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 <cstdio>
using namespace std;
#include <algorithm>
#include <cmath>

const int Wmax = pow(10, 4) + 1;
int s;

int solve(int A[], int n){
    bool T[n];
    int B[n], Index[Wmax];
    for(int i=0; i<n; i++){
        T[i] = false;
        B[i] = A[i];
    }
    int total_w = 0;
    sort(B, B+n);
    for(int i=0; i<n; i++){ Index[B[i]] = i;}
    for(int j=0; j<n; j++){
        if(T[j] == false){
            T[j] = true;
            int wmin, sum = 0, cur, cnt=1;
            wmin = A[j];
            sum += A[j];
            cur = Index[wmin];
            while(cur != j){
                T[cur] = true;
                cnt++;
                sum += A[cur];
                wmin = min(wmin, A[cur]);
                cur = Index[A[cur]];
            }
            total_w += min(sum+(cnt-2)*wmin, sum+wmin+(cnt+1)*s);
        }
    }

    return total_w;
}

int main(){
    int n;
    s = Wmax;
    scanf("%d", &n);
    int A[n];
    for(int i=0; i<n; i++){
        scanf("%d", &A[i]);
        s = min(s, A[i]);
    }

    int ans = solve(A, n);
    printf("%d\n", ans);

    return 0;
}
