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 Bubblesort(vector<int>&);
int main(int argc, char* argv[]) {
  int n, x;
  vector<int> vi;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> x;
    vi.push_back(x);
  }
  cout << Bubblesort(vi) << endl;
  return 0;
}
int Bubblesort(vector<int>& vi) {
  int cnt = 0;
  int key, vecsize = vi.size();
  for (int i = vecsize - 1; i > 0; i--) {
    key = i;
    for (int j = i - 1; j >= 0; j--) {
      if (vi[key] < vi[j]) key = j;
    }
    if (key != i) cnt += vi[key] + vi[i];
    swap(vi[key], vi[i]);
  }
  return cnt;
}
