CF198C.Delivering Carcinogen

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.

Qwerty 探险家抵达了迪亚塔尔（Diatar）星系，肩负一项极其重要的任务：他需将一种特殊的致癌物运送到行星珀耳塞福涅（Persephone），以供科学研究之用。此事十万火急，Qwerty 必须尽快抵达该行星。哪怕延误一天，谈判也可能失败——毕竟，没人愿意为逾期交付的致癌物付款。

你可以将 Qwerty 的飞船、行星珀耳塞福涅以及恒星迪亚塔尔均视为平面上的点。恒星迪亚塔尔位于坐标系原点，即点 $(0,\,0)$。珀耳塞福涅围绕迪亚塔尔沿半径为 $R$ 的圆形轨道作逆时针匀速圆周运动，其线速度为 $v_p$（因此，绕恒星运行一周所需时间为 ）。在初始时刻，珀耳塞福涅位于点 $(x_p,\,y_p)$。

在初始时刻，Qwerty 的飞船位于点 $(x,\,y)$。Qwerty 可朝任意方向移动，最大速度为 $v$（其中 $v > v_p$）。恒星迪亚塔尔温度极高（正如所有恒星一样），因此 Qwerty 无法过于靠近它；当飞船与恒星之间的距离小于 $r$（其中 $r < R$）时，船体金属外壳便会熔化。

求 Qwerty 将致癌物送达行星珀耳塞福涅所需的最短时间。

The first line contains space-separated integers x__p, y__p and v__p ( - 104 ≤ x__p, y__p ≤ 104, 1 ≤ v__p < 104) — 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 ( - 104 ≤ x, y ≤ 104, 1 < v ≤ 104, 1 ≤ r ≤ 104) — 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.

第一行包含用空格分隔的整数 $x_p$、$y_p$ 和 $v_p$（$-10^4 \le x_p, y_p \le 10^4$，$1 \le v_p < 10^4$）——珀耳塞福涅的初始位置及其绕恒星迪亚塔尔运行的速度。

第二行包含用空格分隔的整数 $x$、$y$、$v$ 和 $r$（$-10^4 \le x, y \le 10^4$，$1 < v \le 10^4$，$1 \le r \le 10^4$）——奎尔蒂飞船的初始位置、其最大速度以及到恒星迪亚塔尔的最小安全距离。

保证满足 $r^2 < x^2 + y^2$、$r^2 < x_p^2 + y_p^2$ 以及 $v_p < v$。

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.

输出一个实数——最小可能的配送时间。若答案的绝对或相对误差不超过 $10^{-6}$，则视为正确。