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
import sys
input = sys.stdin.readline
n = int(input())
A = list(map(int,input().split()))
B = []
for i in range(n):
    B.append(A[i] - A[i-1])

m = max(B)
no = 0

if m < 0:
    no = 1
elif m == 0:
    if A[0] % (n*(n+1)//2) > 0:
        no = 1
else:
    c = 0
    for i in range(n):
        if (m - B[i]) % n > 0:
            no = 1
        else:
            c += (m - B[i]) // n

    if c != m:
        no = 1
    if sum(A) != m * n*(n+1)//2:
        no = 1

if no==1:
    print("NO")
else:
    print("YES")