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)

io = STDIN
n=io.gets.chomp.to_i
$base=(1..n).to_a
a=io.gets.chomp.split.map(&:to_i)
def check(ar)
  return false if ar.sort==$base
  return false if ar.any?{|x|x<=0}
  index = ar.each_cons(2).with_index.
       select{|pair,i|pair.first>pair.last}.
       map{|pair,i|i}.first
  return false unless index
  sft=$base.clone
  (index+1).times do
    top=sft.pop
    sft.unshift(top)
  end

  sft
end
ar=a
while(dif=check(ar))
  ar=ar.zip(dif).map{|i,j|i-j}
end
puts ar.sort==$base ? "YES" : "NO"