题目描述
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
输入格式
见题面
输出格式
见题面
样例输入
20
样例输出
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0