Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Delivering Carcinogen

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputQwerty 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}.

Examples

Input

10 0 1

-10 0 2 8

Output

9.584544103

Input

50 60 10

50 60 20 40

Output

0.000000000

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/16/2019 11:30:13 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|