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(arr)
  sorted = arr.sort
  n = arr.length
  used = Array.new(n, false)
  minimum = arr.min
  max = arr.max
  circle_index = Array.new(max)
  arr.each_with_index do |v, i|
    circle_index[v] = i
  end
  # puts circle_index

  ans = 0
  arr.each_with_index do |v, i|
    if used[i]
      next
    end
    if sorted[i] == v
      used[i] = true
      next
    end
    cur_i = i
    m = v
    s = v
    cur_n = 1
    used[i] = true
    while true
      cur_i = circle_index[sorted[cur_i]]
      if used[cur_i] 
        break
      end
      # puts "i: #{i}, cur_i: #{cur_i}, m: #{m} s: #{s}"
      m = [m, arr[cur_i]].min
      s += arr[cur_i]
      cur_n += 1
      used[cur_i] = true
    end
    ans += [(s + (cur_n - 2) * m), (s + m + (cur_n + 1) * minimum)].min
  end
  ans
end

n = gets.to_i
arr = gets.split.map(&:to_i)
puts solve(arr)