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 check(N, A):
    S = N * (1+N) // 2
    total = sum(A)
    if total % S != 0:
        return False
    cnt = total//S
    tmp = cnt
    for i in range(N):
        diff = A[i] - A[(i+1) % N]
        if (diff + cnt) % N != 0 or (diff + cnt) < 0:
            return False
        tmp -= (diff + cnt) // N
    return tmp == 0


def main():
    N = int(input())
    A = list(map(int, input().split()))
    if check(N, A):
        print("YES")
    else:
        print("NO")


if __name__ == "__main__":
    main()
