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.

安卓侦探安德鲁伊德是银河系闻名的侦探。他目前正在调查一起造假案，涉案人员制造了著名斯托尔普齿轮谜题（Stolp's gears）的仿冒品——这种谜题的知名度曾堪比魔方。

该谜题最重要的组成部分是一个按钮和一排 $n$ 个完全相同的齿轮。每个齿轮有 $n$ 个齿，按逆时针顺序依次标有数字 $0$ 到 $n-1$。当你按下按钮时，第一个齿轮顺时针旋转，第二个齿轮逆时针旋转，第三个齿轮顺时针旋转，依此类推。

此外，每个齿轮恰好有一个“激活齿”（active tooth）。当齿轮转动时，新的激活齿即为当前激活齿沿旋转方向的下一个齿。例如，若 $n = 5$，当前激活齿标号为 $0$，则顺时针旋转会使标号为 $1$ 的齿变为激活齿，而逆时针旋转则会使标号为 $4$ 的齿变为激活齿。

安德鲁伊德记得，真正的谜题具有如下性质：存在某种按按钮的次数（可多次），使得最终从第一个齿轮到第 $n$ 个齿轮的激活齿上的数字依次构成序列 $0,\,1,\,2,\,\dots,\,n-1$。请编写一个程序，判断给定的谜题是真品还是赝品。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 1000$）——齿轮的数量。

第二行包含 $n$ 个数字 $a_1, a_2, \dots, a_n$（$0 \leq a_i \leq n - 1$）——活跃齿的序列：第 $i$ 个齿轮的活跃齿上标有数字 $a_i$。

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

如果给定的斯托尔普齿轮谜题是真实的，则在一行中输出“Yes”（不带引号）；否则输出“No”（不带引号）。

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.

在第一个样例测试中，当你第一次按下按钮时，活动齿的序列为 $2\ 2\ 1$；当你第二次按下按钮时，得到 $0\ 1\ 2$。