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.*;

public class C310_1_B {
    public static void main(String []args) throws IOException {
        new Solution().solve();
    }
}

class Solution {
    FastReader fr = new FastReader();
    BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

    public void solve() throws IOException {
        int n = fr.nextInt();
        int []data = new int[n];
        for (int i = 0; i < n; i++) {
            data[i] = fr.nextInt();
        }

        for (int i = 0; i < n; i++) {
            boolean solution = false;
            for (int j = 0; j < n; j++) {
                if (j % 2 == 0) {
                    data[j] = data[j] == n-1 ? 0 : data[j]+1;
                } else {
                    data[j] = data[j] == 0 ? n-1 : data[j]-1;
                }
                if (j == 0) {
                    solution = data[j] == 0;
                }
                if (j > 0) {
                    solution &= data[j-1] == data[j] - 1;
                }
            }
            if (solution) {
                System.out.println("yes");
                return;
            }
        }
        System.out.println("no");
    }
}

class FastReader {
    private InputStream is;
    private int bufferSize = 1 << 17;
    private byte []buffer = new byte[bufferSize];
    private int currentIndex = 0;
    private int lastIndex = 0;

    public FastReader() {
        is = new BufferedInputStream(System.in);
//      try {
//          is = new BufferedInputStream(new FileInputStream(new File("test.txt")));
//      } catch (FileNotFoundException e) {
//          e.printStackTrace();
//      }
    }

    public int nextInt() {
        int result = 0;
        int minus = 1;

        byte character = readNext();

        while (character == ' ' || character == '\n' || character == '\r') {
            character = readNext();
        }

        if (character == '-') {
            minus = -1;
            character = readNext();
        }

        while (character != ' ' && character != '\n' && character != '\r') {
            result = result * 10 + (character - '0');
            character = readNext();
        }

        return minus*result;
    }

    public long nextLong() {
        long result = 0;
        int minus = 1;

        byte character = readNext();

        while (character == ' ' || character == '\n' || character == '\r') {
            character = readNext();
        }

        if (character == '-') {
            minus = -1;
            character = readNext();
        }

        while (character != ' ' && character != '\n' && character != '\r') {
            result = result * 10 + (character - '0');
            character = readNext();
        }

        return minus*result;
    }

    public String nextString() {
        StringBuffer result = new StringBuffer();

        byte character = readNext();

        while (character == ' ' || character == '\n' || character == '\r') {
            character = readNext();
        }

        while (character != ' ' && character != '\n' && character != '\r') {
            result.append((char)character);
            character = readNext();
        }

        return result.toString();
    }

    public String nextLine() {
        StringBuffer result = new StringBuffer();

        byte character = readNext();

        while (character == '\n' || character == '\r') {
            character = readNext();
        }

        while (character != '\n' && character != '\r') {
            result.append((char)character);
            character = readNext();
        }

        return result.toString();
    }

    private byte readNext() {
        if (currentIndex == lastIndex) {
            try {
                lastIndex = is.read(buffer, 0, bufferSize);
            } catch (IOException e) {
                throw new RuntimeException("What?");
            }
            if (lastIndex == -1) {
                buffer[0] = -1;
            }
            currentIndex = 0;
        }

        return buffer[currentIndex++];
    }
}