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>
using namespace std;

int main(){
    int n;
    cin >> n;
    int A[n];
    int B[n];
    for (int i = 0; i < n; i++) {
        cin >> A[i];
        B[i] = A[i];
    }
    sort(B, B + n);
    int cnt = 0;
    // int i = 0;
    for (int i = 0; i < n; i++) {
        // if (A[i] == B[i]) {
        //     i++;
        //     continue;
        // }
        int tgt_idx = find(A, A + n, B[i]) - A;
        int n_cycle = 1;
        while (tgt_idx != i) {
            int dst_idx = find(A, A + n, B[tgt_idx]) - A;
            cnt += A[tgt_idx] + A[dst_idx];
            swap(A[tgt_idx], A[dst_idx]);
            tgt_idx = dst_idx;
            n_cycle++;
        }
        if ((n_cycle - 3) * B[i] > (n_cycle + 1) * B[0]) {
            cnt -= (n_cycle - 3) * B[i] - (n_cycle + 1) * B[0];
        }
    }
    cout << cnt << endl;
    return 0;
}