Burn after reading
Agent Vasya 00* Pupkin has once again received 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 the three vertices of the triangular message will react with the air and ignite. The flame spreads across the message at a speed of 1 cm/sec. Vasya is aware that the most important part of the letter usually burns last. He wants to determine how much time he will have to read the letter and how much he might miss if he decides to make himself a cup of coffee.
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, with absolute values not exceeding 10^5. It is guaranteed that the three vertices do not lie on the same straight line.
Output
Output a single real number on one line, representing the minimum time it will take for the triangle to burn completely. The answer must be given with a precision of at least six decimal places.