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.

Input

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 $*v*_{*p*} < *v*$.

Output

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 $10^{ - 6}$.