Moving walkway#2781
Bob is a renowned scientist who frequently attends various conferences. On one of his trips, he found himself running late for his flight and needed to reach terminal A as quickly as possible. The airport features a horizontal moving walkway that can help Bob move faster. Bob is familiar with the airport's layout, including the entrance, terminal A, and the start and end points of the moving walkway.
Imagine the airport as a coordinate plane: the entrance is at point , terminal is at point x_1, y_1, and the moving walkway starts at x_2, y_2 and ends at x_3, y_3. Bob's walking speed is , while the walkway moves at speed . The walkway can only be used from its start to its end. Your task is to help Bob determine the minimum time required to travel from the airport entrance to terminal . Note that due to the walkway's handrails, Bob cannot cross it; he can only enter at the start and travel to the end at speed .
The first line of input contains six integers: x_1, y_1, x_2, y_2, x_3, y_3 (-10000 \le x_1, x_2, x_3 \le 10000, 0 < y_1, y_2, y_3 \le 10000). These represent the coordinates of terminal A and the start and end points of the moving walkway. The second line contains two integers (0 < v \le 50, 0 < w \le 50), indicating Bob's speed and the walkway's speed.
It is guaranteed that neither terminal nor the airport entrance lies on the moving walkway.
Output the minimum time it will take Bob to travel from the entrance to terminal . The result is considered accurate if it differs from the minimum by no more than 10^{-5}.
Exemple 1