101982: [AtCoder]ABC198 C - Compass Walking

Problem Statement

Takahashi is standing at the origin of a two-dimensional plane.

By taking one step, he can move to a point whose Euclidian distance from his current position is exactly $R$ (the coordinates of the destination of a move do not have to be integers). There is no other way to move.

Find the minimum number of steps Takahashi has to take before reaching $(X, Y)$.

We remind you that the Euclidian distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$.

Constraints

• $1 \leq R \leq 10^5$
• $0 \leq X,Y \leq 10^5$
• $(X,Y) \neq (0,0)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$R$ $X$ $Y$

Output

Print the minimum number of steps Takahashi has to take before reaching $(X, Y)$.

Sample Input 1

5 15 0

Sample Output 1

3

He can reach there in three steps: $(0,0) \to (5,0) \to (10,0) \to (15,0)$. This is the minimum number needed: he cannot reach there in two or fewer steps.

Sample Input 2

5 11 0

Sample Output 2

3

One optimal route is $(0,0) \to (5,0) \to (8,4) \to (11,0)$.

Sample Input 3

3 4 4

Sample Output 3

2

One optimal route is $(0,0) \to (2-\frac{\sqrt{2}}{2}, 2+\frac{\sqrt{2}}{2}) \to (4,4)$.