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

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    n = int(readline())
    a = list(map(int, readline().split()))
    x = n * (n + 1) // 2
    y = sum(a)

    if y % x != 0:
        return print("NO")

    b = [0] * n
    c = y // x
    for i in range(n):
        b[i] = a[i] - a[(i + 1) % n] + c

    p = [0] * n
    for i in range(n):
        if b[i] % n != 0 or b[i] < 0:
            return print("NO")
        else:
            p[i] = b[i] // n

    if sum(p) == c:
        print("YES")
    else:
        print("NO")


if __name__ == '__main__':
    main()
