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;
using System.Text;
using System.Threading.Tasks;

namespace ALDS1_6_D
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = scan[0];
            var A = scan;
            var T = new Dictionary<int,int>();
            var temp = A.OrderBy(i => i).ToArray();
            for (int i = 0; i < n; i++) T[temp[i]] = i;
            var V = new bool[n];
            var s = A.Min();
            var ans = 0;
            for (int i = 0; i < n; i++)
            {
                if (V[i]) continue;
                int cur = i;
                int sum = 0;
                int min = A[cur];
                int an = 0;
                while (!V[cur])
                {
                    V[cur] = true;
                    an++;
                    if (min > A[cur]) min = A[cur];
                    sum += A[cur];
                    cur = T[A[cur]];
                }
                ans += Math.Min(sum + (an - 2) * min, min + sum + (an + 1) * s);
            }
            Console.WriteLine(ans);
        }

        static int[] scan
        {
            get { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
        }
    }
}