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: Runtime Error)

n = gets.to_i
a = gets.split.map(&:to_i)
sum = a.inject(:+)
t = sum / (n * (n+1)/2)
unless sum % (n * (n+1)/2) == 0
  puts "NO"
  exit
end
a.map!{|a|a - t}
sum = a.inject(:+)
deno = ((n * (n - 1) * n / 2))
left = (n - 2) * (n + 1) / 2
n.times do |row|
  s = sum + a[(n - 1 - row) % n] * (left + 1) - a[(n - row) % n] * (left + 1)
  if s % deno != 0 || s < 0
    puts "NO"
    exit
  end
end
puts "YES"