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 <bits/stdc++.h>
using namespace std;

int main()
{
    int n;
    cin >> n;

    int w[n], sorted[n], minimum = 10000;
    bool visited[n];
    for (int i = 0; i < n; i++)
    {
        cin >> w[i];
        sorted[i] = w[i];
        visited[i] = false;
        minimum = min(minimum, w[i]);
    }

    sort(sorted, sorted + n);
    int inv[10001];
    for (int i = 0; i < n; i++)
        inv[sorted[i]] = i;

    int ans = 0;
    for (int i = 0; i < n; i++)
    {
        if (visited[i])
            continue;
        int sum = 0, c = 0, minw = 10000, j = i;
        while (!visited[j])
        {
            sum += w[j];
            c++;
            minw = min(minw, w[j]);
            visited[j] = true;
            j = inv[w[j]];
        }
        ans += min(sum + (c - 2) * minw, sum + minw + (c + 1) * minimum);
    }

    cout << ans << endl;
}
