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
a = gets.split.map(&:to_i)

VMAX = 10000
S = a.min

def solve(a)
  ans = 0
  b = Marshal.load(Marshal.dump(a)).sort
  v = Array.new(N, false)
  t = []

  (0...N).each do |i|
    t[b[i]] = i
  end

  (0...N).each do |i|
    next if v[i]

    cur = i
    s = 0
    m = VMAX
    an = 0

    loop do
      v[cur] = true
      an += 1
      val = a[cur]
      m = [m, val].min
      s += val
      cur = t[val]

      break if v[cur]
    end
    ans += [s + (an - 2) * m, m + s + (an + 1) * S].min
  end
  ans
end

puts solve(a)