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.
//package CF;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class B {

    public static void main(String[] args) throws IOException
    {
	Scanner bf = new Scanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	int n = bf.nextInt();
	int [] a = new int[n];
	for (int i = 0; i < a.length; i++)
	{
	    a[i] = bf.nextInt();
	}
	boolean ans = false;
	for (int i = 0; i < n; i++)
	{
	    boolean flag = true;
	    for (int j = 0; j < a.length && flag; j++)
	    {
		if(((a[j]+((j&1)!=0?-1:1)*i)+n)%n != j)
		    flag = false;
	    }
	    ans |= flag;
	    if(flag)
		break;
	}
	out.println(ans?"Yes":"No");
	out.flush();
	out.close();
    }
    static class Scanner{
	BufferedReader bf;
	StringTokenizer st;
	public Scanner(FileReader f){
	    bf = new BufferedReader(f);
	}
	public Scanner(InputStream f){
	    bf = new BufferedReader(new InputStreamReader(f));
	}

	public String next() throws IOException{
	    while(st == null || !st.hasMoreTokens())
		st = new StringTokenizer(bf.readLine());
	    return st.nextToken();
	}
	public int nextInt() throws NumberFormatException, IOException{
	    return Integer.parseInt(next());
	}
    }
}