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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.util.HashSet;

public class CaseOfFakeNumbers {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        OutputStream out = new BufferedOutputStream(System.out);
        int n = Integer.parseInt(br.readLine());
        String init = br.readLine();
        int[] arr = new int[n];
        String[] l = init.split("\\s+");

        String tar = "";
        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(l[i]);
            tar += i + "";
        }

        init = init.replaceAll("\\s+", "");
        boolean flag = true;
        HashSet<String> set = new HashSet<String>();
        set.add(init);

        while (true) {
            String s = "";
            for (int i = 0; i < n; i++) {
                if (i % 2 == 0) {
                    int temp = arr[i] + 1;

                    if (temp <= n - 1)
                        arr[i]++;
                    else
                        arr[i] = 0;
                } else {
                    int temp = arr[i] - 1;

                    if (temp >= 0)
                        arr[i]--;
                    else
                        arr[i] = n - 1;
                }
                s += arr[i] + "";
            }

            if (!s.equals(tar) && set.contains(s)) {
                flag = false;
                break;
            } else if (s.equals(tar))
                break;
            else
                set.add(s);

        }

        if (flag)
            out.write(("Yes\n").getBytes());
        else
            out.write(("No\n").getBytes());

        out.flush();
        br.close();

    }

}
