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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n, k;
		n = sc.nextInt();
		int[] a = new int[1010];
		int i, j, c = 0, count = 0;
		for (i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
		}
		for (k = 0; k < n; ++k) {
			for (i = 0; i < n; ++i) {
				if (i % 2 == 0 && a[i] != n - 1) {
					a[i]++;
				}
				else if (i % 2 == 1 && a[i] != 0)
					a[i]--;
				else if (i % 2 == 0 && a[i] == n - 1)
					a[i] = 0;
				else if (i % 2 == 1 && a[i] == 0)
					a[i] = n - 1;
			}
			for (j = 0; j < n - 1; ++j) {
				if (a[j] >= a[j + 1])
					c++;
			}
			System.out.println();
			if (c == 0) 
				count++;
			c = 0;
		}
		if (count == 0) 
			System.out.printf("No");
		else
			System.out.printf("Yes");
	}
}