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

inputFormat

input are integers.

• 1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

outputFormat

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

样例

20

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

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