CF556B Case of Fake Numbers

Andrewid the Android is a galaxy-famous detective. He is now investigating a case of frauds who make fake copies of the famous Stolp's gears, puzzles that are as famous as the Rubik's cube once was. Its most important components are a button and a line of $ n $ similar gears. Each gear has $ n $ teeth containing all numbers from $ 0 $ to $ n-1 $ in the counter-clockwise order. When you push a button, the first gear rotates clockwise, then the second gear rotates counter-clockwise, the the third gear rotates clockwise an so on. Besides, each gear has exactly one active tooth. When a gear turns, a new active tooth is the one following after the current active tooth according to the direction of the rotation. For example, if $ n=5 $ , and the active tooth is the one containing number $ 0 $ , then clockwise rotation makes the tooth with number $ 1 $ active, or the counter-clockwise rotating makes the tooth number $ 4 $ active. Andrewid remembers that the real puzzle has the following property: you can push the button multiple times in such a way that in the end the numbers on the active teeth of the gears from first to last form sequence $ 0,1,2,...,n-1 $ . Write a program that determines whether the given puzzle is real or fake.

The first line contains integer $ n $ ( $ 1

In a single line print "Yes" (without the quotes), if the given Stolp's gears puzzle is real, and "No" (without the quotes) otherwise.

In the first sample test when you push the button for the first time, the sequence of active teeth will be 2 2 1, when you push it for the second time, you get 0 1 2.