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;
const int MAXW = 10005;
int main() {
  int n;
  cin >> n;
  vector<int> w(n);
  vector<int> w_sorted(MAXW, -1);
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    w_sorted[w[i]]++;
  }
  int w_cnt = 0;
  for (int i = 0; i < w_sorted.size(); i++) {
    if (w_sorted[i] >= 0) {
      w_sorted[i] += w_cnt;
      w_cnt++;
    }
  }
  int w_min = MAXW;
  int w_sum = 0;
  int w_cnt1 = 0;
  for (int i = 0; i < n; i++) {
    if (w_sorted[w[i]] != i) {
      w_sum += w[i];
      w_min = min(w_min, w[i]);
      int tmp = w[w_sorted[w[i]]];
      if (w[w_sorted[tmp]] != w[i]) w_cnt1++;
    }
  }
  int res = w_sum + w_min * max(w_cnt1 - 2, 0);
  cout << res << endl;
  return 0;
}
