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;
import java.util.ArrayList;
/**
 *
 * @author User
 */
public class B {

    /**
     * @param args the command line arguments
     */

        
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in); 
        int n;
        int var, var1;
        int x = 0;
        boolean flag = true;
        n = sc.nextInt();
        ArrayList<Integer> list = new ArrayList<Integer>(n);
        
        for(int i = 0; i < n; i++){
            var = sc.nextInt();
            list.add(var);
        }
        var1 = n;
        while(var1 > 0){
        for(int j = 0; j < n; j++){
            int a;
            a = list.get(j);
         //   System.out.println(a != j);
                  if(a != j){
                      flag = false;
                  break;
                  }
        }
                  if(flag == true){
                      x = 1;
                      break;
                  }
                 
    
                  flag = true;
                  
       for(int i = 0; i < n; i++){
           if(i % 2 == 0){
             var = list.get(i);
           var = ++var % n;
           list.set(i, var);
       }
       else
       {
               var = list.get(i);
           var = --var;
           if(var == -1)
               var = n - 1;
           var %= n;
           list.set(i, var);
               
                 
                  }
        
       }
          var1--;
      }
if(x == 1)
    System.out.println("Yes");
else
    System.out.println("No");
        // TODO code application logic here
    
    
 }
}