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;

namespace ALDS1_6_D {
    public static class Problem {
        public static int GetMinCost(this int[] source) {
            int n = source.Length;
            int minCost = 0;
            bool[] used = new bool[n];

            int[] sorted = (int[])source.Clone();
            Array.Sort(sorted);
            int minValue = sorted[0];

            Dictionary<int, int> valueToIndex = Enumerable.Range(0, n)
                .ToDictionary(i => source[i], i => i);
            
            for(int i = 0; i < n; i++) {
                if (used[i] || valueToIndex[sorted[i]] == i)
                    continue;

                int minValueInGroup = sorted[i];
                int curPosition = valueToIndex[minValueInGroup];
                int sumOriginal = 0;
                int sumReplace = (minValue + minValueInGroup) * 2;

                while (curPosition != i) {
                    used[curPosition] = true;
                    int nextValue = sorted[curPosition];
                    sumOriginal += nextValue + minValueInGroup;
                    sumReplace += nextValue + minValue;
                    curPosition = valueToIndex[nextValue];
                }
                minCost += Math.Min(sumOriginal, sumReplace);
            }
            return minCost;
        }
    }

    class Program {
        static void Main(string[] args) {
            Console.ReadLine();
            int[] input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            Console.WriteLine(input.GetMinCost());
        }
    }
}