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 <bits/stdc++.h>
using namespace std;
static const int MAX = 1000;
static const int VMAX = 10000;
int a[MAX];
int b[MAX], t[VMAX+1];

int main(){

  int n;
  cin >> n;
  int s = VMAX;
  for(int i = 0; i < n; i++){
    cin >> a[i];
    s = min(s, a[i]);
  }
  int ans = 0;
  bool v[MAX];
  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 ss = 0, an = 0;
    int m = VMAX;
    while(true){
      v[cur] = true;
      an++;
      m = min(m, a[cur]);
      ss += a[cur];
      cur = t[a[cur]];
      if(v[cur]) break;
    }
    ans += min(ss + (an - 2) * m, m + ss + (an + 1) * s);
  }
  cout << ans << endl;
  return 0;
}
