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.*;
import java.io.*;

public class cp{

    public static void main(String[] args) {
    
        Scanner sc = new Scanner();

        int n = sc.nextInt();

        int ar[] = new int[n];

        int tmp[] = new int[n];

        for(int i=0;i<n;i++)
        {
            ar[i]=tmp[i]=sc.nextInt();
        }

//100
//221
//012
//100

boolean poss = false;
        do{
            for(int i=0;i<n;i++)
            {
                if((i&1)==1)
                {
                    ar[i]=(ar[i]-1+n)%n;
                }else ar[i]=(ar[i]+1)%n;
            }
             if(incr(ar))
            {
                poss=true;
                break;
            }

        }while(!same(ar,tmp));

        if(poss)
            out.println("Yes");
        else out.println("No");

        out.close();
    }

    static boolean incr(int ar[])
    {
        for(int i=0;i<ar.length-1;i++)
        {
            if(ar[i+1]<=ar[i])
            {
                return false;
            }
        }
        return true;
    }

    static boolean same(int ar[],int br[])
    {
        int q = 0;

        for(int i=0;i<ar.length;i++)
        {
            if(ar[i]!=br[i])
            {
                q++;
                break;
            }
        }
        return q==0;
    }

    static  PrintWriter out=new PrintWriter(System.out);
    static class Scanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String nextLine() {
            while (!st.hasMoreTokens())
                try { 
                                        st=new StringTokenizer(br.readLine());                             
                                } catch (IOException e) {}
            return st.nextToken();
        }     
        int nextInt() {
            return Integer.parseInt(nextLine());
        }
        Double nextDouble() {
            return Double.parseDouble(nextLine());
        }
        long nextLong() {
            return Long.parseLong(nextLine());
        }
    }
}

//5 4 5 5 5