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.ArrayList;
import java.util.Arrays;

/**
 * Created by Lex on 07.07.15.
 */
public class Shesterenki {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int length = Integer.parseInt(br.readLine());
        String str = br.readLine();
        ArrayList<String> digs = new ArrayList<String>(Arrays.asList(str.split(" ")));
        ArrayList<Integer> ints = new ArrayList<Integer>(length);
        for (int i = 0; i < digs.size(); i++) {
            ints.add(i, Integer.parseInt(digs.get(i)));
        }

        boolean okay=false;
        for(int i=0; i <= length; i++) {
            okay = true;
            for (int j = 0; j < length; j++) {
                ints.set(j, rotate(ints.get(j), length, j));
                if(okay && j>0 && ints.get(j-1)!=ints.get(j)-1){
                    okay=false;
                }
            }
            if(okay){
                out.println("Yes");
                break;
            }
        }
        if(!okay)
            out.println("No");
        out.close();
    }

    public static int rotate(int val, int lng, int pos){
        if(pos == 0 || pos % 2 == 0){
            if(val < lng-1){
                return val+1;
            }else {
                return 0;
            }
        } else {
            if(val>0){
                return val-1;
            } else {
                return lng-1;
            }
        }
    }
}
