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.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

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.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
n = gets.chomp.to_i
arr = gets.chomp.split.map(&:to_i)
t = []
n.times do |i|
  t << arr.shift
end

# swap????????????
def swap(list, idx1, idx2)
  list[idx1], list[idx2] = list[idx2], list[idx1]
  return list
end

def minCostPath(list)
  sorted = list.sort
  total = 0
  
  # list?????????
  list.size.times do |i|
    # ???????????????????????????????????????????????£?????????
    idx1 =sorted[i]
   
    # ??????????????????????????????????±??????????index????????£?????????
    idx2 = list.index idx1
    n = 0 
    while idx2 > i
      # ??????????????????
      n += 1

      sortedidx = list.index sorted[idx2]
      total += list[b]
      list = swap(list, idx2, sortedidx) 
      idx2 = sortedidx
    end
    total += [idx1 * n, t*2+sorted[0]*(n+2)].min
  end
  return total
end

total = minCostPath(t)
p total