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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class B {
    InputStream is;
    PrintWriter out;
    String INPUT = "4\n" +
            "0 2 3 1";

    void solve() {
        int n = ni();
        int[] array = na(n);
        LinkedList<Integer> active = new LinkedList<>();
        for (int i = 0; i < n; i++) {
            active.add(array[i]);
        }
        Set<Gear> res = new HashSet<>();
        while (true) {
            LinkedList<Integer> tmp = new LinkedList<>();
            for (int i = 0; i < array.length; i++) {
                int next = getNext(active.get(i), n - 1, i % 2 == 0);
                tmp.add(next);
            }
            Gear gear = new Gear(tmp);
            if (res.contains(gear)) {
                System.out.println("No");
                return;
            }
            if (isPuzzle(tmp)) {
                System.out.println("Yes");
                return;
            }
            active = (LinkedList<Integer>) tmp.clone();
            res.add(gear);

        }
    }

    private boolean isPuzzle(LinkedList<Integer> list) {
        if (list == null || list.size() == 0) {
            return false;
        }
        for (int i = 0; i < list.size() - 1; i++) {
            if (list.get(i) >= list.get(i + 1)) {
                return false;
            }
        }
        return true;
    }

    int getNext(int i, int n, boolean clockwise) {
        if (clockwise) {
            if (i == n) {
                return 0;
            } else {
                return i + 1;
            }
        } else {
            if (i == 0) {
                return n;
            } else {
                return i - 1;
            }
        }
    }

    private static class Gear {

        private LinkedList<Integer> list;

        public Gear(LinkedList<Integer> list) {
            this.list = list;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Gear gear = (Gear) o;
            int len1 = list.size();
            int len2 = gear.list.size();
            if (len1 != len2)
                return false;
            for (int i = 0; i < len1; i++) {
                if (!list.get(i).equals(gear.list.get(i))) {
                    return false;
                }
            }
            return true;
        }

        @Override
        public int hashCode() {
            return Objects.hash(list);
        }
    }

    void run() throws Exception {
        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }

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

    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}