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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		sa = br.readLine().split(" ");
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sa[i]);
		}
		br.close();

		long one = (long) n * (n + 1) / 2;
		long sum = 0;
		for (int i = 0; i < n; i++) {
			sum += a[i];
		}
		if (sum % one != 0) {
			System.out.println("NO");
			return;
		}

		int[] b = new int[n];
		for (int i = 0; i < n - 1; i++) {
			b[i] = a[i + 1] - a[i];
		}
		b[n - 1] = a[0] - a[n - 1];

		long t = sum / one;
		for (int i = 0; i < n; i++) {
			b[i] -= t;
			if (b[i] > 0) {
				System.out.println("NO");
				return;
			}
			b[i] *= -1;
			if (b[i] % n != 0) {
				System.out.println("NO");
				return;
			}
		}
		System.out.println("YES");
	}
}
