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)

gets
w=gets.split.map.with_index{|l,i|[l.to_i,i]}
x=w.sort_by{|l|l[0]}
x.map.with_index{|l,i|w[w.index l]<<i}
c=0
w.map{|l|_,a,b=l
a==b&&next
q=*a
(_,a,b=w.find{|k|b==k[1]}
q<<a)while q[0]!=b
s=q.map{|r|w[r][2]=r
w[r][0]}
t=s.reduce:+
c+=[t+s[-1]+x[0][0]*z=-~s.size,t+s[-1]*(z-3)].min}
p c