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 static java.lang.Math.*;

public class Main extends PrintWriter {
    BufferedReader br;
    StringTokenizer stok;
    final Random rand = new Random(31);
    final int inf = (int) 1e9;
    final long linf = (long) 1e18;

    void solve() throws IOException {
        int n = nextInt();
        int[] a = nextIntArray(n);
        int l = -1;
        for (int i = 0; i < n; i++) {
            int c;
            if (i % 2 == 0) {
                c = (i - a[i] + n) % n;
            } else {
                c = (a[i] - i + n) % n;
            }
            if (l == -1) {
                l = c;
            } else if (l != c) {
                println("No");
                return;
            }
        }
        println("Yes");
    }

    public static void main(String[] args) throws IOException {
        try (Main main = new Main()) {
            main.solve();
        }
    }

    Main() throws IOException {
        super(System.out);
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    Main(String s) throws IOException {
        super("".equals(s) ? "output.txt" : s + ".out");
        br = new BufferedReader(new FileReader("".equals(s) ? "input.txt" : s + ".in"));
    }

    String next() throws IOException {
        while (stok == null || !stok.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) {
                return null;
            }
            stok = new StringTokenizer(s);
        }
        return stok.nextToken();
    }

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

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

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

    int[] nextIntArray(int len) throws IOException {
        int[] res = new int[len];
        for (int i = 0; i < len; i++) {
            res[i] = nextInt();
        }
        return res;
    }

    <T> List<T>[] createAdjacencyList(int verticesNumber) {
        List<T>[] res = new List[verticesNumber];
        for (int i = 0; i < verticesNumber; i++) {
            res[i] = new ArrayList<>();
        }
        return res;
    }
}
