Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen. You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point (0, 0) . Persephone goes round Diatar along a circular orbit with radius R in the counter-clockwise direction at constant linear speed v p (thus, for instance, a full circle around the star takes of time). At the initial moment of time Persephone is located at point ( x p , y p ) . At the initial moment of time Qwerty's ship is at point ( x , y ) . Qwerty can move in any direction at speed of at most v ( v > v p ). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance r ( r < R ) from the star. Find the minimum time Qwerty needs to get the carcinogen to planet Persephone. The first line contains space-separated integers x p , y p and v p ( - 10 4 ≤ x p , y p ≤ 10 4 , 1 ≤ v p < 10 4 ) — Persephone's initial position and the speed at which it goes round Diatar. The second line contains space-separated integers x , y , v and r ( - 10 4 ≤ x , y ≤ 10 4 , 1 < v ≤ 10 4 , 1 ≤ r ≤ 10 4 ) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar. It is guaranteed that r 2 < x 2 + y 2 , r 2 < x p 2 + y p 2 and v p < v . Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed 10 - 6 .