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 solve(n, aaa):
    added_once = n * (n + 1) // 2
    total = sum(aaa)
    d, m = divmod(total, added_once)
    if m != 0:
        return False
    cnt = 0
    for a1, a2 in zip(aaa, aaa[1:] + aaa[:1]):
        k = d - (a2 - a1)
        kd, km = divmod(k, n)
        if kd < 0 or km != 0:
            return False
        cnt += kd
    assert cnt == d
    return True


n = int(input())
aaa = list(map(int, input().split()))
print('YES' if solve(n, aaa) else 'NO')
