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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 2010-2021 Mike Mirzayanov

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