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.

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author Administrator
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

//codeforce
public class Main {

    private static BufferedReader in;
    private static PrintWriter out;
    private static StringTokenizer input;

    public static void main(String[] args) throws IOException {
        // -------------------------------------------------------------------------
        // Initializing...
        new Main();
        // -------------------------------------------------------------------------
        // put your code here... :)

        int n = nextInt();

        int[] arr = new int[n];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = nextInt();
        }
        boolean found = false;
        int[] tempArr =new int[n];
        System.arraycopy( arr, 0, tempArr, 0, arr.length );
        while (!found) {
            if (containSequence(tempArr,n)) {
                System.out.println("Yes");
                break;
            } else {
                if (Arrays.equals(arr, tempArr)) {
                    found = true;
                    System.out.println("No");
                }else{
                    Arrays.toString(tempArr);
                }
            }
        }

        // writeln("");
        // -------------------------------------------------------------------------
        // closing up
        end();
        // --------------------------------------------------------------------------

    }

    public static void addCycleCounter(int[] myArr, int n) {
        for (int i = 0; i < myArr.length; i += 2) {
            myArr[i] = (myArr[i] + 1) % n;
        }
        for (int i = 1; i < myArr.length; i += 2) {
            myArr[i] = ((((myArr[i] - 1) % n) + n) % n);
        }
    }

    public static boolean containSequence(int[] myArr,int n) {
        for (int i = 0; i < myArr.length; i++) {
            if (myArr[i] != i) {
                addCycleCounter(myArr, n);
                return false;
            }
        }
        return true;
    }

    public Main() throws IOException {
        // Input Output for Console to be used for trying the test samples of
        // the problem
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        // -------------------------------------------------------------------------
        // Initalize Stringtokenizer input
        input = new StringTokenizer(in.readLine());
    }

    private static int nextInt() throws IOException {
        if (!input.hasMoreTokens())
            input = new StringTokenizer(in.readLine());
        return Integer.parseInt(input.nextToken());
    }

    private static long nextLong() throws IOException {
        if (!input.hasMoreTokens())
            input = new StringTokenizer(in.readLine());
        return Long.parseLong(input.nextToken());
    }

    private static double nextDouble() throws IOException {
        if (!input.hasMoreTokens())
            input = new StringTokenizer(in.readLine());
        return Double.parseDouble(input.nextToken());
    }

    private static String nextString() throws IOException {
        if (!input.hasMoreTokens())
            input = new StringTokenizer(in.readLine());
        return input.nextToken();
    }

    private static void write(String output) {
        out.write(output);
        out.flush();
    }

    private static void writeln(String output) {
        out.write(output + "\n");
        out.flush();
    }

    private static void end() throws IOException {
        in.close();
        out.close();
        System.exit(0);
    }

}
