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
# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline


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

    k = sum(A)//(N*(N+1)//2)
    if sum(A) % (N*(N+1)//2) != 0:
        return "NO"

    D = [0]*N
    for i in range(N-1):
        D[i] = A[i+1]-A[i]-k
    D[-1] = A[0]-A[-1]-k

    cnt = sum([v//N for v in D])
    if all(x <= 0 and -x % N == 0 for x in D)and -cnt == k:
        return "YES"
    else:
        return "NO"


print(solve())
