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 static java.lang.Math.max;

import java.awt.Point;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class B implements Runnable {

    final static boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    final static String fileName = "";

    void init() throws IOException {
        if (ONLINE_JUDGE && fileName.isEmpty()) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }
        }
    }

    public static void main(String[] args) {
        new B().run();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws NumberFormatException, IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws NumberFormatException, IOException {
        return Long.parseLong(readString());
    }

    int[] readIntArray(int size) throws NumberFormatException, IOException {
        int[] arr = new int[size];
        for (int i = 0; i < size; i++) {
            arr[i] = readInt();
        }
        return arr;
    }

    static long timeIn;

    void time() {
        System.err.println("Time = " + (System.currentTimeMillis() - timeIn));
    }

    @Override
    public void run() {
        try {
            timeIn = System.currentTimeMillis();
            init();
            solve();
            out.close();
            time();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    private void solve() throws IllegalArgumentException, IOException {
        int n = readInt();
        int[] arr = readIntArray(n);

        int prev = -1;

        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                int cur = arr[i] > i ? i + n - arr[i] : i - arr[i];
                if (prev > -1) {
                    if (prev != cur) {
                        out.println("No");
                        return;
                    }
                }
                prev = cur;
            } else {
                int cur = arr[i] >= i ? arr[i] - i : arr[i] + n - i;
                if (prev > -1) {
                    if (prev != cur) {
                        out.println("No");
                        return;
                    }
                }
                prev = cur;
            }
        }
        
        out.println("Yes");
    }

}
