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;
const int num = 1001,num1 = 10000, INF = 2000000000;
int n, a[num], b[num], c[num1], tf[num], s = INF;
inline int mini() {
    int an = 0;
    int cu = 0;
    for (int i = 0; i < n; i++) {
        if (tf[i]) continue;
        cu = i;
        int m = INF;
        int sum = 0;
        int cnt = 0;
        while (true) {
            tf[cu] = 1;
            int v = a[cu];
            cnt++;
            m = min(v, m);
            sum += v;
            cu = c[v];
            if (tf[cu]) break;
        }
        an += min(sum + m*(cnt - 2), sum + m*(cnt - 2) + 2 * (m + s) - (m - s)*(cnt - 1));
    }
    return an;
}
int main() {
    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        s = min(a[i], s);
        b[i] = a[i];
        tf[i] = 0;
    }
    sort(b, b + n);
    for (int i = 0; i < n; i++) 
        c[b[i]] = i;
    int ans = mini();
    cout << ans << endl;
    return 0;
}
