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.*;
import java.util.*;
import java.math.*;

public class Main{
    static boolean check(int[] arr){
        for(int i=0; i<arr.length; i++)
            if(arr[i]!=i){
                return false;
            }
        return true;
    }
    static boolean isSame(int[] arr1, int[] arr2){
        for(int i=0; i<arr1.length; i++)
            if(arr1[i]!=arr2[i])
                return false;
        return true;
    }
    static void tick(int[] arr){
        int n = arr.length;
        for(int i=0; i<n; i++)
            if((i&1)==1)
                arr[i] = (arr[i]-1+n)%n;
            else
                arr[i] = (arr[i]+1)%n;
    }

    public static void main(String[] args)throws Throwable{
        Escanner sc = new Escanner();
        out = new PrintWriter(System.out);
        //////////
        int n = sc.nextInt();
        int[] arr1 = new int[n];
        int[] arr2 = new int[n];
        for(int i=0; i<n; i++){
            arr1[i] = sc.nextInt();
            arr2[i] = arr1[i];
        }
        tick(arr2);
        boolean printed = false;
        while(!isSame(arr1, arr2)){
            if(check(arr2)){
                out.println("YES");
                printed = true;
                break;
            }
            tick(arr2);
        }
        if(!printed)
            out.println(check(arr2)?"YES":"NO");
        //////////
        out.close();
    }
    static class Escanner {
        BufferedReader in;
        StringTokenizer st;

        Escanner() throws Throwable {
            in = new BufferedReader(new InputStreamReader(System.in),32768);
            st = new StringTokenizer("");
        }
        Escanner(String fileName) throws Throwable {
            in = new BufferedReader(new FileReader(fileName),32768);
            st = new StringTokenizer("");
        }

        String nextStr() throws Throwable {
            while(!st.hasMoreTokens())
                st = new StringTokenizer(in.readLine());
            return st.nextToken();
        }

        int nextInt() throws Throwable {
            return Integer.parseInt(nextStr());
        }

        long nextLong() throws Throwable {
            return Long.parseLong(nextStr());
        }

        BigInteger nextBigInt() throws Throwable {
            return new BigInteger(nextStr());
        }

        double nextDouble() throws Throwable {
            return Double.parseDouble(nextStr());
        }
    }
    static PrintWriter out;
}