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

def solve(N, A):
    k = N * (N + 1) // 2
    s = sum(A)
    if s % k > 0:
        return False
    m = s // k
    # print(k, s, m)
    rs = []
    for i in range(N):
        p = A[i - 1]
        q = A[i]
        delta = q - p
        y = m - delta
        # print(p, q, delta, y, N)
        if y % N > 0:
            return False
        x = y // N
        rs.append(x)
    # print("*", rs)
    R = 0
    for i in range(N):
        x = rs[i]
        l = (N - i) % N + 1
        R += l * x
    # print(1, R)
    if R != A[0]:
        return False
    for i in range(1, N):
        R += m - rs[i]
        R -= rs[i] * (N - 1)
        # print(i, R)
        if R != A[i]:
            return False
    return True

def solve(N, A):
    k = N * (N + 1) // 2
    s = sum(A)
    if s % k > 0:
        return False
    m = s // k
    for i in range(N):
        x = A[i - 1] - A[i] + m
        if x < 0 or (x % N) > 0:
            return False
    return True

if solve(N, A):
    print("YES")
else:
    print("NO")
