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.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class a {
	public static class node {
		int node;
		int val;
		int idx;

		node(int index, int val, int r) {
			node = index;
			this.val = val;
			idx = r;
		}

	}

	public static class point {
		int x;
		int y;

		point(int x, int val) {
			this.x = x;
			this.y = val;
		}

	}

	public static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	public static ArrayList<Integer> prime;

	public static void sieve(int n) {
		boolean vis[] = new boolean[n + 5];
		vis[1] = true;
		vis[0] = true;
		for (int i = 2; i <= n; i++) {
			if (!vis[i]) {
				prime.add(i);
				for (long j = (long) i * (long) i; j <= n; j += i) {
					vis[(int) j] = true;
				}
			}
		}
	}

	public static int tree[][];
	public static boolean end[][];
	public static int counter;

	public static void trie(String a) {
		int st = 0;

		for (int i = 0; i < a.length(); i++) {
			if (tree[a.charAt(i) - 'a'][st] == 0) {
				tree[a.charAt(i) - 'a'][st] = counter++;
			}

			st = tree[a.charAt(i) - 'a'][st];
		}
		end[a.charAt(a.length() - 1) - 'a'][st] = true;

	}

	public static int seg[][];
	public static int a[][];
	public static int m;

	public static void build(int s, int e, int p) {
		if (s == e) {
			for (int i = 0; i < m; i++) {
				// System.out.println(p+" "+s);
				seg[i][p] = a[i][s];
			}
			return;
		}
		int mid = (s + e) / 2;
		build(s, mid, p * 2);
		build(mid + 1, e, p * 2 + 1);
		for (int i = 0; i < m; i++) {
			seg[i][p] = Math.max(seg[i][p * 2], seg[i][p * 2 + 1]);
		}
	}

	public static int get(int s, int e, int p, int from, int to, int seg[]) {
		if (s >= from && e <= to)
			return seg[p];
		if (s > to || e < from)
			return 0;
		int mid = (s + e) / 2;
		int one = get(s, mid, p * 2, from, to, seg);
		int two = get(mid + 1, e, p * 2 + 1, from, to, seg);
		return Math.max(one, two);
	}

	public static long comp(int n, int r) {
		long ans = 1;
		r = Math.min(r, n - r);
		for (int i = 1; i <= r; i++) {
			ans = ans * ((long) n - (long) i + 1L) / (long) i;
		}
		return ans;
	}

	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		// BufferedReader in = new BufferedReader(new FileReader(
		// "B-small-attempt0.in"));

		StringBuilder q = new StringBuilder();
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		// PrintWriter out = new PrintWriter(new FileWriter("out.txt"));
		int n = Integer.parseInt(in.readLine());
		int a[] = new int[n];
		String y[] = in.readLine().split(" ");
		for (int i = 0; i < y.length; i++) {
			a[i] = Integer.parseInt(y[i]);
		}

		for (int i = 0; i < 5000; i++) {
			for (int j = 0; j < n; j++) {
				if (j % 2 == 0) {
					a[j]++;
				} else {
					a[j] += n;
					a[j]--;
				}
				a[j] %= n;
			}
			int j;
			for (j = 0; j < n; j++) {
				if (a[j] != j)
					break;
			}
			if(j==n){
				System.out.println("Yes");
				return ;
			}
		}
		System.out.println("No");

		out.close();
	}
}