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()))
 
sum_a = sum(a)
len_a = len(a)
kaisu = sum_a // ( (1/2)*(len_a)*(len_a+1) )
 
if sum_a % ( (1/2)*(len_a)*(len_a+1) ) !=0:
  print("NO")
  exit()

ans_kaisu = 0
a.append(a[0])

for i in range(n):
  tmp = (kaisu - (a[i+1]-a[i])) // len_a
  if (kaisu - (a[i+1]-a[i])) % len_a !=0 or tmp < 0:
    print("NO")
    exit()
  ans_kaisu += tmp
  
if ans_kaisu ==kaisu:
  print("YES")
else:
  print("NO")