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.IOException;
import java.util.Arrays;
import java.util.Scanner;
import java.util.TreeSet;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author Ivan
 */
public class secondProblem {

    
    static boolean isSorted(int[] array)
    {
        int length=array.length;
        for(int i=0;i<length-1;i++)
            if(array[i+1]<=array[i])
                return false;
        return true;
    }
    static int[] doOperation(int[] array,int length)
    {
        for(int i=0;i<length;i++)
            if((i+1)%2==0)
            {
                if(array[i]==0)
                    array[i]=length-1;
                else
                    array[i]--;
            }
        else
            {
                if(array[i]==length-1)
                    array[i]=0;
                else
                    array[i]++;
            }
        return array;
    }
    public static void main(String[] args) throws IOException {
        Scanner sc=new Scanner(System.in);
        TreeSet<int[]> set=new TreeSet<int[]>();
        int length=sc.nextInt();
        int[] array=new int[length];
        int[] aux=new int[length];
        for(int i=0;i<length;i++)
        {
            array[i]=sc.nextInt();
            aux[i]=array[i];
        }
        boolean truth=true;
        long iteration=0;
        while(true)
        {
            array=doOperation(array,length);
           // System.out.println(Arrays.toString(array));
            if(isSorted(array))
                break;
            if(iteration==50000)
            {
                truth=false;
                break;
            }
            iteration++;
        }
        if(truth)
            System.out.print("Yes");
        else
            System.out.print("No");
            
        
    }
    
}
