p02608 AIsing Programming Contest 2020 - XYZ Triplets
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
```python
n=int(input())
import math
nn=int(math.sqrt(n))+1
a=[0]*(100*n)
for x in range(1,nn+1):
    for y in range(1,nn+1):
        for z in range(1,nn+1):
            a[(x+y+z)**2-x*y-x*z-y*z]+=1
for i in range(1,n+1):
    print(a[i])
```