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: Wrong Answer)

object Main {
  def main(args:Array[String]) {
    val n = scala.io.StdIn.readLine().toInt
    var A = scala.io.StdIn.readLine().split(' ').map(_.toLong)
    if (A.sum % (n*(n+1)/2) == 0) {
      val k = A.sum / (n*(n+1)/2)
      A = A ++ Array(A(0))
      val D = (A zip A.tail) map { case (x,y) => y - x - k }
      if (D.forall(x => x%n == 0 && x <= 0) && D.sum == -k * n)
        println("YES")
      else
        println("NO")
    }
    else
      println("NO")
  }
}