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 Julia (0.5.0) (judge verdict: Runtime Error)

function main()
	N=parse(Int,readline())
	A=map(x->parse(Int,x),split(readline()))
	S=sum(A)
	B=zeros(Int,N)
	for i=1:N
		B[i]=A[mod1(i+1,N)]-A[i]
	end
	all=div((N+1)*N,2)
	if sum%all!=0
		println("NO")
		exit()
	end
	K=div(sum,all)
	for i=1:N
		B[i]-=K
		if B[i]>0||B[i]%N!=0
			println("NO")
			exit()
		end
	end
	println("YES")
end
main()