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()
a=map(int, raw_input().split())
diff=[a[(i+1)%n]-a[i] for i in range(n)]
cnt=max(diff)
diff=[value-cnt for value in diff]
start=[]
for value in diff:
	if value%n:
		print "NO"
		exit()
	else:
		start.append(-value/n)
cnt=sum(start)
b=[0]
for i in range(n):
	b[0]+=start[i]*(n-i)
for i in range(n):
	b.append(b[-1]+cnt-start[i]*n)
assert b[0]==b[-1]
b=b[:-1]
for i in range(n):
	if (a[i]-b[i])%(n*(n+1)/2) or a[i]<b[i]:
		print "NO"
		exit()
print "YES"