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>
const int INF = 1e9;
using namespace std;
bool stable = true;
int main() {
  int n;
  int cost = 0;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < (int)(n); i++) cin >> a[i];
  auto p = a.end();
  for (int max = n - 1; max > 0; max--) {
    int max_index = max_element(a.begin(), p) - a.begin();
    if (max_index != max) {
      swap(a[max_index], a[max]);
      cost += a[max_index] + a[max];
    }
    p--;
  }
  cout << cost << endl;
  return 0;
}
