A8637. Delivering Carcinogen

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 $10^{-6}$ .

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