#include <bits/stdc++.h>
using namespace std;

const int MAXN = 100005;

int n, cnt[MAXN];

int main(){
	scanf("%d", &n);
	
	for(int x = 1; x <= 100; x++)
	for(int y = 1; y <= 100; y++)
	for(int z = 1; z <= 100; z++){
		cnt[x * x + y * y + z * z + x * y + y * z + z * x]++;
	}
	
	for(int i = 1; i <= n; i++)
		printf("%d\n", cnt[i]);
		
	return 0;
}

### Prompt

Generate a CPP solution to the following problem:

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).

Example

Input

20


Output

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int MAXN = 100005;

int n, cnt[MAXN];

int main(){
	scanf("%d", &n);
	
	for(int x = 1; x <= 100; x++)
	for(int y = 1; y <= 100; y++)
	for(int z = 1; z <= 100; z++){
		cnt[x * x + y * y + z * z + x * y + y * z + z * x]++;
	}
	
	for(int i = 1; i <= n; i++)
		printf("%d\n", cnt[i]);
		
	return 0;
}

```