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
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpl_s(): return list(input().split())

N = int(input())
aa = inpl()
MIN,MAX = min(aa),max(aa)
SUM = sum(aa)
S = N*(N+1)//2

def main():
	if SUM%S != 0:
		return 'NO'
	else:
		k = SUM // S
		if MIN < k or k*N < MAX:
			return 'NO'
		tmp = 0
		for i in range(N):
			d = aa[i-1] - aa[i]
			d += k
			if d % N == 0:
				tmp += d//N
			else:
				return 'NO'
		if tmp == k:
			return 'YES'
		else:
			return 'NO'

print(main())
