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 w[1000];
  int sw[1000];
  int solve();
};
int MinCostSort::solve() {
  int cost = 0;
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
    sw[i] = w[i];
  }
  sort(sw, sw + n);
  int j, k;
  for (int i = 0; i < n; ++i) {
    for (j = 0; j < n; ++j) {
      if (sw[i] == w[j]) break;
    }
    for (k = 0; k < n; ++k) {
      if (sw[j] == w[k]) break;
    }
    if (j != k) {
      cost += (w[j] + w[k]);
      swap(w[j], w[k]);
    }
  }
  cout << cost << endl;
  return 0;
}
int main() {
  MinCostSort mcs;
  mcs.solve();
  return 0;
}
