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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.InputMismatchException;

public final class Second
{
	private static int n, a[];
	private static InputReader reader;
	private static OutputWriter writer;
	
	public static void main(String[] args)
	{
		Second second = new Second();
		
		reader = second.new InputReader(System.in);
		writer = second.new OutputWriter(System.out);
		
		getAttributes();
		
		writer.flush();
		
		reader.close();
		writer.close();
	}
	
	public static void getAttributes()
	{
		n = reader.nextInt();
		
		a = new int[n];
		
		int nMinusOne = n - 1;
		boolean isReal = true;
		
		for (int i = 0; i < n; i++)
			a[i] = reader.nextInt();
		
		int r = n - a[0];
		int cmp;
		
		//System.out.println("r : " + r);
		
		for (int i = 0; i < n; i++)
		{
			if (i % 2 == 0)
			{
				// cmp =
				cmp = a[i] + r;
				
				if (cmp >= n)
					cmp -= n;
				
				//System.out.println("cmp : " + cmp);
				
				 if (cmp != i)
				 {
					 isReal = false;
					 
					 break;
				 }
			}
			else
			{
				cmp = a[i] - r;
				
				//System.out.println("b cmp : " + cmp);
				if (cmp < 0)
					cmp += n;
				
				//System.out.println("cmp : " + cmp);
				
				if (cmp != i)
				{
					isReal = false;
					
					break;
				}
			}
		}
		
		if (isReal)
			writer.println("Yes");
		else
			writer.println("No");
	}
	
	class InputReader
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}

		public int read()
		{
			if (numChars == -1)
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			
			return buf[curChar++];
		}

		public int nextInt()
		{
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			int sgn = 1;
			
			if (c == '-')
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				
				res *= 10;
				res += c & 15;
				
				c = read();
			} while (!isSpaceChar(c));
			
			return res * sgn;
		}

		public long nextLong()
		{
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			int sign = 1;
			
			if (c == '-')
			{
				sign = -1;
				
				c = read();
			}
			
			long result = 0;
			
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				
				result *= 10;
				result += c & 15;
				
				c = read();
			} while (!isSpaceChar(c));
			
			return result * sign;
		}
		
		public float nextFloat() // problematic
		{
			float result, div;
			byte c;

			result = 0;
			div = 1;
			c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean isNegative = (c == '-');

			if (isNegative)
				c = (byte) read();

			do
			{
				result = result * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					result += (c - '0') / (div *= 10);

			if (isNegative)
				return -result;

			return result;
		}

		public double nextDouble() // not completely accurate
		{
			double ret = 0, div = 1;
			byte c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean neg = (c == '-');

			if (neg)
				c = (byte) read();

			do
			{
				ret = ret * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);

			if (neg)
				return -ret;

			return ret;
		}

		public String next()
		{
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			StringBuilder res = new StringBuilder();
			
			do
			{
				res.appendCodePoint(c);
				
				c = read();
			} while (!isSpaceChar(c));
			
			return res.toString();
		}

		public boolean isSpaceChar(int c)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public void close()
		{
			try
			{
				stream.close();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}
		}

	}

	class OutputWriter
	{
		private PrintWriter writer;

		public OutputWriter(OutputStream stream)
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
					stream)));
		}

		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}

		public void println(int x)
		{
			writer.println(x);
		}

		public void print(int x)
		{
			writer.print(x);
		}
		
		public void println(int array[], int size)
		{
			for (int i = 0; i < size; i++)
				println(array[i]);
		}
		
		public void print(int array[], int size)
		{
			for (int i = 0; i < size; i++)
				print(array[i] + " ");
		}

		public void println(long x)
		{
			writer.println(x);
		}

		public void print(long x)
		{
			writer.print(x);
		}
		
		public void println(long array[], int size)
		{
			for (int i = 0; i < size; i++)
				println(array[i]);
		}
		
		public void print(long array[], int size)
		{
			for (int i = 0; i < size; i++)
				print(array[i]);
		}
		
		public void println(float num)
		{
			writer.println(num);
		}
		
		public void print(float num)
		{
			writer.print(num);
		}
		
		public void println(double num)
		{
			writer.println(num);
		}
		
		public void print(double num)
		{
			writer.print(num);
		}

		public void println(String s)
		{
			writer.println(s);
		}

		public void print(String s)
		{
			writer.print(s);
		}
		
		public void println()
		{
			writer.println();
		}

		public void printSpace()
		{
			writer.print(" ");
		}

		public void flush()
		{
			writer.flush();
		}

		public void close()
		{
			writer.close();
		}

	}

}
