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>

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

    std::vector< int > ws(n);
    for (auto &w: ws) std::cin >> w;

    const int inf = 1001001001;
    int min_w = inf;
    for (auto w: ws) {
        min_w = std::min(min_w, w);
    }

    std::vector< int > ps(n);
    for (int i = 0; i < n; ++i) {
        ps[i] = i;
    }

    std::sort(ps.begin(), ps.end(), [ws](int a, int b) { return ws[a] < ws[b]; });

    int ans = 0;
    std::vector< bool > used(n);
    for (int i = 0; i < n; ++i) {
        if (used[i]) continue;

        used[i] = true;
        int min_c = ws[i];
        int sum_c = ws[i]; 
        int cnt = 1;
        for (int j = ps[i]; j != i; j = ps[j]) {
            min_c = std::min(min_c, ws[j]);
            sum_c += ws[j];
            cnt++;
            used[j] = true;
        }

        ans += (sum_c - min_c) + std::min((cnt - 1) * min_c, (cnt + 1) * min_w + 2 * min_c);
    }

    std::cout << ans << std::endl;
}


