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;
struct Data {
  Data() : w(0), i(0) {}
  int w;
  int i;
};
struct DataComparator {
  bool operator()(const Data* d1, const Data* d2) { return (d1->w < d2->w); }
};
int main() {
  int n;
  cin >> n;
  vector<Data*> vD, vW;
  vD.reserve(n);
  for (int i = 0; i < n; ++i) {
    Data* d = new Data();
    cin >> d->w;
    d->i = i;
    vD.push_back(d);
  }
  vW = vD;
  sort(vW.begin(), vW.end(), DataComparator());
  int c = 0;
  for (int i = n - 1; i >= 0; --i) {
    if (i == vW[i]->i) continue;
    c += vD[i]->w + vD[vW[i]->i]->w;
    swap(vD[i]->i, vD[vW[i]->i]->i);
    swap(vD[i], vD[vW[i]->i]);
  }
  cout << c << "\n";
  return 0;
}
