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
import sys
N,*A = map(int, open(0).read().split())
S = (N+1)*N//2
if sum(A)%S!=0:
  print('NO')
  sys.exit()
M = sum(A)//S
B = [A[(i+1)%N]-A[i]-M for i in range(N)]
X = 0
for c in B:
  if c%(-N)!=0 or M<c:
    print('NO')
    break
  X += c//(-N)
else:
  if X==M:
    print('YES')
  else:
    print('NO')