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 g_cost = 0;
void swap(int array[], int i0, int i1) {
  int temp = array[i1];
  array[i1] = array[i0];
  array[i0] = temp;
}
void selectionSort(int array[], int start, int end) {
  for (int i = start; i < end - 1; i++) {
    int min = array[i];
    int minIdx = i;
    for (int j = i + 1; j < end; j++) {
      if (min > array[j]) {
        min = array[j];
        minIdx = j;
      }
    }
    if (minIdx != i) {
      ;
      swap(array, i, minIdx);
      g_cost += array[i] + array[minIdx];
    }
  }
}
int main() {
  int numOfArray;
  cin >> numOfArray;
  cin.ignore();
  int array[numOfArray];
  for (int i = 0; i < numOfArray; i++) cin >> array[i];
  const int start = 0;
  const int end = numOfArray;
  selectionSort(array, start, end);
  cout << g_cost << endl;
  return 0;
}
