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
def inpl(): return [int(i) for i in input().split()]
import sys

N = int(input())
A = inpl()

sumA = sum(A)
k = (N*(N+1)//2)
if sumA % k != 0:
    print('NO')
    sys.exit()
k = sumA // k
B = []
for i in range(N-1):
    B.append(A[i+1]-A[i]-k)
B.append(A[0]-A[N-1]-k)
flag = 0
ans = 'NO'
for i in B:
    if i%N != 0:
        break
    if i//N > 0:
        break
    flag -= i//N
else:
    if flag == k:
        ans = 'YES'
print(ans)