Electrons#4942
Professor Finger-in-the-mouth has embarked on a journey into particle physics, focusing on electrons. He is currently tackling the problem of determining the average distance between electrons. For his study, he uses a simplified model:
Imagine a molecule lying on a plane and consisting of two atoms, each containing one electron. Each electron moves along a circular orbit. Since the exact position of an electron cannot be determined, the professor assumes that the electron's position on the orbit is a uniformly distributed random variable. That is, the probability of the electron being located on any given arc is proportional to the length of that arc.
Let the first orbit be a circle centered at (X_1, Y_1) with a radius of R_1, and the second orbit be a circle centered at (X_2, Y_2) with a radius of R_2.
Your task is to calculate the expected value of the distance between the two electrons.
The first line contains the integers X_1, Y_1, R_1.
The second line contains X_2, Y_2, R_2 (-100 \leq X_1, Y_1, X_2, Y_2 \leq 100; 1 \leq R_1, R_2 \leq 100).
Output the expected distance with a precision of 10^{-3}.
Example 1