Run-Track#3360
The organizers of the new Winter Games have decided to include the game "Run-Track". The game takes place in an arena that can be represented as a triangle on the coordinate plane. A participant starts on one of the three sides of the arena. After starting, the participant must touch each side (except the one from which they started) and return to their initial position. You are given information about the next participant. Output the best time they can achieve.
The first three lines give the coordinates of the triangle's vertices, which define the arena. The fourth line gives , — the coordinates of the starting position, and — the speed of the participant (v > 0). It is guaranteed that the starting position lies on one of the given triangle's sides and does not coincide with the triangle's vertices. All numbers in the input are integers and do not exceed 10^9 in absolute value.
Output a single number — the answer to the problem, with at least 10^{-6} precision.
Example 1