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)

n = gets.to_i
baggage = gets.split.map(&:to_i)
sorted = baggage.sort
pos = {}
n.times{ |i| pos[sorted[i]] = i }
cost = 0
used = [false] * n
n.times do |s|
  next if used[s]
  cur = s
  count = 0
  loop do
    count += 1
    used[cur] = true
    w = baggage[cur]
    cost += w
    cur = pos[w]
    break if used[cur]
  end
  cost += [sorted[cur] * (count - 2), sorted[cur] + sorted[0] * (count + 1)].min
end
p cost