Prof. Du and Prof. Pang plan to build a sky garden near the city of Allin. In the garden, there will be a plant maze consisting of straight and circular roads.

On the blueprint of the plant maze, Prof. Du draws circles indicating the circular roads. All of them have center . The radius of the -th circle is .

Meanwhile, Prof. Pang draws lines on the blueprint indicating the straight roads. All of the lines pass through . Each circle is divided into parts with equal lengths by these lines.

Let be the set of the roads. Let be the set of all intersections of two different roads in . Note that each circular road and each straight road have two intersections.

For two different points and , we define to be the shortest distance one needs to walk from to along the roads. Please calculate the sum of for all .

The only line contains two integers .

Output one number -- the sum of the distances between every pair of points in .

Your answer is considered correct if its absolute or relative error does not exceed .

1 2

14.2831853072

2 3

175.4159265359