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<iostream>
#include<algorithm>
#include<vector>
using namespace std;

int main(){
    int n;
    cin >> n;
    vector<int> W(n);
    for (auto& w : W) cin >> w;

    vector<int> Ws = W;
    sort(Ws.begin(), Ws.end());

    int cost = 0;
    int left = 0;
    while (left < n - 1) {
        int min_i = min_element(W.begin() + left, W.end()) - W.begin();
        int cnt = 0;
        while (1) {
            int tgt_i = find(W.begin() + left, W.end(), Ws[min_i])
                        - W.begin();
            if (tgt_i == min_i) break;
            cost += W[min_i] + W[tgt_i];
            swap(W[min_i], W[tgt_i]);
            cnt++;
            min_i = tgt_i;
        }
        int compare = cnt * W[min_i] - 2 * (W[min_i] + Ws[0]) - cnt * Ws[0];
        if (compare > 0) cost -= compare;
        left++;
    }
    cout << cost << endl;

    return 0;
}