402043: GYM100633 A Survival Route

The surface of recently discovered planet i1c5l is a perfectly shaped sphere with radius R. Earth’s aerospace forces sent a research module Waldemar-63 that was supposed to land on the planet’s surface at point A. However, due to miscalculation, Waldemar-63 got to point B instead. Fortunately, Waldemar series are equipped with a train of wheels that will help in getting to the initial destination point. Nevertheless, power capacity is quite limited so it is important to get to point A by minimal distance run.

A major complication is that some point O on the surface of the planet radiates waves of unknown origin. The waves spread inside the radius r (the distance is measured on the surface). As the previous 62 missions show, any device that gets into the radiation area instantly breaks down. Thus, Waldemar-63’s route should avoid the radiation area. Find the minimal distance that the device has to undertake from B to A.

The first line contains integers X_A, Y_A ( - 90 ≤ X_A ≤ 90, 180 ≤ Y_A ≤ 180) — coordinates (latitude and longitude in degrees) of point A. Second line — coordinates of point B. Third — three integers: coordinates of point O and the radiation radius r. In the fourth line — positive integer not exceeding 1000 — planet’s radius R. It is guaranteed that points A and B are beyond the area of radiation.

Output the distance determined. The answer is considered correct if the absolute or relative error is less than 10^- 4.

55 49
55 129
90 0 1
2

1.510687