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Open Ural FU Championship 2013

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H. Planet Ocean Landing

Time limit: 0.5 second
Memory limit: 64 MB
Planet Ocean is completely covered by the water and is spheric in shape, its center is at the origin of coordinates. There is an aircraft carrier at point (x1, y1, z1) on the surface of the planet, and there is a spaceship in the space, at point (x2, y2, z2). In this problem you should consider the carrier and the spaceship to be material points. The carrier can move along the surface of the planet with a maximal speed 1, and the spaceship can fly outside the planet or along its surface with a maximal speed v.
The carrier and the spaceship really want to meet. For that the spaceship should land on the carrier. Your task is to find the minimum time it takes to land.


The first line contains integers x1, y1, z1 that are the initial coordinates of the carrier. The second line contains integers x2, y2, z2 that are the initial coordinates of the spaceship. The absolute value of each coordinate does not exceed 100. The third line contains an integer v that is the maximal speed of the spaceship (1 ≤ v ≤ 100).
It is guaranteed that 0 < x12 + y12 + z12 < x22 + y22 + z22.


Output the minimum time of spaceship landing with an absolute or relative error 10−6.


-1 1 -1
10 10 10
Problem Author: Mikhail Rubinchik
Problem Source: Open Ural FU Championship 2013
To submit the solution for this problem go to the Problem set: 1988. Planet Ocean Landing