Intersections

You are given the following two functions. ($\mathbb{N}\_0$ denotes the set of non-negative integers.)

$f(x)= \begin{cases} 0, & \mbox{if } x < 0 \\\ x - 2k, & \mbox{if } 2k \le x < 2k+1 \\, (k \in \mathbb{N}\_0) \\\ -x + 2(k+1) & \mbox{if } 2k + 1 \le x < 2k+2 \\, (k \in \mathbb{N}\_0) \end{cases}$

$g(x) = {x \over a}$

How many intersections between the graphs of $y=f(x)$ and $y=g(x)$ exist on the XY-plane?

The first and only line of the input contains a single integer $a$.

Print the number of intersections between the graphs of $y = f(x)$ and $y = g(x)$. If there are infinitely many intersections, print INF.

• $\left\vert a \right\vert \le 10^9$; $a \ne 0$
• $a$ is an integer.