Intersections

Time limit1sMemory limit512 MB

Summary

Count the intersection points of the piecewise triangular wave f(x) with the line g(x) = x/a, or report that there are infinitely many.

Level: Medium7 of 10
Topics: Math, Implementation, Brute force, Geometry
Solved: No attempts yet

Problem

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 points do the graphs of $y=f(x)$ and $y=g(x)$ have in common on the XY-plane?

Input

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

Output

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

Constraints

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

Examples1

Example 1
Input
```
2
```
Expected output
```
2
```