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()]

def solve() :
    s = sum(A)
    if s % (N * (N + 1) // 2) != 0 :
        return 'NO'
        
    a = s // (N * (N + 1) // 2)
    ret = 0
    for i in range(N) :
        d = A[i] - A[i-1]
        if (a - d) % N != 0 or (a - d) < 0 :
            return 'NO'
        ret += (a - d) // N
        
    if ret == a :
        return 'YES'
    else :
        return 'NO'
        
print(solve())