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.Arrays;
import java.util.StringTokenizer;
public class Main{
    public static void main(String[] args)throws IOException {
        FastReader sc=new FastReader();
        OutputStream output=System.out;
        PrintWriter out=new PrintWriter(output);
        //InputStream input = System.in;
        //Scanner sc = new Scanner(input);
        int n=sc.nextInt();
        int[] arr=new int[n];
        int[] ans=new int[n];
        int[] value=new int[n];
        for(int i=0;i<n;i++) {
            arr[i]=sc.nextInt();
        }
        for(int i=0;i<n;i++)
            value[i]=i;
        //Arrays.sort(value);
        boolean flag=true,count=true;
        int add=0;
        while (flag) {
            for(int i=0;i<n;i++) {
                if (i % 2 == 1) {
                    ans[i]=(arr[i]+1)%(n);
                }
                else
                    ans[i]=(arr[i]+n-1)%(n);
            }
            if (add == n - 1&&n!=1) {
                count=false;
                out.println("No");
                break;
            }
            if(Arrays.equals(ans,value)||Arrays.equals(arr,value))
                break;
            else if(!Arrays.equals(ans,value)&&!Arrays.equals(arr,value))
                for(int i=0;i<n;i++)
                    arr[i]=ans[i];
            add++;
        }
        if(count)
            out.println("Yes");
        out.close();
    }


    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}