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 <map>

using namespace std;

const int MAXN = 1010;
int w[MAXN];
bool done[MAXN];

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n, mini = 100000;
    cin >> n;
    map<int, int> mp;
    for (int i = 0; i < n; i++) {
        cin >> w[i];
        mp[w[i]] = 0;
        mini = min(mini, w[i]);
    }
    int k = 0;
    for (auto& p : mp) p.second = k++;
    
    int ans = 0;
    for (int i = 0; i < n; i++) {
        if (done[i]) continue;
        int cnt = 0, now = i, mi = 100000, sum = 0;
        while (1) {
            if (done[now]) break;
            cnt++;
            done[now] = true;
            mi = min(mi, w[now]);
            sum += w[now];
            now = mp[w[now]];
        }
        int tmp = sum+(cnt-2)*mi;
        tmp = min(tmp, sum+mi+mini*(cnt+1));
        ans += tmp;
    }
    cout << ans << endl;
    return 0;
}
