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 = [int(x) for x in input().split()]

ok = True
S = sum(A)
T = (1+N) * N // 2
if S % T != 0:
    ok = False
else:
    t = S // T
    count = 0
    for i in range(N):
        a0, a1 = A[i-1], A[i]
        if -(a1 - a0 - t) < 0:
            ok = False
            break
        if -(a1 - a0 - t) % N != 0:
            ok = False
            break
        count += -(a1 - a0 - t) // N
YESNO = lambda tf: print('YES') if tf else print('NO')
YESNO(ok and S // T == count)