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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Collections;
import java.util.Map;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class KSN {

	static PrintWriter out = new PrintWriter(System.out);

	static void input() throws IOException {
		Reader.init(System.in);
	}

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub

		input();
		solve();
	}

	static void solve() throws IOException {

		int N = Reader.nextInt();

		int[] arr = Reader.nextIntArray(N);

		int R = N - 1;

		boolean Nposs = false;
		int steps = N - arr[0];
		int temp;

		myloop: for (int i = 0; i < N; ++i) {

			if (arr[0] == 0) {

				for (int x = 1; x < N; ++x)
					if (arr[x] != x) {
						Nposs = true;
						break myloop;
					}

				break;
			}

			else {

				if (i % 2 == 0) {

					temp = arr[i] + steps;

					if (temp > R)
						temp -= N;

					if (temp != i) {
						Nposs = true;
						break;
					}

				} else {

					temp = arr[i] - steps;

					if (temp < 0)
						temp += N;

					if (temp != i) {
						Nposs = true;
						break;
					}
				}
			}
		}

		if (!Nposs)
			out.println("Yes");
		else
			out.println("No");

		out.flush();
		out.close();
		////////////////////// No Business TO DO HERE... Up Up ^^^

	}

	static class Reader {

		static BufferedReader reader;
		static StringTokenizer tokenizer;

		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}

		static String next() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {

				tokenizer = new StringTokenizer(reader.readLine());
			}
			return tokenizer.nextToken();
		}

		static String nextLine() throws IOException {
			return reader.readLine();
		}

		static char nextChar() throws IOException {
			return (char) reader.read();
		}

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

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

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

		static long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}

			return arr;
		}

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

	}

}
