Contest Duration: - (local time) (100 minutes) Back to Home
C - Compass Walking /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

2 次元平面上の原点に高橋君がいます。

なお、点 (x_1,y_1) と点 (x_2,y_2) のユークリッド距離は \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} で与えられます。

制約

• 1 \leq R \leq 10^5
• 0 \leq X,Y \leq 10^5
• (X,Y) \neq (0,0)
• 入力は全て整数

入力

R X Y


入力例 1

5 15 0


出力例 1

3


(0,0) \to (5,0) \to (10,0) \to (15,0)3 歩で到達できます。 2 歩以下で到達することはできないのでこれが最小です。

入力例 2

5 11 0


出力例 2

3


入力例 3

3 4 4


出力例 3

2


Score : 300 points

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).