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 argc, char const *argv[]) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, tmp, cost = 0;
  std::cin >> N;
  std::vector<int> w, sorted;
  w.reserve(1000);
  sorted.reserve(1000);
  for (size_t i = 0; i < N; i++) {
    std::cin >> tmp;
    w.push_back(tmp);
    sorted.push_back(tmp);
  }
  sort(sorted.begin(), sorted.end());
  for (size_t i = 0; i < N; i++) {
    for (size_t j = i; j < N; j++) {
      if (w[i] == sorted[j] && i != j) {
        cost += w[i] + w[j];
      }
    }
  }
  std::cout << cost << '\n';
  return 0;
}
