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;
long long n;
vector<long long> w;
vector<long long> w_;
long long ans = 0;
long long mini;
int main() {
  cin >> n;
  w = vector<long long>(n);
  w_ = vector<long long>(n);
  for (long long i = 0; i < n; i++) cin >> w[i];
  for (long long i = 0; i < n; i++) w_[i] = i;
  sort(w_.begin(), w_.end(),
       [](long long a, long long b) { return w[a] < w[b]; });
  for (long long i = 0; i < n; i++) {
    long long ans_ = 0, c = 0;
    while (w_[i] != i) {
      ans_ += w[w_[i]] + w[w_[w_[i]]];
      swap(w[w_[i]], w[w_[w_[i]]]);
      swap(w_[i], w_[w_[i]]);
      c++;
    }
    if (c * (w[i] - mini) > 2 * (w[i] + mini)) {
      ans_ -= c * (w[i] - mini) - 2 * (w[i] + mini);
    }
    ans += ans_;
  }
  cout << ans << endl;
  return 0;
}
