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;

#define mod1 1000000007
#define mod2 998244353
#define int long long int
#define pii pair<int,int>
#define vpii vector<pii>
#define vi vector<int>
#define fi first
#define se second
#define psb push_back
#define ppb pop_back
#define fio ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL)
#define all(x) x.begin(),x.end()
// #define endl "\n"

const int maxn=1e4+5;

int ans[maxn];

int f(int i,int j,int k)
{
	return i*i+j*j+k*k+i*j+i*k+j*k;
}

void solve()
{
	int n;
	cin>>n;
	for(int i=0;i<maxn;i++)
		ans[i]=0;
	for(int i=1;i<=200;i++)
		for(int j=1;j<=200;j++)
			for(int k=1;k<=200;k++)
				if(f(i,j,k)<maxn)
					ans[f(i,j,k)]++;
	for(int i=1;i<=n;i++)
		cout<<ans[i]<<endl;

}

int32_t main()
{
	fio;
	int t;
	// cin>>t;
	t=1;
	while(t--)
	{
		solve();
	}
}