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: Time Limit Exceeded)

def op(ary, i)
  ary = ary.dup
  i.upto(i + ary.size - 1).each do |j|
    ary[j % ary.size] -= j - i + 1
    fail 'invalid operation' if ary[j % ary.size] < 0
  end
  ary
end

def solved?(ary)
  ary.inject(:+) == 0
end

def unsolvable?(ary)
  !solved?(ary) && ary.find { |i| i == 0 } != nil
end

def solvable?(ary)
  if solved?(ary)
    return true
  elsif unsolvable?(ary)
    return false
  else
    (0...(ary.size)).each do |i|
      begin
        return true if solvable?(op(ary, i))
      rescue => e
        # p e
      end
    end
    return false
  end
end

gets
a = gets.split.map(&:to_i)
puts solvable?(a) ? 'YES' : 'NO'