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.Arrays;
import java.util.StringTokenizer;

/**
 * Created by Arthur on 3/14/2015.
 */
public class Main {

    public static void main(String[] args) {
        new Main(args.length != 0);
    }

    private final boolean debug;

    private String formatTime(long l) {
        long minutes = l / 60000;
        l %= 60000;
        long seconds = l / 1000;
        long ms = l % 1000;
        String res = "";
        if (minutes != 0)
            res += " " + minutes + "m";
        if (seconds != 0)
            res += " " + seconds + "s";
        if (ms != 0)
            res += " " + ms + "ms";
        return res;
    }

    Main(boolean args) {
        debug = args;
        initIO(debug);
        long startTime = 0;
        if (debug)
            startTime = System.currentTimeMillis();
        solve();
        close();
        if (debug)
            System.err.println("Program work time:" + formatTime(System.currentTimeMillis() - startTime));
    }

    FastScanner sc;
    PrintWriter pw;

    private void initIO(boolean files) {
        if (files) {
            sc = new FastScanner("input.txt");
            try {
                pw = new PrintWriter(new FileOutputStream("output.txt"), false);
            } catch (Exception e) {
                e.printStackTrace();
            }
        } else {
            sc = new FastScanner(System.in);
            pw = new PrintWriter(System.out);
        }
    }

    private void close() {
        sc.close();
        pw.close();
    }

    static final int N = 200010;

    private void solve() {
        int n = sc.nextInt();
        int change = n - sc.nextInt();
        for (int i = 1; i < n; i++) {
            int y = sc.nextInt();
            if (i % 2 == 1) y = (n + y - change) % n;
            else y = (y + change) % n;
            if (y != i) {
                pw.println("No");
                return;
            }
        }
        pw.println("Yes");
    }
}

class FastScanner {

    BufferedReader br;
    StringTokenizer st;

    FastScanner(String file) {
        try {
            br = new BufferedReader(new FileReader(file));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
        st = new StringTokenizer("");
    }

    FastScanner(InputStream is) {
        br = new BufferedReader(new InputStreamReader(is));
        st = new StringTokenizer("");
    }

    String next() {
        try {
            while (!st.hasMoreElements()) {
                st = new StringTokenizer(br.readLine());
            }
        } catch (Exception e) {
            e.printStackTrace();
        }
        return st.nextToken();
    }

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

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

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

    public void close() {
        try {
            br.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}

class Vi {
    private int capacity = 2;
    private int d[] = new int[capacity];
    private int size = 0;

    public Vi() {
    }

    public Vi(int n) {
        super();
        setSize(n);
    }

    void pb(int x) {
        if (size == capacity) grow();
        d[size++] = x;
    }

    void clear() {
        capacity = 2;
        d = new int[2];
        size = 0;
    }

    int rm() {
        if (size == 0) throw new IndexOutOfBoundsException();
        return d[--size];
    }

    int a(int x) {
        if (x >= size) throw new IndexOutOfBoundsException();
        return d[x];
    }

    private void grow() {
        capacity = size + (size >> 1);
        d = Arrays.copyOf(d, capacity);
    }

    private void grow(int newSize) {
        capacity = newSize;
        d = Arrays.copyOf(d, capacity);
    }

    void setSize(int newSize) {
        if (newSize > capacity) {
            grow(newSize);
        }
        size = newSize;
    }

    int size() {
        return size;
    }

    void readIn(FastScanner sc, int n) {
        int lastSize = size;
        setSize(size + n);
        for (int i = 0; i < n; i++) {
            d[lastSize + i] = sc.nextInt();
        }
    }

    void print(PrintWriter pw) {
        for (int i = 0; i < size; i++) {
            pw.print(d[i] + " ");
        }
        pw.println();
    }

    void sort(int l, int r) {
        Arrays.sort(d, l, r);
    }

    void sort() {
        sort(0, size);
    }
}

class Algo{

    static long binpow(long x, long st) {
        long res = 1;
        while (st > 0) {
            if ((st & 1) > 0) res *= x;
            x *= x;
            st >>= 1;
        }
        return res;
    }

    static long binpow(long x, long st, long mod) {
        long res = 1 % mod;
        x %= mod;
        while (st > 0) {
            if ((st & 1) > 0) res = (res * x) % mod;
            x = (x * x) % mod;
            st >>= 1;
        }
        return res;
    }
}

class Pi implements Comparable<Pi>{

    int f, s;

    Pi(int f, int s) {
        this.f = f;
        this.s = s;
    }

    @Override
    public int compareTo(Pi pi) {
        if (f > pi.f) return 1;
        if (f < pi.f) return -1;
        if (s > pi.s) return 1;
        return s == pi.s ? 0 : -1;
    }

    @Override
    public String toString() {
        return "(" + f + "; " + s + ")";
    }
}

