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 <vector>
#include <algorithm>
using namespace std;

int main() {

  long long int n;
  cin >> n;

  vector< long long int > v, vs;

  for ( long long int i = 0; i < n; i++ ) {

    long long int in;
    cin >> in;
    v.push_back( in );
    vs.push_back( in );

  }

  sort( vs.begin(), vs.end() );

  vector< long long int > t;

  long long int mi = 100000;

  for ( long long int i = 0; i < n; i++ ) {
    mi = min( mi, v[i] );
    for ( long long int j = 0; j < n; j++ ) {
      if ( v[i] == vs[j] ) {
	t.push_back( j );
	break;
      }
    }
  }

  long long int ans = 0;

  for ( long long int i = 0; i < n; i++ ) {

    if ( vs[i] != v[i] ) {

      long long int k = t[i];
      long long int m = v[i];
      long long int cnt = v[i];
      long long int num = 1;

      while( k != i ) {
	num++;
	cnt += v[k];
	m = min( m, v[k] );
	swap( v[i], v[k] );
	k = t[k];
      }

      ans += min( ( num - 2 ) * m, m + ( num + 1 ) * mi ) + cnt;

    }
    /*
    for ( long long int j = 0; j < n; j++ ) {
      cout << " " << v[j];
    }
    cout << endl;
    */
  }

  cout << ans << endl;

}