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

def solve(li,n):
  cnt=sum(li)
  s=((n+1)*n)//2
  if cnt % s !=0:
    print("NO")
    return
  
  cnt//=s
  
  ch=[cnt for x in range(n)]
  res=[]
  for i in range(n-1):
    res.append(li[i+1]-li[i])
  res.append(li[0]-li[-1])
  
  for i in range(n):
    if ch[i] != res[i]:
      if abs(ch[i]-res[i]) % n !=0:
        print("NO")
        return
      else:
        cnt-=abs(ch[i]-res[i])//n
  if cnt==0:
    print("YES")
    return
  else:
    print("NO")
    return

solve(A,N)