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 <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

int main(){
    int n, w[1000], a[1000], mi=1e6;
    cin >> n;
    for(int i=0;i<n;i++){
        cin >> w[i];
        a[i]=w[i];
        mi=min(mi, w[i]);
    }
    sort(a, a+n);
    int idx[100001];
    for(int i=0;i<n;i++) idx[w[i]]=i;

    ll cost = 0;
    ll ccost, cnt;
    for(int i=0;i<n;i++){
        if(a[i]==w[i]) continue;
        int j=idx[a[i]];
        int s=w[j];
        ccost = 0;
        cnt = 0;
        while(true){
            int k=idx[a[j]];
            ccost += w[k];
            cnt++;
            w[j]=w[k];
            w[k]=s;
            j=k;
            if(w[k]==a[k]) break;
        }
        cost += min(ccost + cnt*a[i], ccost + (a[i]+mi)*2 + cnt*mi);
    }
    std::cout << cost << endl;
    
    return 0;
}
