Clear after burning
Agent Vasya 00* Pupkin discovered a triangular letter in his mailbox—a message from the Center. To ensure confidentiality, all messages from the Center are equipped with a self-destruct mechanism. Vasya knows that once he opens the envelope, a special substance applied to all three vertices of the triangular message will react with the air and ignite.
After calculating the burning time of the letter and enjoying a cup of coffee, Vasya encountered a new challenge. The letter left a triangular-shaped ash mark on the table, and he now wants to gather it into a single point using a dustpan with a straight edge. Vasya can slide the base of the dustpan across the table to move the ash. The direction of the dustpan's movement remains constant and is not necessarily perpendicular to the base. It can be assumed that the points of the triangle that align with the base of the dustpan do not shift relative to the dustpan but stay on the table.
Let's fix a point on the base of the dustpan; we can then determine the distance this point will travel as Vasya gathers the ash. We will refer to this distance as the cleaning penalty. Since Vasya aims to optimize everything, he is interested in finding the minimum cleaning penalty.
Input
The input consists of three lines. Each line contains a pair of numbers representing the coordinates of the triangle's vertices. All coordinates are integers and do not exceed 10^5 in absolute value. It is guaranteed that the three vertices do not lie on a single straight line.
Output
Output a single real number on one line—the minimum penalty. The answer must be provided with at least six decimal places.