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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

    public void solve() {
        int n = in.nextInt();
        int a[] = new int[n];
        boolean check = true;
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            if (a[i] != i) check = false;
        }
        if (check) {
            out.println("Yes");
            return;
        }
        
        int steps = a[0] == 0 ? 0 : n - a[0];
        for (int i = 1; i < n; i++) {
            int t = a[i];
            if (i % 2 == 1) {
//                for (int j = 0; j < steps; j++)
//                    if (t - 1 < 0)
//                        t = n - 1 ;
//                    else t--;
                if (a[i] > steps)
                    t = a[i] - steps;
                else 
                    t = n - (steps - a[i]);
            } else {
                for (int j = 0; j < steps; j++)
                    t = (a[i] + steps) % n;
            }
            if (t != i) {
                out.println("No");
                return;
            }
        }
        out.println("Yes");
        
    }

    String file = "";
    FastReader in;
    PrintWriter out;

    public void run() throws FileNotFoundException {
        if (file.length() == 0) {
            in = new FastReader();
            out = new PrintWriter(System.out);
        } else {
            in = new FastReader(file + ".in");
            out = new PrintWriter(new File(file+".out"));
        }
        solve();
        out.flush();
        out.close();
    }

    public static void main(String[] args) throws FileNotFoundException {
        new B().run();
    }

    class FastReader {

        BufferedReader bf;
        StringTokenizer st;

        public FastReader() {
            bf = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String file) {
            try {
                bf = new BufferedReader(new FileReader(file));
            } catch (FileNotFoundException ex) {
            }
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(bf.readLine());
                } catch (IOException ex) {
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }

}
