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 Solution {

    private static void solve(InputReader in, OutputWriter out) {
        int n = in.nextInt();
        int[] a = in.nextIntArray(n);
        int rt = (n - a[0]) % n;
        boolean genuine = true;
        int x;

        for (int i = 1; i < n; i++) {
            if (i % 2 != 0) {
                x = a[i] - rt;
                if (x < 0) x += n;

            } else {
                x = a[i] + rt;
                if (x >= n) x -= n;
            }

            if (x != i) {
                genuine = false;
                break;
            }
        }

        if (genuine)
            out.print("Yes");
        else
            out.print("No");
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        solve(in, out);
        in.close();
        out.close();
    }

    private static class InputReader {

        private BufferedReader br;
        private StringTokenizer st;

        InputReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }

        String nextLine() {
            String line = null;

            try {
                line = br.readLine();

            } catch (IOException e) {
                e.printStackTrace();
            }

            return line;
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String line = nextLine();

                if (line == null)
                    return null;

                st = new StringTokenizer(line);
            }

            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];

            for (int i = 0; i < n; i++)
                a[i] = nextInt();

            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];

            for (int i = 0; i < n; i++)
                a[i] = nextLong();

            return a;
        }

        void close() {
            try {
                br.close();

            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    private static class OutputWriter {

        BufferedWriter bw;

        OutputWriter(OutputStream os) {
            bw = new BufferedWriter(new OutputStreamWriter(os));
        }

        void print(int i) {
            print(Integer.toString(i));
        }

        void println(int i) {
            print(i);
            print('\n');
        }

        void print(long l) {
            print(Long.toString(l));
        }

        void println(long l) {
            print(l);
            print('\n');
        }

        void print(double d) {
            print(Double.toString(d));
        }

        void println(double d) {
            print(d);
            print('\n');
        }

        void print(boolean b) {
            print(Boolean.toString(b));
        }

        void println(boolean b) {
            print(b);
            print('\n');
        }

        void print(char c) {
            try {
                bw.write(c);

            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(char c) {
            print(c);
            print('\n');
        }

        void print(String s) {
            try {
                bw.write(s);

            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(String s) {
            print(s);
            print('\n');
        }

        void close() {
            try {
                bw.close();

            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}
