There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

* Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.



Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

* 1 ≦ N ≦ 10^5
* 1 ≦ A_i ≦ 10^9

Input

The input is given from Standard Input in the following format:


N
A_1 A_2 … A_N


Output

If it is possible to remove all the stones from the boxes, print `YES`. Otherwise, print `NO`.

Examples

Input

5
4 5 1 2 3


Output

YES


Input

5
6 9 12 10 8


Output

YES


Input

4
1 2 3 1


Output

NO
import java.util.Scanner;

/**
 * Created by zzt on 17-2-4.
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long[] a = new long[n];
        long s = 0;
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextLong();
            s += a[i];
        }
        long t = n * (n + 1L) / 2;
        if (s % t != 0) {
            System.out.println("NO");
            return;
        }
        long k = s / t;
        long[] d = new long[n];
        for (int i = 0; i < n; i++) {
            d[i] = a[(i + 1) % n] - a[i];
            if (k < d[i] || (k - d[i]) % n != 0) {
                System.out.println("NO");
                return;
            }
        }
        System.out.println("YES");
    }
}