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
# 入力
N = int(input())
A = list(map(int, input().split()))

S = sum(A)

# A_{i + 1} - A_i から解を求める
ans = (
    'YES' if (2 * S) % (N * (N + 1)) == 0 and all(
        k % N == 0 and k >= 0
        for k in (
            (2 * S) // (N * (N + 1)) - (A[i] - A[i - 1])
            for i in range(N)
        )
    ) else
    'NO'
)

# 出力
print(ans)
