Problem:
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Minimum Cost Sort

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.

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.

Constraints

$1 \leq n \leq 1,000$

$0 \leq w_i\leq 10^4$

$w_i$ are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

Solution in Scala (judge verdict: Runtime Error)

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(i: Int): Int = {
      val e@(cost, seq) = heap.dequeue()
      if (isSorted(seq)) cost
      else {
        if (i < seq.length && seq.slice(i, seq.length).min == seq(i)) heap.enqueue(e)
        for (j <- i+1 until seq.length)
          heap.enqueue((cost + seq(i) + seq(j), seq.updated(i,seq(j)).updated(j, seq(i))))
        loop(i+1)
      }
    }
    loop(0)
  }

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