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.*;

public class Test {


    static Scanner sc = new Scanner(System.in);

    static  boolean binSearch(ArrayList<Long> arr, long key) {
        int max = arr.size() - 1;
        int min = 0;
        int mid;
        while (min <= max) {
            mid = (max + min) / 2;
            if (key > arr.get(mid) ) {
                min = mid  + 1;
            }
            else if (key == arr.get(mid))
                return true;
            else if(key < arr.get(mid)) {
                max = mid - 1;
            }
        }
        return false;
    }

    static int partition(int arr[], int left, int right)
    {
        int i = left, j = right;
        int tmp;
        int pivot = arr[(left + right) / 2];

        while (i <= j) {
            while (arr[i] < pivot)
                i++;
            while (arr[j] > pivot)
                j--;
            if (i <= j) {
                tmp = arr[i];
                arr[i] = arr[j];
                arr[j] = tmp;
                i++;
                j--;
            }
        }

        return i;
    }

    static int[] quickSort(int arr[], int left, int right) {
        int index = partition(arr, left, right);
        if (left < index - 1)
            quickSort(arr, left, index - 1);
        if (index < right)
            quickSort(arr, index, right);

        return arr;
    }

    static int[] nextInts(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }
        return arr;
    }


    public static void main(String[] args) {

        int n = sc.nextInt();
        int[] a = nextInts(n);

        int key = a[0];

        for (int i = 1; i < n; i++) {
            if (i%2 == 1) {
                a[i] = a[i]+key < n ?
                        a[i]+key :
                        a[i]+key-n;
            }
            else {
                a[i] = a[i]-key >= 0 ?
                        a[i]-key :
                        n + a[i]-key;
            }

//            System.out.println(a[i]);

            if (a[i] != i) {
                System.out.println("No");
                return;
            }
        }



        System.out.println("Yes");
    }

}
