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)

N = gets.to_i
M = N * (N + 1) / 2

a_list = gets.strip.split(/ /).collect{|num| num.to_i}

sum = a_list.inject(:+)

if sum % M == 0
	L = sum / M
	
	start_points = 0
	
	prev_a = a_list[N - 1]
	(0...N).each{|i|
		a = a_list[i]
		diff = a - prev_a
		if diff > L
			puts "NO1"
			exit
		elsif diff != L
			# x - (N - 1)(L - x) = diff
			# x = (diff + NL - L) / N
			if (diff + N * L - L) % N != 0
				puts "NO2"
				exit
			else
				start_points += L - (diff + N * L - L) / N
				if start_points > L
					puts "NO3"
					exit
				end
			end
		end
		prev_a = a
	}

	if (L - start_points) % L == 0
		puts "YES"
	else
		puts "NO"
	end
	
else
	puts "NO"
end