A9970 | Chip 'n Dale Rescue Rangers

The first line of the input contains four integers $x_{1}$ , $y_{1}$ , $x_{2}$ , $y_{2}$ ( $|x_{1}|,|y_{1}|,|x_{2}|,|y_{2}|<=10000$ ) — the coordinates of the rescuers' headquarters and the point, where signal of the distress came from, respectively.

The second line contains two integers  and $t$ ( $0<v,t<=1000$ ), which are denoting the maximum speed of the chipmunk dirigible relative to the air and the moment of time when the wind changes according to the weather forecast, respectively.

Next follow one per line two pairs of integer $(v_{x},v_{y})$ and $(w_{x},w_{y})$ , describing the wind for the first $t$ seconds and the wind that will blow at all the remaining time, respectively. It is guaranteed that  and .

Print a single real value — the minimum time the rescuers need to get to point $(x_{2},y_{2})$ . You answer will be considered correct if its absolute or relative error does not exceed $10^{-6}$ .

Namely: let's assume that your answer is $a$ , and the answer of the jury is $b$ . The checker program will consider your answer correct, if .

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