Big track
The organizers of the new winter games have introduced a game called "Big Track." This game is set in an arena shaped like a triangle on a coordinate plane. Participants start on one of the three sides of the triangle. After starting, they must touch each of the other two sides and then return to their starting point. You are provided with details about the next participant. Your task is to determine the shortest time they can achieve.
Input
The first three lines contain the coordinates of the triangle's vertices, defining the arena. The fourth line contains the x, y coordinates of the starting position and v, the participant's speed (v > 0). It is guaranteed that the starting position is on one of the triangle's sides and does not coincide with any of the vertices. All numbers in the input are integers and do not exceed 10^9 in absolute value.
Output
Output a single number, representing the answer to the problem, with a precision of at least 10^{-6}.