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()))

tn = N*(N+1)//2
ta = sum(A)


if ta % tn != 0:
  print('NO')
  exit()

num = ta // tn

count = 0
seq = [0]*N

for i in range(N):
  a = A[i-1]
  b = A[i]

  c = b-a - num
  if c % N != 0 or c > 0:
    print('NO')
    exit()
  else:
    t = -c//N
    seq[i] = t
    count += t

if count != num:
  print('NO')
else:
  print('YES')