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.
/*
 * 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.
 */
//package codeforces_reloded;

import java.util.Scanner;

/**
 *
 * @author shubham
 */
public class B_310 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner s=new Scanner(System.in);
        
        int a=s.nextInt();
        String str="";
        for (int i = 0; i < a; i++) {
            str+=""+i;
            
        }
        int ar[]=new int[a];
        for (int i = 0; i < a; i++) {
            ar[i]=s.nextInt();
            
        }
        
        for (int j = 0; j < a; j++) {
            
        String str1="";
        for (int i = 0; i < a; i++) {
            
            if(i%2==0){
                if(ar[i]==a-1){
                    ar[i]=0;
                }
                else
                    ar[i]++;
            }
            else{
                if(ar[i]==0){
                    ar[i]=a-1;
                }
                else{
                    ar[i]--;
                }
            }
            str1+=ar[i];
        }
        
        if(str1.trim().equals(str.trim())){
            System.out.println("YES");
            return;
        }
        }
        
        System.out.println("NO");
    }
    
}
