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() {
  int32_t n;
  cin >> n;
  vector<int32_t> w(n);
  for (int32_t i = 0; i < n; i++) {
    cin >> w[i];
  }
  vector<int32_t> sorted(w);
  sort(sorted.begin(), sorted.end());
  unordered_map<int32_t, int32_t> index;
  for (int32_t i = 0; i < n; i++) {
    index[sorted[i]] = i;
  }
  int32_t cost = 0;
  for (int32_t i = 0; i < n; i++) {
    if (w[i] != sorted[i]) {
      int32_t size = 1, sum = w[i], minval = INT32_MAX;
      int32_t j = index[w[i]], j_new;
      while (j != i) {
        size++;
        sum += w[j];
        minval = min(minval, w[j]);
        j_new = index[w[j]];
        w[j] = sorted[j];
        j = j_new;
      }
      cost += sum + minval * (size - 2);
    }
  }
  cout << cost << endl;
  return 0;
}
