B. Amr and Pins
geometry; math
Amr loves Geometry. One day he came up with a very interesting problem.Amr has a circle of radius r and center in point (x, y). He wants the circle center to be in new position (x', y').In one step Amr can put a pin to the border of the circle in a certain point, then rotate the circle around that pin by any angle and finally remove the pin.Help Amr to achieve his goal in minimum number of steps.
Input consists of 5 space-separated integers r, x, y, x' y' (1 ≤ r ≤ 105, - 105 ≤ x, y, x', y' ≤ 105), circle radius, coordinates of original center of the circle and coordinates of destination center of the circle respectively.
Output a single integer — minimum number of steps required to move the center of the circle to the destination point.
In the first sample test the optimal way is to put a pin at point (0, 2) and rotate the circle by 180 degrees counter-clockwise (or clockwise, no matter).