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.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * DOCUMENT ME!
 */
public class FakeNumbersTest
{
   /**
    * DOCUMENT ME!
    *
    * @param args DOCUMENT ME!
    */
   public static void main(String[] args)
   {
      List<Integer> activePoints = new ArrayList<Integer>();

      Scanner in = new Scanner(System.in);
      int n = in.nextInt();

      for (int i = 0; i < n; i++)
      {
         int activePoint = in.nextInt();
         activePoints.add(activePoint);
      }

      int nSteps = 0;
      int firstActivePoint = activePoints.get(0);

      if (firstActivePoint > 0)
      {
         nSteps = n - firstActivePoint;
      }

      boolean real = true;

      if (firstActivePoint == 0 && n == 1)
      {
         System.out.println("Yes");
      }
      else
      {
         for (int i = 1; i < n; i++)
         {
            int newActivePoint = rotate(n, activePoints.get(i), nSteps, i);

            if (newActivePoint != i)
            {
               real = false;

               break;
            }
         }

         if (real)
         {
            System.out.println("Yes");
         }
         else
         {
            System.out.println("No");
         }
      }
   }

   private static int rotate(int number, int currentActivePoint, int steps, int i)
   {
      if (i % 2 == 0)
      {
         return ((currentActivePoint + steps) % number);
      }
      else
      {
         int newActivePoint = currentActivePoint - steps;

         if (newActivePoint < 0)
         {
            newActivePoint += number;
         }

         return newActivePoint;
      }
   }
}