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
import heapq
from operator import itemgetter
from collections import deque, defaultdict
from bisect import bisect_left, bisect_right
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
MOD = 10**9 + 7

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

    S = sum(A)

    if S % (N * (N + 1) // 2) != 0:
        print('NO')
        return

    K = S // (N * (N + 1) // 2)
    for diff in [A[i] - A[i - 1] for i in range(N)]:
        if K - diff < 0 or (K - diff) % N != 0:
            print('NO')
            return

    print('YES')


sol()