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.StringTokenizer;

/**
 * Created by Юля on 14.09.2015.
 */
public class SolverB556 {
    public static void main(String[] args) throws IOException {
        new SolverB556().run();
    }

    BufferedReader br;
    PrintWriter pw;
    StringTokenizer tokenizer;

    public String nextToken() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(br.readLine());
        }
        return tokenizer.nextToken();
    }

    public int nextInt() throws IOException, NumberFormatException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws IOException, NumberFormatException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws IOException, NumberFormatException {
        return Double.parseDouble(nextToken());
    }

    public void run() throws IOException {
//        br = new BufferedReader(new FileReader("input.txt"));
//        pw = new PrintWriter("output.txt");
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new OutputStreamWriter(System.out));

        solve();

        pw.flush();
        pw.close();
    }

    private void solve() throws IOException {
        int n=nextInt();
        int[] mas=new int[n];
        boolean ok =true;
        mas[0]=nextInt();
        for(int i=1;i<n;i++){
            mas[i]=nextInt();
            if(mas[i]-mas[i-1]!=1)
                ok=false;
        }

        if(ok) {
            pw.println("Yes");
            return;
        }
        for(int i=0;i<1000;i++){
            if(mas[0]==n-1)
                mas[0]=0;
            else
                mas[0]++;
            ok=true;
            for(int j =1;j<n;j++){
                if(j%2==0){
                    if(mas[j]==n-1)
                        mas[j]=0;
                    else
                        mas[j]++;
                }else {
                    if(mas[j]==0)
                        mas[j]=n-1;
                    else
                        mas[j]--;
                }
                if(mas[j]-mas[j-1]!=1)
                    ok=false;
            }
            if(ok){
                pw.println("Yes");
                return;
            }
        }
        pw.println("No");

    }
}
