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.
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package caseoffakenumbers;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 *
 * @author PrudhviNIT
 */
public class Main{

    /**
     * @param args the command line arguments
     */
    static int clock(int active, int n, int times){
        
        int ans =  active+times;
        //System.out.println("ans is "+ans+"active is "+active+" times is "+times);
        return ans%n;
    }
    static int anticlock(int active, int n , int times){
        times = n-times;
        //System.out.println("Rotate "+times+" times");
        return clock(active,n,times);
    }
    
    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine().trim());
        int a[] = new int[n],i;
        String str[] = br.readLine().trim().split(" ");
        for(i=0;i<n;i++){
            a[i] = Integer.parseInt(str[i]);
        }
        int t = a[0],count=0;
        while(t!=0){
            t = clock(t,n,1);
            count++;
        }
        //System.out.println("Count is "+count);
        boolean flag = true;
        for(i=1;i<n;i++){
            t = a[i];
            if(i%2==1){
                t = anticlock(t,n,count);
            }
            else{
                t = clock(t,n,count);
            }
            //System.out.println("t is "+t);
            if(t!=i){
                flag = false;
                break;
            }
        }
        if(flag){
            System.out.println("Yes");
        }
        else{
            System.out.println("No");
        }
    }
    
}
