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

P = "possible"

Nsum = N *(N+1)//2
if sum(A) % Nsum == 0:
  K = sum(A) // Nsum
  for i in range(N):
    A[i] -= K * (i + 1)
  A0 = A[0]
  for i in range(N):
    A[i] -= A0
  B = [0] * N
  for i in range(1, N):
    if (A[i] - A[i-1])%N != 0:
      P = "impossible"
    else:
      B[i] = (A[i-1] - A[i]) // N
  B[0] = K - sum(B)
  for i in range(N):
    if B[i] < 0:
      P = "impossible"
  for i in range(1, N):
    A0 -= B[i] * (N-i)
  if A0 != 0:
    P = "impossible"
else:
  P = "impossible"
  
if P == "impossible":
  print("NO")
else:
  print("YES")