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.Reader;
import java.io.FileInputStream;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.util.Locale;
import java.io.UnsupportedEncodingException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;
import java.io.File;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Yakutov Dmitry
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastReader in = new FastReader(inputStream);
		FastWriter out = new FastWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, FastReader in, FastWriter out) {
        int n = in.nextInt();
        int[] a = in.nextArrayInt(n);
        int count = a[0];
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                a[i] = (a[i] + n - count) % n;
            } else {
                a[i] = (a[i] + count) % n;
            }
        }
        boolean ans = true;
        for (int i = 0; i < n; i++) {
            ans &= a[i] == i;
        }
        out.println(ans ? "Yes" : "No");
    }
}

class FastReader extends BufferedReader {

    private StringTokenizer stringTokenizer;

    public FastReader(InputStream inputStream) {
        super(new InputStreamReader(inputStream));
    }

    public String nextToken() {
        try {
            while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                stringTokenizer = new StringTokenizer(readLine());
            }
            return stringTokenizer.nextToken();
        } catch (IOException e) {
            return null;
        }
    }

    public int nextInt() {
        return Integer.parseInt(nextToken());
    }

    public int[] nextArrayInt(int size) {
        int[] ret = new int[size];
        for (int i = 0; i < size; i++) {
            ret[i] = nextInt();
        }
        return ret;
    }

}

class FastWriter extends PrintWriter {

    public PrintWriter printf(String format, Object ... args) {
        return super.printf(Locale.US, format, args);
    }

    public FastWriter(OutputStream out) {
        super(out);
    }

}

