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.util.*;

public class Pzzl {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = Integer.valueOf(sc.nextLine());

		String s = sc.nextLine();
		String[] sa = s.split(" ");
		int[] ia = new int[n];
		for (int j = 0; j < sa.length; j++) {
			ia[j] = Integer.valueOf(sa[j]);
		}

		StringBuilder sb = new StringBuilder();

		for (int k = 0; k < n; k++) {
			sb.append(k);
		}

		String fin = sb.toString();

		boolean b = false;
		int p = 0;
	//	System.out.println(fin);
		while (p < 5000) {
			String tep = str(ia);
	//		System.out.println(tep);
			if (tep.equals(fin)) {
				b = true;
				break;
			}
			int kk = 0;
			for (int u = 0; u < n; u++) {
				if (kk == 0)
					ia[u] = (ia[u] + 1) % n;
				else {
					if (ia[u] == 0)
						ia[u] = n - 1;
					else
						ia[u] = (ia[u] - 1) % n;
				}
				kk = 1 - kk;
			}
			p++;
		}

		if (b)
			System.out.println("Yes");
		else
			System.out.println("No");

	}

	private static String str(int[] ia) {
		StringBuilder sb = new StringBuilder();

		for (int k = 0; k < ia.length; k++) {
			sb.append(ia[k]);
		}

		return sb.toString();

	}

}
