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, w[1000], a[1000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    a[i] = w[i];
  }
  sort(a, a + n);
  unordered_map<int, deque<int>> idx;
  for (int i = 0; i < n; i++)
    if (w[i] != a[i]) idx[w[i]].push_back(i);
  long long cost = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] == w[i]) continue;
    int j = idx[a[i]].front();
    int s = w[j];
    while (true) {
      int k = idx[a[j]].back();
      idx[a[j]].pop_back();
      cost += w[j] + w[k];
      w[j] = w[k];
      w[k] = s;
      j = k;
      if (w[k] == a[k]) break;
    }
  }
  std::cout << cost << endl;
  return 0;
}
