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 = [int(i) for i in input().split()]
if sum(a)%(n*(n+1)//2) != 0: print("NO")
else:
	x,flag,num = sum(a)//(n*(n+1)//2),True,0
	for i in range(n):
		if (a[i]-a[i-1]-x)%n!=0:
			flag = False
			break
		else: num+=abs((a[i]-a[i-1]-x)//n)
	if flag and num==x: print("YES")
	else: print("NO")