A9891 | 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 $n$ ( $1<=n<=1000$ ) — the number of gears.

The second line contains $n$ digits $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=n-1$ ) — the sequence of active teeth: the active tooth of the $i$ -th gear contains number $a_{i}$ .

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