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 n = 0, a[1000] = {0}, c = 0;
int partition(int a[1000], int p, int r) {
  int x = a[r - 1];
  int i = p - 1;
  for (int j = p; j < r; j++) {
    if (a[j - 1] <= x) {
      i++;
      swap(a[i - 1], a[j - 1]);
      if (i != j) c += a[i - 1] + a[j - 1];
    }
  }
  swap(a[i], a[r - 1]);
  if (i != r - 1) c += a[i] + a[r - 1];
  return i + 1;
}
void QuickSort(int a[1000], int p, int r) {
  if (p < r) {
    int q = partition(a, p, r);
    QuickSort(a, p, q - 1);
    QuickSort(a, q + 1, r);
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  QuickSort(a, 1, n);
  cout << c << endl;
  return 0;
}
