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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        int n = in.readInt();
                int[] a = new int[n];
                for(int i = 0; i < n; ++i)
                    a[i] = in.readInt();
                int[] d = new int[n];
                for(int i = 0; i < n; ++i){
                    if(i%2 == 0){
                        if(a[i] < i){
                            d[i] = n - i + a[i];
                        }
                        else{
                            d[i] = a[i] - i;
                        }
                    }
                    else{
                        d[i] = i - 0;
                        if(a[i] < n && a[i] > i){
                            d[i] += n - a[i];
                        }
                        else{
                            d[i] -= a[i];
                        }
                    }
                }
                //for(int i = 0; i < n; ++i){
                //    out.println(d[i]);
                //}
                int ans = 1;
                for(int i = 1; i < n; ++i){
                    if(d[i] != d[i-1]){
                        ans = 0;
                        break;
                    }
                }
                if(ans == 1){
                    out.println("Yes");
                }
                else{
                    out.println("No");
                }
        out.close();
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public void print(long[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(array[i]);
        }
    }

    public void printLine(long[] array) {
        print(array);
        writer.println();
    }
        public void println(Object o){
            writer.println(o);
        }
    public void close() {
        writer.close();
    }

}

class ArrayUtils {

    public static int[] createOrder(int size) {
        int[] order = new int[size];
        for (int i = 0; i < size; i++)
            order[i] = i;
        return order;
    }

//  public static int[] sort(int[] array, IntComparator comparator) {
//      return sort(array, 0, array.length, comparator);
//  }
//
//  public static int[] sort(int[] array, int from, int to, IntComparator comparator) {
//      if (from == 0 && to == array.length)
//          new IntArray(array).inPlaceSort(comparator);
//      else
//          new IntArray(array).subList(from, to).inPlaceSort(comparator);
//      return array;
//  }

}
