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.*;
    import java.io.*;

    public class Codeforces {

        
        public static void main(String[] args) throws IOException {
            Reader.init(System.in);
            int n = Reader.nextInt();
            int arr[] = new int[n], dis[] = new int[n];
            
            for(int i = 0; i < n; i++){
                arr[i] = Reader.nextInt();
            }
            
            for(int i = 0; i < n; i++){
                if(i % 2 == 0){
                    if(arr[i] > i)
                        dis[i] = n - arr[i] + i;
                    else
                        dis[i] = i - arr[i];
                }
                
                else{
                    if(arr[i] < i)
                        dis[i] = arr[i] + (n-i);
                    else
                        dis[i] = arr[i] - i;
                }
            }
            
            for(int i = 0; i < n; i++){
                for(int j = 0; j < n; j++){
                    if(dis[i] == dis[j])
                        continue;
                    
                    int x = Math.abs(dis[i] - dis[j]);
                    
                    if(x % n != 0){
                        System.out.println("No");
                        return;
                    }
                }
            }
            System.out.println("Yes");
            
        }
        
        
        
    }

    class Reader {

        static BufferedReader reader;
        static StringTokenizer tokenizer;

        /**
         * call this method to initialize reader for InputStream
         */
        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /**
         * get next word
         */
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        static byte nextByte() throws IOException {

            return Byte.parseByte(next());
        }

        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }