	cin>>n;
	rep(x,1,101)
	{
		rep(y,1,101)
		{
			rep(z,1,101)
			{
				book[x*x+y*y+z*z+x*y+y*z+z*x]+=1;
			}
		}
	}
	int ans=0; 
	rep(i,1,n+1)
	{
		cout<<book[i]<<endl;
	}
	return 0;
}