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: Accepted)

object Main extends App {
  val _ = io.StdIn.readInt()
  val arr: Array[Int] = io.StdIn.readLine().split(" ").map(_.toInt)
  val min = arr.min

  def mkGroup(s: IndexedSeq[Int]): Seq[Seq[Int]] = {
    val sorted: Seq[Int] = s.sorted
    val m: collection.mutable.Map[Int, Int] = collection.mutable.Map.empty
    s.indices.foreach(i => m.update(i, sorted.indexOf(s(i))))
    def getCycle(n: Int): List[Int] = m.get(n) match {
      case None => List()
      case Some(x) => m.remove(n); n :: getCycle(x)
    }
    s.indices.map(i => getCycle(i)).filterNot(_.isEmpty)
  }

  def cost(inds: Seq[Int]): Int = {
    val s = inds.map(arr(_))
    val sum = s.sum
    val smin = s.min
    ((s.length - 2) * smin + sum) min ((s.length+1) * min + smin + sum)
  }

  val groups = mkGroup(arr)
  println((groups map cost).sum)
}