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  final class stolp
{
	public static void main(String arg[])
	{
		Scanner br=new Scanner(System.in);
		int n=Integer.parseInt(br.nextLine());
		int a[]=new int[n+1];
		int done=0,flag=0;
		a[0]=-1;
		for(int i=1;i<=n;i++)
			a[i]=br.nextInt();
		if(n==1)
		{
			System.out.print("Yes");
			System.exit(0);

		}
		for(int j=1;j<=n;j++)
			{flag=1;
				for(int k=1;k<=n;k++)
				{
					if(k%2!=0)
					{
						if(a[k]!=n-1)
						a[k]+=1;
						else
							a[k]=0;
					}
					else
					{
						if(a[k]!=0)
							a[k]-=1;
						else
							a[k]=n-1;
					}
					if(k>=2 && a[k]-a[k-1]==1 && a[1]==0)
						done=1;
					else if(k==1)
						done=1;
					else done=0;
					if(done==0)
						flag=0;

				}
				if(flag==1)
					break;
			}
			if(flag==1)
				System.out.print("Yes");
			else
				System.out.print("No");
}
}