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>
#define MAX 10000
int main(void){
    int n, mmin, min, ans, sum;
    ans = 0;
    std::cin >> n;
    std::vector<int> A(n), B(n);
    for(int i = 0; i < n; i++){
        std::cin >> A[i];
    }

    B = A;
    std::sort(B.begin(), B.end());

    std::vector<bool> flag(n, false);
    std::vector<int> order(MAX + 1);

    
    for(int i = 0; i < n; i++){
        order[B[i]] = i;
    }
    mmin = B[0];
    for(int i = 0; i < n; i++){
        if(B[i] == A[i]) continue;
        int cur = i;
        int a = 0;
        sum = 0;

        
        if(flag[cur] == true){
            continue;
        }

        min = 1001001001;
        while(true){
            a++;
            flag[cur] = true;
            int v = A[cur];
            min = std::min(min, v);
            sum += v;

            
            cur = order[v];
            if(flag[cur] == true){
                break;
            }
        }

        
        ans += std::min(sum + (a - 2) * min, sum + min + (a + 1) * mmin);
        
    }

    std::cout << ans << std::endl;
    
}
