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()))
S = sum(A)
if S % (N*(N+1)//2):
  print('NO')
  quit()

k = S // (N*(N+1)//2)
d = [A[0] - A[-1] - k]
for i in range(N-1):
  d.append(A[i+1] - A[i] - k)

time = 0
for di in d:
  if di <= 0 and (-di) % N == 0:
    time += -di // N
  else:
    print('NO')
    quit()

if time == k:
  print('YES')
else:
  print('NO')