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;
static const int MAX = 1000;
static const int VMAX = 10000;

int solve(int a[], int n, int vmin) {
    int ans = 0;
    int b[MAX], t[VMAX+1];
    bool p[MAX];
    for (int i = 0; i < n; i++) {
        b[i] = a[i];
        p[i] = false;
    }
    sort(b, b + n);
    for (int i = 0; i < n; i++) t[b[i]] = i;
    for (int i = 0; i < n; i++) {
        if (p[i]) continue;
        int cur = i;
        int sum = 0;
        int m = VMAX;
        int an = 0;
        while (true) {
            p[cur] = true;
            an++;
            int v = a[cur];
            m = min(m, v);
            sum += v;
            cur = t[v];
            if (p[cur]) break;
        }
        ans += min(sum + (an - 2) * m, m + sum + (an + 1) * vmin);
    }

    return ans;
}

int main() {
    int n, a[MAX];
    int vmin = VMAX;

    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        vmin = min(vmin, a[i]);
    }
    cout << solve(a, n, vmin) << endl;
}

