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;
  cin >> n;
  int *w = new int[n];
  int pos[10001];
  for (int i = 0; i < 10001; ++i) {
    pos[i] = -1;
  }
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
    pos[w[i]] = i;
  }
  unsigned long long cost = 0;
  int j = n - 1;
  for (int i = 10000; i >= 0; --i) {
    if (pos[i] != -1) {
      if (pos[i] != j) {
        cost += w[j];
        cost += i;
        int temp = w[j];
        w[j] = i;
        w[pos[i]] = temp;
        pos[temp] = pos[i];
        pos[i] = j;
      }
      --j;
      if (j == 0) {
        break;
      }
    }
  }
  cout << cost << endl;
  delete[] w;
  return 0;
}
