Description

We rewrite formula $4$ in the following form:

$$\arctan(\frac{1}{a}) = \arctan(\frac{1}{b}) + \arctan(\frac{1}{c})$$

where $a, b, c \in \mathbb{N^+}$.

Our task is: for each given $a$, find the value of $b + c$. We guarantee that for any $a$ there is an integer solution. If there are multiple solutions, you must output the one with the smallest $b + c$.

Input Format

The input file contains only one positive integer $a$.

Output Format

The output file contains only one integer, which is the value of $b + c$.

1

5

Hint

$1 \le a \le 6\times 10^4$。

Translated by ChatGPT 5