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;


public class Solution {
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		in.nextLine();
		int[] a = new int[n];
		int[] b = new int[n];
		for(int i=0;i<n;i++){
			a[i] = in.nextInt();
		}
		for(int i=0;i<n;i++){
			b[i] = i;
		}
		int c = n;
		int p = 0;
		for(int i=n;i>0;i--){
			int o = f1(a,b);
			p = p+o;
		}
		if(p>0){
			System.out.println("YES");
		}
		else{
			System.out.println("NO");
		}
		
		
		
	}
	
	
	public static int f1(int[] a, int[] b){
		int count = 0;
		int max = a.length;
		int c = max;
		for(int i=0;i<a.length;i++){
			if(a[i] == b[i]){
				count++;
			}
		}
		if (count == a.length){
			return 1;
		}
		else{
			for(int i=0;i<b.length;i++){
				if (i%2 == 0){
					b[i] = (b[i]+1) % max;
				}
				else if(1%2 != 0 && b[i] == 0){
					b[i] = max - 1;
				}
				else if(i%2 != 0 && b[i] != 0){
					b[i] = (b[i] -1)%max;
				}
			}
		}
		return 0;
	}
		
	}
	


