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 Solution {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] x = new int[N];
        
        for(int i = 0;i<x.length;i++){
            x[i] = sc.nextInt();
        }
        int steps = x.length - x[0];
        
        for(int i = 1;i<x.length;i++){
            int tmp = 0;
            if(i % 2 == 0){
                tmp = x[i] + steps;
                if(tmp > N - 1){
                    tmp = tmp - N;
                }
            }else{
                tmp = x[i] - steps;
                if(tmp < 0){
                    tmp = tmp + N;
                }
            }
            x[i] = tmp;
        }
        x[0] = 0;
        boolean check = true;
        for(int i = 0;i<x.length;i++){
            if(x[i] != i){
                check = false;
                break;
            }
            
        }
        if(check)
            System.out.println("Yes");
        else
            System.out.println("No");
        
    }

}
