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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class Test
{
	public static void Main()
	{
		int n = int.Parse(Console.ReadLine());
        int[] A = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        
        Dictionary<int, int> T = new Dictionary<int, int>();
        var tmp = A.OrderBy(a => a).ToArray();
        for(int i = 0; i < n; i++) { T[tmp[i]] = i; }
        
        bool[] V = new bool[n];
        
        int s = A.Min();
        int result = 0;
        
        for (int i = 0; i < n; i++) {
        	if (V[i]) { continue; }
        	
        	int cur = i;
        	int sum = 0;
        	int min = A[cur];
        	int an = 0;
        	
        	while(!V[cur]) {
        		V[cur] = true;
        		an++;
        		
        		if (min > A[cur]) min = A[cur];
        		sum += A[cur];
        		cur = T[A[cur]];
        	}
        	result += Math.Min(sum + (an - 2) * min, min + sum + (an + 1) * s);
        }
        Console.WriteLine(result);
	}
}