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.io.File;
import java.io.FileNotFoundException;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;
import java.util.regex.Matcher;
import java.util.regex.Pattern;


public class Sol {

	
	public static void main(String args[]) throws FileNotFoundException {
		
		//Scanner sc = new Scanner(new File("in.in"));
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int tab[] = new int[n];
		int mir[]=new int[n];
		int des[] = new int[n];
		sc.nextLine();
		for(int i=0;i<n;i++){
			tab[i]=sc.nextInt();
			des[i] = tab[i];
			mir[i]=i;
		}
		int a=0;
		boolean find =false;
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				if(j%2==0){
					tab[j]++;
					if(tab[j]==n)
						tab[j]=0;
				}
				else{
					tab[j]--;
					if(tab[j]==-1)
						tab[j]=n-1;
				}
			
				
			}

			
			if(tab[0]==0){
				find = compareArray(tab,mir);
				break;
			}
			
			
		}
		
		
		if(find){
			System.out.println("Yes");
		}
		else
			System.out.println("No");
		
	}
	
	public static boolean compareArray(int t[],int m[]){
		for(int i=0;i<t.length;i++)
		{
			if(t[i]!=m[i])
				return false;
			
		}
		return true;
		
	}
	
}


