Circle on Tiles

Time limit

Memory limit

128 MB

Problem

Square tiles with side length 1 cm are placed without gaps to form a large square whose side length is N cm. N is even.

Draw a circle tangent to all four sides of the large square. Among the N \times N tiles in the square, determine how many tiles the circumference of the circle passes through.

Input

The first line contains an even integer N. (2 \le N \le 150,000,000)

Output

Print the number of tiles that the circumference of the circle passes through.