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()))
suma = sum(A)
unit = N*(N+1)//2
if suma % unit:
    print('NO')
    exit()
ope = suma // unit

d = A[0]-A[-1]
for a,b in zip(A,A[1:]):
    if (b-a)%N != d%N:
        print('NO')
        exit()

AA = A + [A[0]]
k = 0
for a,b in zip(AA,AA[1:]):
    if b-a > ope:
        print('NO')
        exit()
    k += (ope - (b-a)) // N

print('YES' if k==ope else 'NO')