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;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] A = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            
            Dictionary<int, int> T = new Dictionary<int, int>();
            var temp = A.OrderBy(a => a).ToArray();
            for (int i = 0; i < n; i++) T[temp[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 = int.MaxValue;
                int an = 0;

                while (true)
                {
                    V[cur] = true;
                    an++;

                    if (min > A[cur]) min = A[cur];
                    sum += A[cur];
                    cur = T[A[cur]];

                    if (V[cur]) break;
                }
                result += Math.Min(sum + (an - 2) * min, min + sum + (an + 1) * s);
            }
            Console.WriteLine(result);
        }
    }
}