#include <iostream>
#include <stdio.h>
using namespace std;
int i,j,k,n;
static int a[60001];
int main()
{
    for(i=1;i<100;i++)
        for(j=1;j<100;j++)
            for(k=1;k<100;k++)
                a[i*i+j*j+k*k+i*j+i*k+k*j]++;
    scanf("%d",&n);
    for(i=1;i<=n;i++)
        printf("%d\n",a[i]);
    return 0;
}

### Prompt

Please formulate 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 <iostream>
#include <stdio.h>
using namespace std;
int i,j,k,n;
static int a[60001];
int main()
{
    for(i=1;i<100;i++)
        for(j=1;j<100;j++)
            for(k=1;k<100;k++)
                a[i*i+j*j+k*k+i*j+i*k+k*j]++;
    scanf("%d",&n);
    for(i=1;i<=n;i++)
        printf("%d\n",a[i]);
    return 0;
}

```