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.Integer.parseInt;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.nio.charset.StandardCharsets;
import java.util.StringTokenizer;


public class con556_B {

	static int MB = 1 << 20;
	static BufferedReader br = new BufferedReader(new InputStreamReader(
			System.in, StandardCharsets.US_ASCII), 10 * MB);
	static StringTokenizer st;

	static String NL() throws Exception {
		String s = br.readLine();
		st = new StringTokenizer(s);
		return s;
	}

	static String NT() {
		return st.nextToken();
	}

	public static void main(String[] args) throws Exception {
		NL();
		int n = parseInt(NT());
		NL();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = parseInt(NT());
		}
		System.out.println(solve(n, a) ? "Yes" : "No");
	}

	static boolean solve(int n, int[] a) {
		int m = n - a[0];
		for (int i = 0; i < n; i++) {
			if ( (i & 1) == 1) {
				a[i] = (a[i] + n - m) % n;
			} else {
				a[i] = (a[i] + m ) % n;
			}
		}
		return check(a);
	}

	private static boolean check(int[] a) {
		for (int i = 1; i < a.length; i++) {
			if (a[i] != a[i-1] + 1) return false;
		}
		return true;
	}
	
}
