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()))

S = sum(A)
ok = True
if S % ((N+1)*N//2) != 0:
    ok = False
else:
    K = S // ((N+1)*N//2)
    c = 0
    for i in range(N):
        a = K-A[i]+A[i-1]
        if a % N != 0:
            ok = False
            break
        x = a // N
        if 0 <= x <= K:
            c += x
        else:
            ok = False
            break
    if c != K:
        ok = False

if ok:
    print('YES')
else:
    print('NO')