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 ProblemSet_556B {
    FastScanner in;
    PrintWriter out;
    boolean deadflag;
    
    public void solve() throws IOException {
    	int n = in.nextInt();
    	int[] teeth = new int[n];
    	
    	for(int i = 0; i < n; i++){
    		teeth[i] = in.nextInt();
    	}
    	
    	int diff = teeth[0] == 0 ? 0 : n - teeth[0];
    	
    	deadflag = false;
    	
    	for(int i = 0; i < n && !deadflag; i+=2){
    		teeth[i] += diff;
    		teeth[i] = teeth[i] >= n ? teeth[i] - n : teeth[i];
    		if(teeth[i] != i) deadflag = true;
    	}
    	
    	for(int i = 1; i < n && !deadflag; i+=2){
    		teeth[i] -= diff;
    		teeth[i] = teeth[i] < 0 ? teeth[i] + n : teeth[i];
    		if(teeth[i] != i) deadflag = true;
    	}
    	
    	out.println(deadflag ? "No" : "Yes");
    	
    }   
    

    public void run() throws IOException {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }
        
        String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

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

    public static void main(String[] arg) throws IOException {
        new ProblemSet_556B().run();
    }
}
