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B. Case of Fake Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAndrewid 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.

Input

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}.

Output

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

Examples

Input

3

1 0 0

Output

Yes

Input

5

4 2 1 4 3

Output

Yes

Input

4

0 2 3 1

Output

No

Note

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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