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.Scanner;


public class P006 {
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner scr = new Scanner(System.in);
        Gear g = new Gear();
        int n = scr.nextInt();
        int arr[] = new int[n];
        for(int i=0;i<n;i++){
            arr[i] = scr.nextInt();
        }
        boolean flag = false;
        for(int i=n;i>0;i--){
            for(int j=0;j<n;j++){
                if(j%2==0)
                arr[j] = g.clockwise(n,arr[j]);
                else
                arr[j] = g.counterclockwise(n, arr[j]);
            }

            int cnt=0;
            for(int k=0;k<n;k++){
                if(arr[k]!=k)
                    break;
                else
                    cnt++;
            }
            if(cnt==n){
                flag = true;
                break;
            }
        }
        if(flag==true)
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

class Gear{
    public int clockwise(int n,int a){
        if(a!=n-1)
            a++;
        else
            a=0;
        return a;
    }
    
    public int counterclockwise(int n,int a){
        if(a!=0)
            a--;
        else
            a=n-1;
        return a;
    }
}