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()]

RejectStones = N * (N+1) // 2
if sum(A) % RejectStones != 0: print("NO")
else:
    TotalOperation = sum(A) // RejectStones
    sumcheck = 0
    for i in range(N-1):
        if (TotalOperation - A[i+1] + A[i]) % N != 0 or TotalOperation < A[i+1] - A[i]:
            print("NO")
            break
        else:
            sumcheck += (TotalOperation - A[i+1] + A[i]) // N
    else:
        if (TotalOperation - A[0] + A[-1]) % N != 0 or TotalOperation < A[0] - A[-1]: print("NO")
        else: 
            sumcheck += (TotalOperation - A[0] + A[-1]) // N
            if sumcheck == TotalOperation: print("YES")
            else: print("NO")