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.*;
public class main {
public static void main(String args[])
    {
    Scanner s = new Scanner(System.in);
    int n =s.nextInt();
    int a[] = new int [n];
    for(int i=0 ; i<n;i++)
    {
        a[i] = s.nextInt();
    }
        int x = a[0];
        int p=0;
        if(x!=0)
        {
            int y = n-a[0];
            
            for(int j=1;j<n;j++)
            {
            
                if(j%2==1)
                {
                    
                    
                    if(a[j] - j <0)
                    {
                        if( n-Math.abs((a[j] - j))!=y)
                        {
                            p=1;
                            break;
                        }
                    }
                    else
                    {
                        if((a[j] - j)!=y)
                        {
                            p=1;
                            break;
                        }
                    }
                }
                else
                {
                    
                    if(j-a[j]<0)
                    {
                        if( n-Math.abs((j-a[j]))!=y)
                        {
                            p=1;
                            break;
                        }
                    }
                    else
                    {
                        if((j-a[j])!=y)
                        {
                            p=1;
                            break;
                        }
                    }
                }
            }
        }
        else
        {
            
            for(int j=1;j<n;j++)
            {
                if(a[j]!=j)
                {
                    p=1;
                    break;
                }
            }
            
        }
        if(p==1)
        {
            System.out.println("NO");
        }
        else
            System.out.println("Yes");
            
    }
}