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

namespace aizu1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] w = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);

            int cost = 0;

            cost = findMin(w,n,cost);

            Console.WriteLine(cost);
        }

        static int findMin(int[] w, int n, int cost)
        {
            if (n ==1) return cost;

            int m=0,p=0;
            max(w, n,out m, out p);

            if(w[n-1]!=m)
            {
                int t = w[n - 1];
                w[n - 1] = m;
                w[p] = t;
                cost += (w[n - 1] + w[p]);
            }

            return findMin(w, n-1, cost);
            
        }

        static void max(int[]w, int n, out int m, out int p)
        {
            m = w[0];
            p = 0;
            for(int i=1;i<n;i++)
            {
                p = (m >= w[i] ? p : i);
                m =( m >= w[i] ? m : w[i]);
               
            }
        }
    }
}