Problem Statement

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 $f(i)$.

Sample Input 1

20

Sample Output 1

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

• For $n=6$, only $(1,1,1)$ satisfies both of the conditions. Thus, $f(6) = 1$.
• For $n=11$, three triples, $(1,1,2)$, $(1,2,1)$, and $(2,1,1)$, satisfy both of the conditions. Thus, $f(6) = 3$.
• For $n=17$, three triples, $(1,2,2)$, $(2,1,2)$, and $(2,2,1)$, satisfy both of the conditions. Thus, $f(17) = 3$.
• For $n=18$, three triples, $(1,1,3)$, $(1,3,1)$, and $(3,1,1)$, satisfy both of the conditions. Thus, $f(18) = 3$.