Problem Description

Just indulge in your own fantasy!

Given an elliptic equation $\Gamma:t=x^2+xy+y^2$ satisfying $t > 0$, if the trajectory of the ellipse $\Gamma$ passes through a point $(x_0,y_0)$ where both the horizontal and vertical coordinates are integers, then $t$ is called an "elliptic number". For example, $7$ is an "elliptic number" because $(-1,3)$ satisfies the condition, while $6$ is not an "elliptic number".

Given a number $n$, find the sum of the factors of each number $i$ from $1$ to $n$ that are "elliptic number".

Input

Input a positive integer $n$ satisfying $1 \leqslant n \leqslant 1\times 10^4$.

Output

Output a line containing $n$ integers, separated by spaces.

Samples

6

1 1 4 5 1 4

Note

When $i=4$, its factors are $1, 2, 4$, where $1$ and $4$ are "elliptic number", so the $4$th digit is output as $5$.

When $i=6$, its factors are $1, 2, 3, 6$, where $1$ and $3$ are "elliptic number", so the $6$th digit outputs $4$.