Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 Ruby (judge verdict: Accepted)

n = gets.to_i
w = gets.split.map(&:to_i)
ws = w.sort
pos = {}
(0...n).each do |i|
  pos[ws[i]] = i
end
min = ws[0]
flag = [true]*n
cost = 0
(0...n).each do |i|
  if flag[i]
    flag[i] = false
    count = 0
    startPos = i
    nextPos = pos[w[i]]
    while nextPos != startPos do
      flag[nextPos] = false
      cost += ws[nextPos]
      count += 1
      nextPos = pos[w[nextPos]]
    end
    if min*count + 2*(min+ws[i]) < ws[i]*count
      cost += min*count + 2*(min+ws[i])
    else
      cost += ws[i]*count
    end
  end
end
printf("%d\n",cost)