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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.util.Scanner

/**
 * Created by sonetsuyoshi on 2015/12/16.
 */

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt
  val a = Array.fill(n)(sc.nextInt)


  def run(): Boolean = {
    val max = a.max
    val min = a.min

    if(min < 0) false
    else if(max == 0) true
    else {
      val id = a.indexOf(max)
      for(i <- 1 to n) {
        a((id + i) % n) -= i
      }
      run()
    }
  }

  if(run()) println("YES")
  else println("NO")

}