Square

Kostya was so fascinated by geometry that he began drawing circles everywhere. One day, he drew a square with a side length of a. From each vertex of the square, he drew a circle with a radius of a. This created a shape inside the square that looked like a rounded square. To challenge his friends' understanding of geometry, Kostya asked them to calculate the area of this "round square."

Input

The side length of the square is given as a real number a.

Output

Provide the area of the shape, rounded to three decimal places.

Examples