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
input = sys.stdin.readline

n=int(input())
A=[int(i) for i in input().split()]
if sum(A)%(n*(n+1)//2)!=0:
  print("NO")
else:
  k=sum(A)//(n*(n+1)//2)
  AA=[0]*n
  for i in range(n):
    if i==n-1:
      AA[i]=A[0]-A[-1]-k
    else:
      AA[i]=A[i+1]-A[i]-k
  ans="YES"
  for i in range(n):
    if AA[i]>0 or AA[i]%n!=0:
      ans="NO"
  print(ans)
