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;
int main(void) {
  int num;
  cin >> num;
  vector<int> a(num);
  vector<int> sorted(num);
  int pos[1000];
  int order[1000];
  int cost = 0;
  for (int i = 0; i < num; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < num; i++) sorted[i] = a[i];
  sort(sorted.begin(), sorted.begin() + num);
  for (int i = 0; i < num; i++) pos[sorted[i]] = i;
  for (int i = 0; i < num; i++) {
    int x = order[0] = i;
    int minn = 1000;
    int start = 0;
    if (i == pos[a[i]]) continue;
    for (int j = 1;; j++) {
      x = pos[a[x]];
      if (x == i) break;
      if (a[x] < minn) {
        minn = a[x];
        start = j;
      }
      order[j] = x;
    }
    for (int j = start - 1; j >= 0; j--) {
      cost += (minn + a[order[j]]);
      a[order[j + 1]] = a[order[j]];
      a[order[j]] = minn;
    }
  }
  cout << cost << endl;
}
