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())
a = list(map(int, input().split()))

bl = True

amount = N * (N + 1) // 2  # 一回の操作で除去される石の量
q1, r1 = divmod(sum(a), amount)  # q: 操作の回数
if r1 != 0:
    bl = False
else:
    d = [a[(i + 1) % N] - a[i] for i in range(N)]
    d = list(map(lambda x: x - q1, d))

    cnt = 0
    for dd in d:
        if dd > 0:
            bl = False
            break
        else:
            q2, r2 = divmod(-dd, N)
            if r2 > 0:
                bl = False
                break
            else:
                cnt += q2
    bl &= (cnt == q1)

print('YES' if bl else 'NO')
