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.util.Scanner;
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;
 
public class Main implements Runnable{
 
	static class InputReader
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			do 
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
	static LinkedList <Integer> adj[];
    static int co=0,f=0;
    
    static void Check2(int n){
        adj=new LinkedList[n+1];
        for(int i=0;i<=n;i++){
            adj[i]=new LinkedList();
        }
        
    }
    static void add(int i,int j){
       // if(!adj[i].contains(j))
        adj[i].add(j);
   // if(!adj[j].contains(i))
        adj[j].add(i);
        
     //   adj[j].add(i);
        
    }
	  public static void main(String[] args) throws Exception { 
    new Thread(null, new Main(), "Check2", 1<<26).start();// to increse stack size in java 
  }
  public void run(){
        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        //Scanner in=new Scanner(System.in);
    InputReader in=new InputReader(System.in);		
		PrintWriter w=new PrintWriter(System.out);
	
 
		
 
                int n=in.nextInt();
      int a[]=new int[n];
      
      
      int b[]=new int[n];
      for(int i=0;i<n;i++){
a[i]=in.nextInt();
          b[i]=i;
      
      }
      
      
      
      int val=(n-a[0])%n;
      
      int flag=0;
      for(int i=1;i<n;i++)
      {
          if(i%2!=0){
            
          int v=abs(a[i]-b[i]);
          int    v2=n-v;
              if(b[i]>a[i])v=v2;
        //      w.println(a[i]+" "+v);
              if(val!=v)flag=1;
              
          }
               else{
          int v=abs(a[i]-b[i]);
          int    v2=n-v;
              if(b[i]<a[i])v=v2;
      //        w.println(a[i]+" "+v);
              if(val!=v)flag=1;
                   
               }
      
      }
      if(flag==0)w.println("Yes");
      else
          w.println("No");
      
      
      
        w.close();
        
           
    }
    
    static void dfs(int i,int v[]){
        if(v[i]==1){
            return ;
        }
        else{
            
            v[i]=1;
            Iterator <Integer>p=adj[i].iterator();
            while(p.hasNext()){
                 Integer ne=p.next();
                
                    
                    
              dfs(ne,v);
     //          
       //        System.out.println(q+" "+i);
            //System.out.println(i+" "+max1+" "+max2);
            }
            
            
            
            
            
        }
        
        
    }
    static class node{
        
        int y;
        int val;
        
        node(int a,int b){
            
            y=a;
            val=b;
            
        }
        
        
    }
    
} 