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
#include <stdio.h>
#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>
using namespace std;
#define N 40

bool comp1(const pair<int, int> &a, const pair<int, int> &b)
{
    return a.first < b.first;
}
bool comp2(const pair<int, int> &a, const pair<int, int> &b)
{
    return a.second < b.second;
}
int main()
{
    int n;
    cin >> n;
    int w[n], x[n];
    for (int i = 0; i < n; i++)
    {
        cin >> w[i];
        x[i] = w[i];
    }

    sort(x, x + n);
    for (int i = 0; i < n; i++)
    {
        if (i != 0)
            cout << " ";
        cout << x[i];
    }
    cout << endl;
    int *p, *q;
    int sum = 0, tmp;
 }
    for (int i = 0; i < n; i++)
    {
        p = find(w, w + n, x[i]);
        while (i != p - w)
        {
            q = find(w, w + n, x[p - w]);
            tmp = *p;
            *p = *q;
            *q = tmp;
            sum += *p + *q;
            p = q;
        }
    }

    cout << sum << "\n";
    return 0;
}
