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(n,list)
  total = 0
  list.each do |e|
    total += e
  end

  os = onestep_sum(n)
  return "NO" if total % os != 0

  count = total / os
  hand = 0

  (0...n).each do |idx|
    ni = idx + 1
    ni = 0 if ni == n
    diff = list[ni] - list[idx]
    next if diff == count
    hand += ((diff - count) * -1) / n
  end
  if hand == count
    return "YES"
  else
    return "NO"
  end
end

def onestep_sum(n)
  (n * (n + 1) / 2)
end

def main
  n = gets.to_i
  list = gets.split.map {|e| e.to_i}
  puts solve(n,list)
end

main