# p02608 AIsing Programming Contest 2020 - XYZ Triplets

## Problem Description
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

## Contest Information
- **Contest ID**: 0
- **Problem Index**: 
- **Points**: 0.0
- **Rating**: 0
- **Tags**: 
- **Time Limit**: {'seconds': 2, 'nanos': 0} seconds
- **Memory Limit**: 1073741824 bytes

## Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.