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.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.Scanner;

/**
 *
 * @author таня
 */
public class KF2 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        CK jk = new CK();
    }
}

class CK {

    StreamTokenizer in;
    PrintWriter out;

    int nextInt() throws IOException {
        in.nextToken();
        return (int) in.nval;
    }

    String next() throws IOException {
        in.nextToken();
        return in.sval;
    }

    double nextDouble() throws IOException {
        in.nextToken();
        return (double) in.nval;
    }
    int n;
    String s;

    public CK() throws IOException {
        in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(new OutputStreamWriter(System.out));
       int n=nextInt();
       int array[]= new int[n];
       for(int i=0;i<n;i++){
       array[i]=nextInt();
       }
       for(int i=0;i<n;i++){
           for(int j=0;j<n;j++){
           if(j%2==0){
           array[j]++;
           array[j]=array[j]%n;
           }
           else{
           array[j]=array[j]+n-1;
           array[j]=array[j]%n;
           }
           }
           if(test(array)){
           out.print("YES");
           out.flush();
           return;
           }
       }
       out.print("NO");
        out.flush();
    }
    boolean test(int a[]){
    for(int i=0;i<a.length;i++){
    if(i!=a[i]){
    return false;
    }
    }
    return true;
    }
}
