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
def minimum_cost_sort(ary, n)
  cost = 0
  (n-1).downto(0) { |i|
    max = ary[0..i].max
    idx = ary.index(max)
    if i != idx
      tmp = ary[idx]
      ary[idx] = ary[i]
      ary[i] = tmp
      cost += ary[i] + ary[idx]
    end
  }
  cost
end

# main
n = gets.to_i
ary = gets.split(' ').map(&:to_i)
w = minimum_cost_sort(ary, n)
puts w