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(a) for a in input().split()]

S = N * (N+1) // 2

A_sum = sum(A)

if A_sum % S != 0:
	print("NO")
	exit(0)
T = A_sum // S

diff = [A[(i+1)%N] - A[i%N] for i in range(N)]
zure = 0
for i in range(N):
	d = diff[i]
	if T - d >= 0 and (T - d) % N == 0:
		zure += (T - d) // N

if zure == T:
	print("YES")
else:
	print("NO")