#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int ans[10007];
int main() {
	for(int x=1; x<=100;x++) {
	for(int y=1; y<=100;y++) {
	for(int z=1; z<=100;z++) {
		int a=x+y,b=y+z,c=x+z;
		int t=a*a+b*b+c*c;
		if(t<=20000 && t%2==0) ans[t/2]++;
	}
	}
	}
	int n; scanf("%d", &n);
	for(int i=1; i<=n; i++) printf("%d\n", ans[i]);
}

### Prompt

Your challenge is to write 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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int ans[10007];
int main() {
	for(int x=1; x<=100;x++) {
	for(int y=1; y<=100;y++) {
	for(int z=1; z<=100;z++) {
		int a=x+y,b=y+z,c=x+z;
		int t=a*a+b*b+c*c;
		if(t<=20000 && t%2==0) ans[t/2]++;
	}
	}
	}
	int n; scanf("%d", &n);
	for(int i=1; i<=n; i++) printf("%d\n", ans[i]);
}

```