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: Wrong Answer)

n = gets.chomp.to_i
t = []
arr = gets.chomp.split.map(&:to_i)
n.times do |i|
  t << arr.shift
end

def minindexvalue(list)
  min = 10001 
  idx = 1001

  list.each.with_index do |x,i|
    if min > x
      idx = i
      min = x
    end
  end
  return idx
end

total = 0

res = []
until t.empty?
  idx = minindexvalue(t) 
  if idx == 0
    res << t.shift
  else
    total += t[0] + t[idx]
    t[0], t[idx] = t[idx], t[0]
    res << t.shift
  end
end
p total