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()))

M = N * (N + 1) // 2
d, m = divmod(sum(A), M)

def no():
  print("NO")
  exit()

if m != 0:
  no()

cnt = 0
for i in range(N):
  t = A[i - 1] - A[i]
  t += d
  if t < 0:
    no()
  dd, mm = divmod(t, N)
  if mm != 0:
    no()
  cnt += dd

if cnt == d:
  print("YES")
else:
  no()