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 = int(input())
a = [int(x) for x in input().strip().split()]

total = sum(a)
nn = n * (n + 1) / 2
if total % nn != 0 :
  print('NO')
else:
  m = total / nn
  l = 0
  flg = True
  for i in range(n):
    j = i - 1
    if i == 0:
      j = n - 1
    if a[j] + m - a[i] < 0 or (a[j] + m - a[i]) % n != 0:
      flg = False
      break
    l += (a[j] + m - a[i]) / n

  if flg == True:
    print('YES')
  else:
    print('NO')