H. Hawarma
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

One evening, Eduardo was feeling hungry and decided to order a delivery of his favorite food: Shawarma. Upon opening the delivery app and selecting his favorite restaurant, Eduardo noticed a new intriguing option on the menu: the Hawarma. Although it seemed like a typo, he found out that it was a legitimate option. In the item's description, the restaurant had written: "Order the Hawarma, if you can." Curious, Eduardo continued, provided the delivery address, selected the payment method, and when everything seemed to be going smoothly, he encountered the following message:

To complete the order, consider the integer $$$N$$$ and the function $$$f: \mathbb{Z} \to \mathbb{R}$$$ defined as follows:
$$$f(x) = \frac{5xN^2}{x^2+3xN-5N^2}$$$

Determine all values $$$a$$$ for which $$$f(a) = a$$$

The truth is that, at this point, most people look and think "What a prank!" and end up ordering something else. But not Eduardo: motivated by the challenge and curiosity, he won't give up on the Hawarma. Suppose you are Eduardo, inform how many values satisfy the condition for a certain value of $$$N$$$ and what those values are.

Input

The input consists of a single line containing an integer $$$N$$$ $$$(-300 \le N \le 300, N \ne 0)$$$.

Output

The output should consist of two lines. Print on the first line the quantity $$$K$$$ of values that satisfy the condition. On the second line, print the $$$K$$$ values separated by spaces. You may print the values in any order. It is guaranteed that the quantity of values that satisfy the condition for a given value of $$$N$$$ does not exceed $$$10^4$$$.

Example
Input
3
Output
3
-15 0 6
Note

In the example, we have $$$N = 3$$$, so our function $$$f$$$ is:

$$$f(x) = \frac{5x \cdot 3^2}{x^2+3x \cdot 3 - 5 \cdot 3^2} = \frac{45x}{x^2+9x-45}$$$

We have $$$K=3$$$ values of $$$a$$$ such that $$$f(a)=a$$$. They are:

  • -15: $$$f(-15) = \frac{45 \cdot (-15) }{(-15)^2+9 \cdot (-15) - 45} = \frac{-675}{45} = -15$$$
  • 0: $$$f(0) = \frac{45 \cdot (0) }{(0)^2+9 \cdot (0) - 45} = \frac{0}{-45} = 0$$$
  • 6: $$$f(6) = \frac{45 \cdot (6) }{(6)^2+9 \cdot (6) - 45} = \frac{270}{45} = 6$$$