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 calc_cost cycle, min_num
  x = cycle.sum + (cycle.length - 2) * cycle.min
  y = cycle.sum + cycle.min + (cycle.length + 1) * min_num
  [x, y].min
end

n = gets.chomp.to_i
as = gets.chomp.split(' ').map(&:to_i)
min_num = as.min
bs = as.sort
cycles = []
while !as.empty?
  a = as.shift
  b = bs.shift
  next if a == b
  cs = [a, b]
  while fb = as.find_index(b)
    b = bs[fb]
    cs << b
    as.delete_at(fb)
    bs.delete_at(fb)
  end
  cycles << cs
end

cost = 0
cycles.each do |c|
  c.pop
  cost += calc_cost(c, min_num)
end
puts cost