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.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
		
	public static void main(String[] args) throws IOException {
		new Main().solve();
	}
	
	PrintWriter out;
	int n;
	int m;
	boolean[] use;
	int mod = 1000000007;
	int rv = 0;
	ArrayList<Integer>[] g;
	int[] res;
	int p, q;
	HashMap<Long, Long> map = new HashMap();
	void solve() throws IOException{
		Reader in = new Reader("input.txt");
		out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
		//out = new PrintWriter(new FileWriter(new File("output.txt"))); 
		
		
		int n = in.nextInt();
		int[] a = new int[n];
		
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		
		boolean ans = true;
		
		for (int i = 0; i < n+2; i++) {
			
			ans = true;
			
			for (int j = 0; j < n; j++) {
				if ((j & 1) == 0)
					a[j] = (a[j]+1)%n;
				else {
					a[j] = (a[j]-1);
					if (a[j] < 0)
						a[j] = n-1;
				}
				if (j > 0) {
					if (a[j]-a[j-1] != 1)
						ans = false;
				}
			}
			
			if (ans)
				break;
			
		}
		
		out.print(ans?"Yes":"No");
		out.flush();
		out.close();
		
	}
	
	long pow(int x, int m) {
		if (m == 0)
			return 1;
		return x*pow(x, m-1);
	}

	
class Pair implements Comparable<Pair> {
		
		int a;
		int b;
		
		Pair (int a, int b) {
			this.a = a;
			this.b = b;
		}

		@Override
		public int compareTo(Pair p) {
			if (a < p.a)
				return -1;
			if (a > p.a)
				return 1;
			
			if (b < p.b)
				return -1;
			
			if (b > p.b)
				return 1;
			
			return 0;
		}
		
	}

	class Item implements Comparable<Item> {

		int a;
		int b;
		long u;
		
		Item(int v, int l, long z) {
			this.a = v;
			this.b = l;
			this.u = z;
		}
		
		@Override
		public int compareTo(Item item) {
			
			if (u > item.u)
				return 1;
			else
			if (u < item.u)
				return -1;
			else {
				return 0;
			}
						
		}
		
	}
	
	class Reader {
	    
	    StringTokenizer token;
	    BufferedReader in;
	    
	    public Reader(String file) throws IOException {
	       // in = new BufferedReader( new FileReader( file ) );
	       in = new BufferedReader( new InputStreamReader( System.in ) );
	    }
	    
	    public byte nextByte() throws IOException {
	        return Byte.parseByte(Next());
	    }
	    
	    public int nextInt() throws IOException {
	        return Integer.parseInt(Next());
	    }
	    
	    public long nextLong() throws IOException {
	        return Long.parseLong(Next());
	    }
	    
	    public String nextString() throws IOException {
	        return in.readLine();
	    }
	    
	    public String Next() throws IOException {
	        while (token == null || !token.hasMoreTokens()) {
	            token = new StringTokenizer(in.readLine());
	        }
	        return token.nextToken();
	    }

	    
	}
	
}
	
	

	
