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;
#define MAX 1000
#define VMAX 10000

int A[MAX], n, m, ans;
int B[MAX], T[VMAX + 1];

void solve(){
    bool V[MAX];
    ans = 0;
    
    sort(B, B+n);
    for(int i = 0; i < n; i++){
        T[B[i]] = i;
        V[i] = false;
    }
    for(int i = 0; i < n; i++){
        if(V[i]) continue;
        int cur = i;
        int s = VMAX;
        int sum = 0;
        int num_men = 0;
        while(1){
            V[cur] = true;
            num_men++;
            sum += A[cur];
            s = min(A[cur], s);
            cur = T[A[cur]];
            if(V[cur]) break;
        }
        
        ans += min((sum + (num_men -  2) * s), (sum + s + (num_men + 1) * m));
    }
}

int main(void){
    cin >> n;
    m = VMAX;
    
    for(int i = 0; i < n; i++){
        cin >> A[i];
        B[i] = A[i];
        m = min(m, A[i]);
    }
    
    solve();
    
    cout << ans << endl;
    
    return 0;
}

