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
# 解説AC
N = int(input())
A = [int(i) for i in input().split()]

if sum(A) % (N * (N + 1) // 2) == 0:
    # 操作回数
    k = sum(A) // (N * (N + 1) // 2)
else:
    print("NO")
    exit()

sub = []
for i in range(N):
    sub.append(A[i] - A[i-1] - k)

flag,cnt = True,0
for i in range(N):
    # 負 かつ Nの倍数
    if sub[i] <= 0 and sub[i] % N == 0:
        cnt += abs(sub[i]) // N
    else:
        flag = False

if flag and k == cnt:
    print("YES")
else:
    print("NO")