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 mod 1000000007
#define M 998244353


void sumSquare(int a[],int n) 
{ 
    long long int m;
    for(int i=1;i<=sqrt(n);i++)
    {
        for(int j=1;j<=sqrt(n);j++)
        {
            for(int k=1;k<=sqrt(n);k++)
            {
                m=(i*i)+(k*k)+(j*j)+(i*j)+(j*k)+(k*i);
                if(m>n)
                {
                    break;
                }
                else
                {
                    if((i!=j)&&(i!=k)&&(k!=j))
                    {
                        a[m-1]=6;
                    }
                    else if((i==j)&&(j==k))
                    {
                        a[m-1]=1;
                    }
                    else
                    {
                        a[m-1]=3;
                    }
                }
            }
        }
    }
}
	
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
    int n,x=1,y=1,z=1,pos;
	cin>>n;
	int a[n]={0};
    sumSquare(a,n);
	for(int i=0;i<n;i++)
	{
	    cout<<a[i]<<endl;
	}
	
	return 0;
}