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)

object Main {

  import scala.math._

  def main(args: Array[String]) {

    val sc = new java.util.Scanner(System.in)

    val n = sc.nextInt()
    val arr = Array.fill(n)(sc.nextInt())

    if (check(arr)) println("YES")
    else println("NO")

  }
  def check(arr: Array[Int]): Boolean = {
    val n = arr.length
    def f(arr: Array[Int]): Boolean = {
      def calc(idx: Int, max_idx: Int): Int = {
        if (idx-max_idx > 0 ) arr(idx) - (idx - max_idx)
        else arr(idx)-(n + idx - max_idx)
      }
      def is_all_0(arr: Array[Int]): Boolean = {
        if (arr.filter(_ != 0).isEmpty) true
        else false
      }
      def exist_not_positive(arr: Array[Int]): Boolean = {
        if (arr.filter(_ < 1).length > 0) true
        else false
      }
      val max_idx = (0 until n).toList.maxBy(arr(_))
      val new_arr = (0 until n).toArray.map(calc(_, max_idx))

      if (is_all_0(new_arr)) true
      else if (exist_not_positive(new_arr)) false
      else f(new_arr)
    }
    f(arr)
  }
}