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.util.*;
public class Sol2
{
    public static void main(String[] args)throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        String[] t1=br.readLine().split(" ");
        int[] co=new int[n];
        for(int i=0;i<n;i++)
        {
            co[i]=Integer.parseInt(t1[i]);
        }
        int flag=1;
        for(int j=0;j<n;j++)
        {
            if(co[j]!=j)
            {
                flag=-1;
                break;
            }
        }
        if(flag==1)
        {
            System.out.println("Yes");
        }
        else
        {
            flag=1;
            int mark=-1;
            for(int k=0;k<n;k++)
            {
                flag=1;
                for(int l=0;l<n;l++)
                {
                    if(l%2==0)
                    {
                        if(co[l]!=n-1)
                        {
                            co[l]++;
                        }
                        else if(co[l]==n-1)
                        {
                            co[l]=0;
                        }
                    }
                    else if(l%2!=0)
                    {
                        if(co[l]!=0)
                        {
                            co[l]--;
                        }
                        else if(co[l]==0)
                        {
                            co[l]=n-1;
                        }
                    }
                }
                for(int j=0;j<n;j++)
                {		
                    if(co[j]!=j)
                    {
                        flag=-1;
                        break;
                    }
                }
                if(flag==1)
                {
                    System.out.println("Yes");
                    mark=1;
                    break;
                }
            }
            if(mark==-1)
            {
                System.out.println("No");
            }
        }
    }
}