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
def main():
    N = int( input())
    A = list( map( int, input().split()))
    if sum(A)%(N*(N+1)//2) != 0:
        print("NO")
        return
    t = sum(A)//(N*(N+1)//2)
    d = [0]*N
    for i in range(N):
        d[i] = A[i] - A[i-1] - t
    for i in range(N):
        if d[i] > 0 or d[i]%N != 0:
            print("NO")
            return
    print("YES")
    
if __name__ == '__main__':
    main()
