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 getlist():
	return list(map(int, input().split()))

#初期化
N = int(input())
A = getlist()
S = sum(A)
if S % (N * (N + 1) // 2) != 0:
	print("NO")
#計算
else:
	judge = "YES"
	n = S // (N * (N + 1) // 2)
	for i in range(N):
		val = A[(i + 1) % N] - A[i]
		if val < n * (1 - N) or val > n or (val - n) % N != 0:
			judge = "NO"

	print(judge)