Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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
array=gets.chomp.split(" ").map(&:to_i)
sorted = array.sort

ret = 0

(0..(n-1)).each do |i|
    t = sorted[i]
    t_index = array.index(t)
    count = 0
    while t_index > i do
        count+=1
        s = sorted[t_index]
        s_index = array.index(s)
        ret+=s
        array[t_index], array[s_index] = array[s_index], array[t_index]
        t_index = s_index
    end
    ret += [t*count, t*2+sorted[0]*(count+2)].min
end

puts ret