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
def main():
    N = int(input())
    A = [int(a) for a in input().rstrip().split()]
    sum_A = sum(A)
    sum_N = (N + 1) * N // 2
    if sum_A % sum_N:
        print('NO')
        return

    ope_num = sum_A // sum_N
    diffs = [r - l - ope_num for l, r in zip(A[:-1], A[1:])] + [A[0] - A[-1] - ope_num]
    if all([d % N == 0 and d <= 0 for d in diffs]):
        print('YES')
    else:
        print('NO')


if __name__ == '__main__':
    main()
