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()))


# 毎回1+2+...+N個の石が取り除かれる
Sum = sum(A)
if Sum % (N * (N + 1) // 2) != 0:
    print('NO')
    exit()


# 操作回数
K = Sum // (N * (N + 1) // 2)

Diff = [A[i] - A[(i - 1)] for i in range(N)]
# 変化量-1が(N-1)箇所、+(N-1)が一か所を、すべて-1した後に、一か所+1と置き換える
Diff = [d - K for d in Diff]

for d in Diff:
    if d < 0:
        if d % N != 0:
            print('NO')
            exit()
        else:
            K -= abs(d // N)

if K == 0:
    print('YES')
else:
    print('NO')
