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 Main
{
    public static void main(String args[])throws IOException
    {
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
            int n=Integer.parseInt(in.readLine());
            StringTokenizer st=new StringTokenizer(in.readLine());
            int q=0;
            int val,r=0;
            for(int i=0;i<n;i++)
            {
                int x=Integer.parseInt(st.nextToken());
                if(i==0)
                {
                    if(x==0)
                    r=0;
                    else
                    r=n-x;
                    val=0;
                    //System.out.println(r+" "+val+" "+x);
                }
                else
                {
                    if(i%2!=0)
                    {
                        val=x-r;
                        //System.out.println(val);
                        if(val<0)
                        val=n+val;
                        
                    }
                    else
                    {
                        val=x+r;
                        if(val>=n)
                        val=val-n;
                    }
                }
            //  System.out.println(val+" "+i+" "+r);
                if(val!=q)
                {
                    break;
                }
                q+=1;
            }
            if(q==n)
            System.out.printf("Yes\n");
            else
            System.out.printf("No\n");
        }
    }