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
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    N = int(input())
    A = list(map(int,input().split()))

    s = N*(N + 1)//2
    tot = sum(A)
    if tot%s == 0:
        cnt = tot//s
    else:
        print('NO')
        return
    
    A.append(A[0])
    x = 0
    for i in range(N):
        diff = A[i + 1] - A[i]
        if cnt - diff < 0:
            print('NO')
            return
        if (cnt - diff)%N == 0:
            x += (cnt - diff)//N
        else:
            print('NO')
            return
    print('YES' if x == cnt else 'NO')
if __name__ == '__main__':
    main()