In a country far far away there lived a King. That King had two sons. The first one, the younger one, loved math puzzles a lot, and his name was Alex Pop-o-witch. The older one, Ilya Murr-o-metz, wasn't fond of math. He was learning martial arts in order to be able to protect his motherland from enemies. Nevertheless, there were common activities for them to play together every day. Once the King decided to give a cherry orchard to his children as a gift. The orchard was in a form of a square with the opposite corners placed at the coordinates (0, 0) and (1, 1). All cherry trees were placed strictly inside the square. The sons were very happy with the gift because they now could not only run and play there, but also eat sweet cherries.

But soon the boys had a serious disagreement: Ilya didn't like the fact that Alex was doing math and had no interest in the martial arts, because the motherland was in danger and enemies may come at any moment. So the brothers were to split the cherry orchard. In this country far far away the older son always gets more than the younger one, and Ilya decided to take the part of the orchard that had more cherry trees to himself (he does not mind if both parts have the same amount). Alex didn't even object in order to avoid being lectured about enemies, fighting and battles. The boys selected two random points on the distinct sides of the orchard (each pair of points had the same probability to be picked) and connected both points using the rope thus splitting the orchard into two parts — one at each side of the rope. The section that had more cherry trees now belonged to Ilya, and the one with less — to Alex. You can consider that there is a zero a probability for the rope to cross the tree i.e. it is always possible to clearly distinguish to which part every tree belongs.

During the next year Ilya was eating cherries and doing sports. But soon Ilya got bored, because there were no cherries left and no one attacked the motherland. Meanwhile, Alex devoted himself to math. He is thinking about how many cherry tries he could have had if the brothers picked other random points during the orchard split. The only important condition is that Alex wouldn't have more trees than Ilya. He is curious to know what was the expected amount of cherry trees in his section of the orchard. Help Alex solve this tricky problem.