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
n = int(input())
a = list(map(int, input().split()))
if n == 1:
	print('YES')
	exit()
tot = 0
for i in range(n):
	tot += a[i]
 
if tot % (n*(n+1)//2) != 0:
	print('NO')
	exit()
times = tot//(n*(n+1)//2)
 
x = a[n-1]-a[0]+times
if (x < 0) |(x % n != 0):
	print('NO')
	exit()
for i in range(1,n):
	x = a[i-1]-a[i]+times
	#print(i, x, times)
	if (x < 0) | (x % n != 0):
		print('NO')
		exit()
print('YES')