#include <stdio.h>
int n, m, i, j, k, c[10005];
int main(){
	scanf("%d", &n);
	for(i=1; i<100; i++){
		for(j=1; j<100; j++){
			for(k=1; k<100; k++){
				m = i*i+j*j+k*k+i*j+j*k+i*k;
				if(m <= n) c[m]++;
			}
		}
	}
	for(i=1; i<=n; i++) printf("%d\n", c[i]);
	return 0;
}
### Prompt

Your task is to create 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 <stdio.h>
int n, m, i, j, k, c[10005];
int main(){
	scanf("%d", &n);
	for(i=1; i<100; i++){
		for(j=1; j<100; j++){
			for(k=1; k<100; k++){
				m = i*i+j*j+k*k+i*j+j*k+i*k;
				if(m <= n) c[m]++;
			}
		}
	}
	for(i=1; i<=n; i++) printf("%d\n", c[i]);
	return 0;
}
```