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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class CaseOfFakeNumbers {
    private static BufferedReader br;
    private static StringTokenizer st;
    
    public static void main(String[] args) throws Exception {
        PrintWriter pw = new PrintWriter(System.out);
        reader(System.in);
        int n = nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        int period = n - a[0];
        int temp = 0;
        boolean status = true;
        for (int i = 2; i <= n; i++) {
            if (i % 2 == 0) {
                temp = a[i - 1] - period;
                if (temp < 0) {
                    temp = n + temp;
                }
                if (temp != i - 1) {
                    status = false;
                    break;
                }
            }
            else {
                temp = (a[i - 1] + period) % n;
                if (temp != i - 1) {
                    status = false;
                    break;
                }
            }
        }
        pw.println(status ? "Yes" : "No");
        pw.close();
    }

    static void reader(InputStream stream) {
        try {
            br = new BufferedReader(new InputStreamReader(stream));
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    static String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }
}
