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
# -*- coding: utf-8 -*-

def io_generator():
	return input()

#+++++++++++++++++++

def main(io):
	ret_ng='NO'
	ret_ok='YES'
	
	n=int(io())
	l= list(map(int, io().split()))
	
	v_one_act =n*(n+1)/2
	
	if sum(l)%v_one_act != 0:
		return ret_ng
		
	act_num=sum(l)//v_one_act	
	st_num=0
	
	for a,b in zip(l, l[1:]+l):
		diff = b - a
		if (act_num-diff)%(n)!=0:
			return ret_ng
		if (act_num-diff)<0:
			return ret_ng
		st= (act_num-diff)//(n)
		st_num+=st
	
	if act_num!=st_num:
		return ret_ng
		
	
		
	return ret_ok

#++++++++++++++++++++

if __name__ == "__main__":
	io= lambda : io_generator()
	print (main(io))
