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

n = input()
v = map(int, raw_input().split(' '))
startHere = [0 for i in range(n)]

if sum(v) % ((n * (n + 1)) / 2) != 0:
	print "NO"
	sys.exit()

operations = sum(v) / ((n * (n + 1)) / 2)
operationsFound = 0

for i in range(n):
	diff = v[(i + 1) % n] - v[i]

	if (operations - diff) % n != 0 or operations - diff < 0:
		print "NO"
		sys.exit()
	else:
		operationsFound += (operations - diff) / n

if operationsFound == operations:
	print "YES"
else:
	print "NO"
