You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
import scala.collection.mutable

object Main extends App {
  implicit val ordering: Ordering[(Int, Vector[Int])] = Ordering.by(- _._1)
  val heap = mutable.PriorityQueue.empty[(Int, Vector[Int])]

  def isSorted(s: Seq[Int]): Boolean =
    (0 until s.length-1).dropWhile(i => s(i) < s(i+1)).isEmpty

  def solution(a: Vector[Int]): Int = {

    def loop(): Int = {
      val (cost, seq) = heap.dequeue()
      if(isSorted(seq)) cost
      else {
        for{
          i <- seq.indices
          j <- i+1 until seq.length
          si = seq(i)
          sj = seq(j)
        } heap.enqueue((cost + si + sj, seq.updated(i, sj).updated(j, si)))
        loop()
      }
    }

    loop()
  }

  val _ = io.StdIn.readInt()
  val init: Vector[Int] = io.StdIn.readLine().split(" ").map(_.toInt).toVector
  heap.enqueue((0, init))
  println(solution(init))
}