6583: ALDS1_6_D : Minimum Cost Sort
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Description
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.
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.
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
$0 \leq w_i\leq 10^4$
$w_i$ are all different
Sample 1 Input
5
1 5 3 4 2
Sample 1 Output
7
Sample 2 Input
4
4 3 2 1
Sample 2 Output
10