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;
void show(int arr[], size_t size) {
  cout << arr[0] << flush;
  for (size_t i = 1; i < size; i++) {
    cout << ' ' << arr[i] << flush;
  }
  cout << endl;
}
int selectionSort(int* arr, size_t arr_s) {
  size_t imin, cost = 0;
  for (size_t i = 0; i < arr_s - 1; i++) {
    imin = i;
    for (size_t j = i + 1; j < arr_s; j++) {
      imin = (arr[imin] > arr[j]) ? j : imin;
    }
    if (imin != i) {
      swap(arr[imin], arr[i]);
      cost += arr[imin] + arr[i];
    }
  }
  return cost;
}
int main() {
  size_t arr_s;
  cin >> arr_s;
  int* arr = new int[arr_s];
  for (size_t i = 0; i < arr_s; i++) {
    cin >> arr[i];
  }
  long long minCost = selectionSort(arr, arr_s);
  cout << minCost << endl;
}
