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()))

ok = 1
sum_A = sum(A)
M, mod = divmod(sum_A, (N * (N + 1)) // 2)
if mod != 0:
    ok = 0

diff = [0] * N
for i in range(N):
    diff[i] = A[i] - A[i - 1]
count = 0
for i in range(N):
    x, mod = divmod(diff[i] - (1 - N) * M, N)
    count += (M - x)
    if mod != 0 or x < 0 or x > M:
        ok = 0
if count != M:
    ok = 0

if ok:
    print('YES')
else:
    print('NO')
