Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

def solve(box,n)
	sum=[box.inject(&:+)]
	s=true
	while s==true && sum[0]>0
		s=bdec(box,n,sum)
	end
	puts sum[0]==0 ? "YES" : "NO"
end

def bdec(box,n,sum)
	m=midx(box)
	i=m; d=1; s=true
	n.times do |x|
		box[i]-=d
		sum[0]-=d
		if box[i]<0 then s=false end
		i+=1
		d+=1
		if i>n-1 then i=0 end
	end
	return s
end

def midx(box)
	mx=1000000000
	idx=0
	for i in 0..box.length-1
		if box[i]<mx
			mx=box[i]
			idx=i
		end
	end
	return idx
end

def dec(box,n)
	for i in 0..n-1
		box[i]-=(i+1)
	end
end

if __FILE__==$0
	
	rl_i=lambda{|str,dl|str.strip.split(dl).map(&:to_i)}
	r_i=lambda{|str|str.strip.to_i}
	dl=" "
	n=r_i[gets]
	num=rl_i[gets,dl]
	solve(num,n)
end