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 bucky{




public static void main (String args[]) {

Scanner input=new Scanner(System.in);

HashMap<String, Integer> map1= new HashMap<String, Integer>();
HashMap<Integer, Integer> map2= new HashMap<Integer, Integer>();
HashMap<Integer, Integer> linieleft= new HashMap<Integer, Integer>();
HashMap<Integer, Integer> linieright= new HashMap<Integer, Integer>();

	
	
			
			int n=input.nextInt();
			
			
			int nums[]=new int[n];
			int x=0;
			int adev=0;
			
			for(int i=0;i<n;i++){
			nums[i]=input.nextInt();
			
			if(i==0) {x=n-(nums[0]+n)%n; nums[0]=0;
			
		//	System.out.println("x="+x);
		}
			
			
			else {
			if(i%2==1) {if(nums[i]-x<0) nums[i]=n+nums[i]-x;
						else nums[i]-=x;
						
						
						}
						
			else {nums[i]+=x;	nums[i]=nums[i]%n;}
			
		
			
			
			
			}
			
				if(i>0 && i<n && nums[i]-nums[i-1]!=1) {adev=1;break;}
			//	System.out.println(i+"  nums[i]="+nums[i]);
				
			}
			
			if(adev==0) System.out.println("Yes");
			else System.out.println("No");
			
	
		}
		
		}
		
		
		
		
		
		
		
		
	