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;
class MinCostSort {
 public:
  int solve();
};
int MinCostSort::solve() {
  int cost = 0;
  int n;
  cin >> n;
  vector<int> w(n, -1);
  vector<int> sw(n);
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
    sw[i] = w[i];
  }
  sort(sw.begin(), sw.end());
  int mw = sw[0];
  for (auto i = 0; i < n; ++i) {
    if (w[i] < 0) continue;
    if (w[i] == sw[i]) {
      w[i] = -1;
      sw[i] = -1;
      continue;
    }
    int mlw = 2000;
    int ii = i;
    int j;
    int sm = 0;
    int ct = 0;
    while (true) {
      for (j = 0; j < n; ++j) {
        if (sw[j] == w[ii]) break;
      }
      if (mlw > w[ii]) mlw = w[ii];
      sm += w[ii];
      ++ct;
      w[ii] = -1;
      sw[j] = -1;
      ii = j;
      if (ii == i) break;
    }
    cost += min(sm + (ct - 2) * mlw, sm + (ct + 1) * mw + mlw);
  }
  cout << cost << endl;
  return 0;
}
int main() {
  MinCostSort mcs;
  mcs.solve();
  return 0;
}
