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
n = int(input())
aa = [int(a) for a in input().split()]

s = sum(aa)
remove = (n+1) * n // 2
if s % remove != 0:
    print('NO')
else:
    k = s // remove
    diffs = [aa[i+1] - aa[i] for i in range(n-1)] + [aa[0] - aa[-1]]
    diffs = [d - k for d in diffs]
    if all(d <= 0 and d % n == 0 for d in diffs):
        print('YES')
    else:
        print('NO')
