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 main() {
  int n;
  cin >> n;
  vector<int> W(n);
  for (auto& w : W) cin >> w;
  int cnt = 0;
  for (int i = n - 1; i >= 1; i--) {
    int max_i = max_element(W.begin(), W.begin() + i + 1) - W.begin();
    if (i == max_i) continue;
    cnt += W[i] + W[max_i];
    swap(W[i], W[max_i]);
  }
  cout << cnt << endl;
  return 0;
}
