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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class CaseOfFakeNumbers {

    public static void main(String[] args) throws Exception{
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        int size = Integer.parseInt(inp.readLine());
        
        String[] x = inp.readLine().split("\\s+");
        Obj[] array = new Obj[size];
        
        for(int i = 0; i < size; i++)
            array[i] = new Obj(size, Integer.parseInt(x[i]));
        
        String res = "Yes";      //To be handled 
        
        //for(int i = 0; i < size; i++)
        //  System.out.println(array[i]);
        int c = 0;
        
        while(c < size){
            for(int i = 0; i < size; i++){
                int j = i & 1;
                if(j == 0)                                     //even
                    array[i].clockwise();

                else                                                //odd
                    array[i].counterClockwise();
            }
            //for(int i = 0; i < size; i++)
            //  System.out.print(array[i]);
            //System.out.println();
            
            res = "Yes";
            
            for(int k = 0; k < size-1; k++)
                if(array[k+1].activePointer - array[k].activePointer != 1){
                    res = "No";
                    break;
                }
            
            if(res.equals("Yes"))
                break;
            
            c++;
            //System.out.println(c);
        }

        System.out.println(res);
    }
    
    private static class Obj{
        int[] a;
        int activePointer;
        
        public String toString(){
            return activePointer + " ";
        }
        
        public Obj(int size, int activePointr){
            activePointer = activePointr;
            a = new int[size];
            for(int i = 0; i < size; i++)
                a[i] = i;
        }
        
        public void clockwise(){
            activePointer++;
            activePointer %= a.length;
        }
        
        public void counterClockwise(){
            activePointer--;
            if(activePointer == -1)
                activePointer = a.length-1;
        }
    }
}
