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<cstdio>
#include<algorithm>

#define MIN(X,Y) ((X)>(Y)?(Y):(X))

using namespace std;
int w[2000],sa[2000],idx[2000];
char sorted[2000];

int main(void) {
    int n;
    scanf("%d",&n);
    for(int i=0; i<n; i++)
        scanf("%d",&w[i]), sa[i]=w[i];
    sort(sa,sa+n);
    for(int i=0; i<n; i++)
        idx[i] = lower_bound(sa,sa+n,w[i])-sa;

//    for(int i=0; i<n; i++)
//        printf("%d ", idx[i]);
//    printf("\n");

    int min = sa[0];
    int res = 0;
    for(int i=0; i<n; i++) {
        int rescur=0, j=i, localmin=30000, cnt=0;
        if(sorted[j]) continue;
        while(!sorted[j]) {
            sorted[j]=1;
            cnt++;
            if(localmin > w[j]) localmin = w[j];
            rescur+=w[j];
            j = idx[j];
        }
//        printf("%d, %d, %d\n", rescur, localmin, cnt);
//        printf("%d : %d\n",rescur+(cnt-2)*localmin, rescur+localmin+2*min+(cnt-1)*min);
        res += MIN(rescur+(cnt-2)*localmin, rescur+localmin+2*min+(cnt-1)*min);
    }
    printf("%d\n",res);


    return 0;
}