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.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

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.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
using System;
using System.Collections.Generic;
using System.Linq;

namespace ALDS1_6_D
{
    class Program
    {
        static int n = 0;
        static bool[] vis = new bool[1001];
        static void Main(string[] args)
        {
            Console.ReadLine();
            var a = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse).ToList();
            var b = new List<int>(a);
            b.Sort();
            for (int i = 0; i < a.Count; i++)
            {
                if (!vis[i])
                {
                    vis[i] = true;
                    Check(a[i], i, a, b, new List<int>() { i });
                }
            }
            Console.WriteLine(n);
        }

        static void Check(int target, int p, List<int> a, List<int> b, List<int> temp)
        {
            var pb = b.IndexOf(a[p]);
            if (pb == p) return;
            if (a[pb] == target)
            {
                var min = a[temp[0]];
                var mini = 0;
                for (int i = 1; i < temp.Count; i++)
                    if (a[temp[i]] < min)
                    {
                        min = a[temp[i]];
                        mini = temp[i];
                    }
                foreach (var i in temp)
                {
                    vis[i] = true;
                    if (i != mini) n += a[i] + min;
                }
                return;
            }
            else temp.Add(pb);
            Check(target, pb, a, b, temp);
        }
    }
}