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())
alist = list(map(int, input().split()))
suma = sum(alist)

if suma % (n * (n+1) // 2) != 0:
  print('NO')
else:
  k = suma // (n * (n+1) // 2)
  da = []
  for preva, a in zip(alist, alist[1:]):
    da.append(a - preva - k)
  da.append(alist[0] - alist[-1] - k)
  nk = 0
  is_a = True
  for _da in da:
    if abs(_da) % n != 0:
      is_a = False
      break
    nk += abs(_da) // n
  if not is_a:
    print('NO')
  else:
    if nk != k:
      print('NO')
    else:
      print('YES')
