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.InputStream;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.Arrays;
import java.util.StringTokenizer;

// Codeforces Round #310 (Div. 2)
// Case of Fake Numbers
public class Problem_556_B {


  public static void main(String[] args)
  {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    PrintWriter out = new PrintWriter(outputStream);
    Problem_556_B solver = new Problem_556_B();
    solver.solve(1, new InputStreamReader(inputStream), out);
    out.close();
  }

  public void solve(int test, Reader input, PrintWriter out)
  {
    MyScanner in = new MyScanner(input);

    int n = in.nextInt();

    int[] active = in.nextIntArray(n);
    int[] initial = Arrays.copyOf(active, n);
    int targetSum = 0;
    for(int i = 0; i < n; i++) targetSum += i;
    int activeSum = 0;
    for(int i = 0; i < n; i++) activeSum += active[i];
    int initialSum = activeSum;
    for(int loop = 0; loop < n+1; loop++) {
      if(activeSum == targetSum) {
        boolean found = true;
        for(int i = 0; i < n; i++) {
          if(active[i] != i) {
            found = false;
            break;
          }
        }
        if(found) {
          out.println("Yes");
          return;
        }
      }
      activeSum = 0;
      for(int i = 0; i < n; i++) {
        if(i % 2 == 0) {
          active[i] = (active[i] + 1) % n;
        } else {
          active[i] = (n + active[i] - 1) % n;
        }
        activeSum += active[i];
      }
      if(activeSum == initialSum) {
        boolean found = true;
        for(int i = 0; i < n; i++) {
          if(active[i] != initial[i]) {
            found = false;
            break;
          }
        }
        if(found) {
          out.println("No");
          return;
        }
      }

    }
    out.println("No");
  }

  //-----------MyScanner class for faster input----------
  public static class MyScanner {
    BufferedReader br;
    StringTokenizer st;

    public MyScanner(Reader reader) {
      br = new BufferedReader(reader);
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

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

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

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

    int[] nextIntArray(int n) {
      int[] res = new int[n];
      for(int i = 0; i < n; i++)
        res[i] = nextInt();
      return res;
    }

    String nextLine(){
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }

  }
  //--------------------------------------------------------

}
