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.*;


public class Main {

	static IO io;
	static int n;
	static long mod = 1000000007L;
	static Stack<Integer> stack;
	
	public static void main(String args[]) throws Exception{
	
		io = new IO();
		io.init();
		stack = new Stack<Integer>();
		//----------------------------------------
		n = io.nextInt();
		
		int array[] = new int [n];
		
		for( int i = 0 ; i< n; ++i ){
			array[i] = io.nextInt();
		}
		
		
		for( int turn = 0 ; turn <= 2*n + 1 ; ++turn){
			
			for( int i = 0 ; i < n ;++i ){
				if( i%2 == 0){ // even // anti
					array[i] =  ( n + array[i] - 1 ) %n; 
				}
				
				else{
					array[i] = (array[i]+1)%n;
				}
				
			}
			
			boolean ans = true;
			for( int i = 0 ; i < n ; ++i ){
				if( i != array[i]) ans = false;
			}
			
			if( ans ) 
			{
				io.println( "Yes");
				io.destroy();
				System.exit(0);
			}
			
		}
		
		io.println("No");
		//----------------------------------------
		io.destroy();
	}
	
	static long pow( long base , long exp){	//with mod
		
		if( exp == 0 ) return 1;
		
		long temp = pow( base,exp/2);
		temp =(temp*temp);
		
		if( exp%2 == 0 ) 
			return temp;
		else
			return (temp*base);
	}

	static long ncr ( int n , int r ){ // with mod
		
		long num = 1;
		long den = 1;
		
		for( int i = n ; i >= n -r+1 ; --i )
			num = (num*i)%mod;
		
		for( int i = 1 ; i <= r ; ++i )
			den = (den*i)%mod;
		
		return  (num*pow(den,mod-2))%mod;
	}
	
	static long gcd(long a, long b){
		if( a == 0 ) return b;
		if( b == 0 ) return a;
		if( a > b) return gcd(a%b,b);
		else return gcd(a,b%a);
	}
	
	static long pow_with_mod( long base , long exp){	//with mod
		
		if( exp == 0 ) return 1;
		
		long temp = pow_with_mod( base,exp/2);
		temp =(temp*temp)%mod;
		
		if( exp%2 == 0 ) 
			return temp;
		else
			return (temp*base)%mod;
	}
	
	static class IO{
		
		
		BufferedReader reader;
		StringTokenizer tokenizer;
		PrintWriter writer;

		public void init() {
			try {
				reader = new BufferedReader(new InputStreamReader(System.in),8*1024);
				writer = new PrintWriter(System.out);
			} catch (Exception e) {
				e.printStackTrace();
				System.exit(261);
			}
		}

		void destroy() {
			writer.close();
			System.exit(0);
		}

		void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		void println(Object... objects) {
			print(objects);
			writer.println();
		}

		String nextLine() throws IOException {
			return reader.readLine();
		}

		String nextToken() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens())
				tokenizer = new StringTokenizer(nextLine());
			return tokenizer.nextToken();
		}

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

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(nextToken());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(nextToken());
		}
	}
}
