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<math.h>
#include<iomanip>
#include<string.h>
#include<cstdio>
#include<cstdlib>
#include<stack>
#include<algorithm>

using namespace std;

int cost = 0;

void mincost(int c[], int a[], int k, int mina){
  int minc = 10000;
  int sum = 0;
  for(int i = 0; i < k; i++){
    minc = min(a[c[i]], minc);
    sum += a[c[i]];
  }
  cost += min(sum + (k - 2) * minc, sum + minc + (k + 1) * mina);
}

int main(){

  int n, mina = 10000;
  cin >> n;

  int a[n], b[n], c[n];
  for(int i = 0; i < n; i++){
    cin >> a[i];
    b[i] = a[i];
    mina = min(mina, a[i]);
  }

  sort(b, b + n);

  int k = 0, i = 0, flag = 0;

  while(flag != n){


    c[k] = i;

    for(i = 0; i < n; i++){
      if(a[c[k]] == b[i]){
        k++;
        if(c[0] == i){
          if(k > 1) mincost(c, a, k, mina);
          for(int j = 0; j < k; j++){
            a[c[j]] = -1;
          }
          k = 0;

          flag  = 0;
          for(int l = 0; l < n; l++){
            if(a[l] == -1) flag++;
            else{
              i = l;
              break;
            }
          }
        }
        break;
      }
    }
  }





cout << cost << endl;

}

