Clear after burning#3170
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 as soon as 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 now he wants to gather it into a single point using a dustpan with a straight base. Vasya can slide the base of the dustpan across the table to move the ash. The movement vector of the dustpan remains fixed and is not necessarily perpendicular to the base. It can be assumed that the points of the triangle that are on the base of the dustpan do not change their relative position with respect to the dustpan, but remain on the table.
Let us fix a point on the base of the dustpan; we can then determine the distance this point will travel as Vasya collects the ash. We will refer to this value as the cleaning penalty. Since Vasya tries to optimize everything, he is interested in finding the minimum cleaning penalty.
The input consists of three lines. Each line contains a pair of integers—coordinates of the vertices of the triangle. 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 a single real number—the minimum penalty. The answer must be printed with at least six digits after the decimal point.
Example 1