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(raw_input())
a = [int(x) for x in raw_input().split()]

def m():
	s = n * (n + 1) / 2
	sa = sum(a)
	if sa % s != 0:
		return False
	j = sa / s
	sj = 0
	for x, y in zip(a, a[1:] + [a[0]]):
		iN = j - (y - x)
		if iN % n != 0 or iN < 0:
			return False
		i = iN / n
		sj += i
	if sj != j:
		return False
	return True

print "YES" if m() else "NO"
