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<algorithm>
using namespace std;
static const int MAX = 1000;
static const int VMAX = 10000;

int n, A[MAX], s;
int B[MAX],T[VMAX + 1];

int solve(){
  int ans = 0;
  bool V[VMAX];
  for( int i = 0 ; i < n ; i++ ){
    B[i] = A[i];
    V[i] = false;
  }
  sort( B, B + n );
  for( int i = 0 ; i < n ; i++ )T[B[i]] = i;
  for( int i = 0 ; i < n ; i++ ){
    if( V[i] )continue;
    int cur = i;
    int S = 0;
    int m = VMAX;
    int an = 0;
    while( 1 ){
      V[cur] = true;
      an++;
      int v = A[cur];
      m = min( m, v);
      S += v;
      cur = T[v];
      if( V[cur] )break;
    }
    ans += min( S + ( an - 2 ) * m, m + S  + ( an + 1 ) * s);
  }
  return ans;
}

int main( void ){
  cin >> n;
  s = VMAX;
 
  for( int i = 0 ; i < n ; i++ ){
    cin >> A[i];
    s = min(s,A[i]);
  }
  int ans = solve();
  cout << ans << endl;

  return 0 ;
}