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.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of gears.

The second line contains n digits a1, a2, ..., an (0 ≤ ai ≤ n - 1) — the sequence of active teeth: the active tooth of the i-th gear contains number ai.

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.
import java.lang.*;
import java.io.*;
import java.util.*;


public class Numbers {
	
	public static void main(String[] args) throws java.lang.Exception {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(in, out);
		out.close();
	}
}

class TaskA {
	public final static int maxn = 1005;
	int[] a = new int[maxn];
	
	public void solve(InputReader in, PrintWriter out) {
		int n = in.nextInt();
		int[] c = new int[n];
		int[] c_ = new int[n];
		int i, j;
		
		// clockwise
		for (i=0; i<n-1; ++i)
			c[i] = i+1;
		c[n-1] = 0;
		// counter-clockwise
		for (i=n-1; i>0; --i)
			c_[i] = i-1;
		c_[0] = n-1;
		
		for (i=0; i<n; ++i)
			a[i] = in.nextInt();
		
		for (i=0; i<n; ++i) {
			if (judge(n)) {
				out.println("Yes");
				return ;
			}
			for (j=0; j<n; ++j) {
				if ((j&1) > 0) {
					a[j] = c_[a[j]];
				} else {
					a[j] = c[a[j]];
				}
			}
		}
		out.println("No");
	}
	
	private boolean judge(int n) {
		for (int i=0; i<n; ++i)
			if (a[i] != i)
				return false;
		return true;
	}
}

class InputReader {
	public BufferedReader reader;
	public StringTokenizer tokenizer;
	
	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}
	
	public String next() {
		while (tokenizer==null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}
	
	public int nextInt() {
		return Integer.parseInt(next());
	}
	
	public long nextLong() {
		return Long.parseLong(next());
	}
}
