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 Ruby (judge verdict: Accepted)

def solve(orig_arr)
  sorted_arr = orig_arr.sort
  smallest = sorted_arr.first
  cost = 0
  visited = {}
  value_to_sorted_index = {}

  sorted_arr.size.times do |i|
    value_to_sorted_index[sorted_arr[i]] = i
  end

  orig_arr.size.times do |i|
    next if visited[i]

    current = i
    sum = 0
    min = Float::INFINITY
    n = 0

    loop do
      visited[current] = true
      n += 1
      value = orig_arr[current]
      min = [value, min].min
      sum += value
      current = value_to_sorted_index[value]
      break if visited[current]
    end

    cost1 = sum + (n - 2) * min
    cost2 = min + sum + (n + 1) * smallest

    cost += [cost1, cost2].min
  end

  cost
end

if $PROGRAM_NAME == __FILE__
  n = gets.to_i

  arr = gets.chomp.split.map(&:to_i)

  puts solve(arr)
end