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.Scanner;

// Case of Fake Numbers
public class ID_556_B {
	static int n;
	static int[] a;
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		a = new int[n];
		for (int i = 0; i < n; i++) a[i] = sc.nextInt();
		
		int first, i;
		if (a[0] == 0) first = 0;
		else first = (n - 1) - a[0] + 1;
		
		boolean isNo = false;
		
		for (i = 0; i <= n - 1; i += 2) {
			if (plus(a[i], first) != i || 
					(i + 1 <= n -1 && minus(a[i+1], first) != i + 1)) {
				System.out.println("NO");
				isNo = true;
				break;
			}
		}
		
		// if (i < n - 2)
		if (isNo == false)
			System.out.println("YES");
		sc.close();
	}
	
	public static int plus(int x, int y) {
		if (x + y > n - 1) return (x - (n - y));
		else return (x + y);
	}
	
	public static int minus(int x, int y) {
		if (x - y < 0) return (x + (n - y));
		else return (x - y);
	}
}
