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.*;
import java.math.BigInteger;
public class B {
public static void main(String[] args) throws IOException
{
    PrintWriter out = new PrintWriter(System.out);
    input.init(System.in);
    
    int n = input.nextInt();
    
    int[] a = new int[n];
    for (int i = 0; i < n; i ++) {
        a[i] = input.nextInt();      
    }
    
    int press = n - a[0]; // number times we need to press to get config
    int config;
    
    for (int i = 1 ; i < n ; i++) {
      if (i % 2 == 0) {
        config = (a[i] + press) % n;
        if (config != i) {
          System.out.println("No");
          System.exit(0);
        }
      } else {
        config = a[i] - press;
        if (config < 0) {
          config = n + config;
        }
        if (config != i) {
          System.out.println("No");
          System.exit(0);
        } 
      }
    }
    
    System.out.println("Yes");
       
    out.close();
}
public static class input {
    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("");
    }
    
    static String nextLine() throws IOException
    {
      return reader.readLine();
    }

    /** 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 double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}

public static int mod = 1000000007;
public static BigInteger MOD = BigInteger.valueOf(1000000007);
  
public static int binom(int n, int k) {
  long a = BigInteger.valueOf(fac(k)).modInverse(MOD).longValue();
  long b = BigInteger.valueOf(fac(n - k)).modInverse(MOD).longValue();
  long ans = fac(n);
  ans = (ans * a)%mod;
  ans = (ans * b)%mod;
  
  return (int) ans;
}

public static int fac(int n) {
  long fak = 1;
  while ( n > 1 )
  {
    fak = (fak * n) % mod;
    n   = n - 1;
  }
  
  return (int) fak;
}
}
