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.*;
import java.math.*;

public class Main { 
    
    public static void main(String[] args) throws java.lang.Exception { 
        Reader pm =new Reader(); 
        //Scanner pm = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int t = 1;
        while(t-- > 0){
            int n = pm.nextInt();
            int[] a = new int[n];

            ArrayList<Integer> al = new ArrayList();
            for(int i=0;i<n;i++)
                a[i] = pm.nextInt();

            int[] d = new int[n];
            int dot = 0;
            HashSet<Integer> hs = new HashSet<>();

            if(n == 1) {
                System.out.println("Yes");
                return;
            }
            int cnt= 0;
            for(int i=0;i<n;i++){
                if(a[i] == i) {
                    dot = 1;
                    cnt++;
                }
                if(i % 2 == 0) {
                    if(a[i] > i) 
                        d[i] = (n-1-a[i] + (i+1));
                    else
                        d[i] = (i - a[i]);
                }
                else {
                    if(a[i] < i) 
                        d[i] = (a[i] + (n-i));
                    else
                        d[i] = a[i] - i;
                }
                hs.add(d[i]);
            }
            // for(int i=0;i<n;i++)
            //     System.out.println(d[i]);
            // System.out.println(hs);
            if(dot == 1 && cnt == n) {
                System.out.println("Yes");
                continue;
            }

            if(hs.size() == 1) {
                int ele = -1;
                for(int i:hs) 
                    ele = i;
                if(dot == 1 && ele == n) {
                    System.out.println("Yes");
                }
                else if(dot == 0) 
                    System.out.println("Yes");
                else
                    System.out.println("No");
            }
            else
                System.out.println("No");
        }
        //end of tests
        
    }
    //end of main class

    static int countInRange(int arr[], int n, int x, int y) { 
        // initialize result 
        int count = 0; 
        count = upperIndex(arr, n, y) -  
                lowerIndex(arr, n, x) + 1; 
        return count; 
    } 
    
    
    static int lowerIndex(int arr[], int n, int x) { 
        int l = 0, h = n - 1; 
        while (l <= h)  
        { 
            int mid = (l + h) / 2; 
            if (arr[mid] >= x) 
                h = mid - 1; 
            else
                l = mid + 1; 
        } 
        return l; 
    } 
      
    // function to find last index <= y 
    static int upperIndex(int arr[], int n, int y) { 
        int l = 0, h = n - 1; 
        while (l <= h)  
        { 
            int mid = (l + h) / 2; 
            if (arr[mid] <= y) 
                l = mid + 1; 
            else
                h = mid - 1; 
        } 
        return h; 
    }
    
    public static StringBuilder dec_to_bin(long n) {
        // decimal to binary upto 30 binaries
        if(n==0) {
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<30;i++) {
                str.append("0");
            }
            return str;
        }
        StringBuilder str=new StringBuilder("");
        while(n!=0) {
            str.append(n%2L);
            n/=2L;
        }
        str=str.reverse();
        StringBuilder tmp_str=new StringBuilder("");
        int len=str.length();
        while(len!=30) {
            tmp_str.append("0");
            len++;
        }
        tmp_str.append(str);
        return tmp_str;
    }
    
    private static int binarySearchPM(int[] arr, int key){
        int n = arr.length;
        int mid = -1;
        int begin = 0,end=n;
        while(begin <= end){
            mid = (begin+end) / 2;
            if(mid == n){
                return n;
            }
            if(key < arr[mid]){
                end = mid-1;
            } else if(key > arr[mid]){
                begin = mid+1;
            } else {
                return mid;
            }
        }
        //System.out.println(begin+" "+end);
        return -begin; //expected Index
    }
    
    static class Reader { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
}    