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)

cost=0
N = gets.to_i
A = gets.split.map &:to_i
min = A.min
sorted = Array.new(N, false)
sortedA = A.sort

A.each_with_index {|e, i|
    index = sortedA.index(e)
    next if sorted[i] or index == i
    sorted[i] = true
    sum = e
    cycleMin = e
    num = 1
    value = e
    until sorted[index]
        sorted[index] = true
        num+=1
        value = A[index]
        sum += value
        if value < cycleMin
            cycleMin = value
        end
        index = sortedA.index(value)
    end
    cost1 = cycleMin * (num - 3)
    cost2 = min * (num + 1)
    cost += sum + cycleMin + (cost1<=cost2 ? cost1 : cost2)
}
puts cost