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()))
s=sum(A)
if s%((n*(n+1))//2):
    print('NO')
else:
    k=s//(n*(n+1)//2)
    D=[]
    for i in range(n-1):
        D.append(A[i+1]-A[i]-k)
    D.append(A[0]-A[n-1]-k)
    ans='YES'
    for i in range(n):
        if D[i]>0 or D[i]%n!=0:
            ans='NO'
    print(ans)