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.Text;

namespace ALDS1_6_D
{
    class Program
    {
        int sum;

        public Program ()
        {
            this.sum = 0;
        }

        public void Proc()
        {
            int N = int.Parse(Console.ReadLine());
            int[] list = new int[N];
            string[] num = Console.ReadLine().Split(' ');
            for (int i = 0; i < N; i++)
            {
                list[i] = int.Parse(num[i]);
            }

            quickSort(list, 0, N - 1);

            Console.WriteLine(this.sum);
        }

        static void Main(string[] args)
        {
            Program prg = new Program();
            prg.Proc();
        }

        public void quickSort(int[] arr_i, int p, int r)
        {
            if (p < r)
            {
                int q = partition(arr_i, p, r);
                quickSort(arr_i, p, q - 1);
                quickSort(arr_i, q + 1, r);
            }
        }
        public int partition(int[] arr_i, int p, int r)
        {
            int x = arr_i[r];
            int i = p - 1;
            int tmp_i = 0;
            for (int j = p; j < r; j++)
            {
                if (arr_i[j] <= x)
                {
                    i++;
                    tmp_i = arr_i[i];
                    arr_i[i] = arr_i[j];
                    arr_i[j] = tmp_i;
                    if (i != j) this.sum += arr_i[i] + arr_i[j];
                }
            }
            tmp_i = arr_i[i + 1];
            arr_i[i + 1] = arr_i[r];
            arr_i[r] = tmp_i;
            if (i + 1 != r) this.sum += arr_i[i + 1] + arr_i[r];
            return i + 1;
        }
    }
}