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())
l=list(map(int,input().split()))
sl=sum(l)
if sl%(n*(n+1)//2):
    print("NO")
    quit()
t=sl//(n*(n+1)//2)
x=0
for i in range(n):
    if (l[i-1]-l[i]+t)%n or (l[i-1]-l[i]+t)//n<0:
        print("NO")
        quit()
    else:
        x+=(l[i-1]-l[i]+t)//n
if t==x:
    print("YES")
else:
    print("NO")