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.Linq;

namespace ALDS1_6_D
{
    public static class Sort
    {
        public delegate void SwapperAction<T>(ref T a, ref T b);
        public static void SelectionSort<T>(this T[] a, SwapperAction<T> swapper, bool desc = false) where T : IComparable
        {
            int n = a.Length;
            if (!desc)
            {
                for (int i = 0; i < n; ++i)
                {
                    int t = i;
                    for (int j = i + 1; j < n; ++j)
                    {
                        if (a[t].CompareTo(a[j]) > 0) t = j;
                    }
                    if (i != t) swapper.Invoke(ref a[i], ref a[t]);
                }
            }
            else
            {
                for (int i = 0; i < n; ++i)
                {
                    int t = i;
                    for (int j = i + 1; j < n; ++j)
                    {
                        if (a[t].CompareTo(a[j]) < 0) t = j;
                    }
                    if (i != t) swapper.Invoke(ref a[i], ref a[t]);
                }
            }
        }
    }
    class Program
    {
        static int n = 0;
        static void Main(string[] args)
        {
            Console.ReadLine();
            var a = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var b = a.Reverse().ToArray();
            b.SelectionSort(Swapper,true);
            Console.WriteLine(n);
        }

        static void Swapper(ref int a, ref int b)
        {
            if (a != b)
            {
                a ^= b;
                b ^= a;
                a ^= b;
            }
            n += a + b;
        }
    }
}