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

# sum must be 1+2+3+...+n
asum = sum(a)
if asum % ((n + 1)*n // 2) != 0:
    print("NO")
    exit()
k = asum // ((n + 1)*n // 2)

# Drop must be k
a.append(a[0])
drop = 0
for i in range(n):
    diff = a[i] + k - a[i+1]
    if diff == 0:
        continue
    else:
        if diff % n != 0 or diff < 0:
            print("NO")
            exit()
        else:
            drop += diff // n
if drop != k:
    print("NO")
    exit()

print("YES")