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 Programa {

	 public static int mod;
	// A utility function that returns true if there is a subset of arr[]
	// with sun equal to given sum
	 
	public static boolean isSubsetSum (int arr[], int n, int sum)
	{
	   // Base Cases
	   if (sum == 0)
	     return true;
	   if (n == 0 && sum != 0)
	     return false;
	 
	   // If last element is greater than sum, then ignore it
	   if (arr[n-1] > sum)
	     return isSubsetSum (arr, n-1, sum);
	 
	   /* else, check if sum can be obtained by any of the following
	      (a) including the last element
	      (b) excluding the last element
	   */
	   return isSubsetSum (arr, n-1, sum) || isSubsetSum (arr, n-1, sum-arr[n-1]);
	}
	 
	// Returns true if arr[] can be partitioned in two subsets of
	// equal sum, otherwise false
	public static boolean findPartiion (int arr[], int n)
	{
	    // Calculate sum of the elements in array
	    int sum = 0;
	    for (int i = 0; i < n; i++)
	       sum += arr[i];
	 
	    // If sum is odd, there cannot be two subsets with equal sum
	    if (sum%2 != 0)
	       return false;
	 
	    // Find if there is subset with sum equal to half of total sum
	    return isSubsetSum (arr, n, sum/2);
	}
	 
	public static double expectedActions(int[] p)
	{
		double mini = 0.0;
		
		for(int i = 0; i < p.length - 1; i++){
			// zeros
			double tem = 1.0;
			for(int j = 0; j < i; j++){
				tem *= (100 - p[i])/100.0;
			}
			// ones
			for(int j = i; j < p.length; j++){
				tem *= (p[i])/100.0;
			}
			mini += tem;
		}
		for(int i = 1; i < p.length; i++){
			// ones
			double tem = 1.0;
			for(int j = 0; j < i; j++){
				tem *= (p[i])/100.0;
			}
			// zeros
			for(int j = i; j < p.length; j++){
				tem *= (100 - p[i])/100.0;
			}
			mini += tem;
		}
		return mini;
	}
	public static void secuencia(int curr, int obj , int size){
		System.out.print(curr+" ");
		while(curr != obj){
			if( curr - 1 >= 0)
				curr -= 1;
			else
				curr = size - 1;
			System.out.print(curr+" ");
		}
	}
	 public static void main(String [] args){	
	    	Scanner scan = new Scanner (System.in);
	    	//secuencia(2,3,5);
	    	
	    	int n = scan.nextInt();
	    	int [] a = new int[n];
	    	int [] moves = new int[n];
	    	
	    	for(int i = 0; i < n; i++){
	    		a[i] = scan.nextInt();
	    		//move closewise
	    		int k = a[i], cont = 0;
	    		if (i % 2== 0){
		    		while(k != i){
		    			k = (k + 1) % n;
		    			cont++;
		    		}
	    		}
	    		else{
	    			//move count-closewise	
	    			while(k != i){
	    				if(k - 1 >= 0)
	    					k -= 1;
	    				else
	    					k = n - 1;
	    				cont++;
	    			}
	    		}
	    		
	    		
	    		a[i] = k;
	    		moves[i] = cont;
	    	}
	    	
	    	for(int i = 1; i < n; i++){
	    		if(moves[i] != moves[i - 1]){
	    			System.out.println("No");
	    			System.exit(0);
	    		}
	    	}
	    	System.out.println("Yes");
	    	
	    }
	
	 public static long fastPower(long base, long exponent){
		 if(exponent == 0){
			 return 1;
		 }
		 long x = fastPower(base, exponent >> 1);
		 x = x * x % mod;
		 if((exponent & 1) != 0) 
			 x = x * base % mod;
		 return x;
	 }	
	 
	 public static long fibonacci(long n){
		 Matrix matrix = new Matrix(new long[][]{{1,1},{1,0}});
		 matrix = fastPower(matrix, n);
		 return matrix.matrix[0][0];
	 }
	 
	 
	 public static Matrix fastPower(Matrix base, long exponent){
		 if(exponent == 1) return base;
		 Matrix x = fastPower(base, exponent >> 1);
		 x = myltiplyMatrix(x,x);
		 return x;
	 }
	 
	 public static Matrix myltiplyMatrix(Matrix a, Matrix b){
		 Matrix matrix = new Matrix();
		 for(int i = 0; i < 2; i++)
			 for(int j = 0; j < 2; j++)
				 for(int k = 0; k < 2; k++)
					 matrix.matrix[i][k] = (matrix.matrix[i][k]	+ a.matrix[i][j]*b.matrix[j][k]) & mod;
		 return matrix;
	 }
	 
	 public static class Matrix{
		 private long[][] matrix;
		 public Matrix(){
			 matrix = new long[2][2];
		 }
		 public Matrix(long[][] c){
			 matrix = c.clone();
		 }
	 }
    /*
     
    	 
	 
    	
     */
}
