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;
void read_problem(vector<int>& ws) {
  int n;
  scanf("%d\n", &n);
  ws.reserve(n);
  for (int i = (0); i < (n); ++i) {
    int w;
    scanf("%d", &w);
    ws.emplace_back(w);
  }
}
int argmax(const vector<int>& ws, int start, int end) {
  int maxi = start;
  for (int i = start; i < end; ++i) {
    if (ws[i] > ws[maxi]) {
      maxi = i;
    }
  }
  return maxi;
}
int selsort(vector<int>& ws) {
  int n = ws.size();
  int cost = 0;
  for (int cnt = n; cnt >= 2; --cnt) {
    int i = argmax(ws, 0, cnt);
    if (i != cnt - 1) {
      cost += ws[i] + ws[cnt - 1];
      swap(ws[i], ws[cnt - 1]);
    }
  }
  return cost;
}
int main() {
  vector<int> ws;
  read_problem(ws);
  int n = ws.size();
  int cost = selsort(ws);
  printf("%d\n", cost);
  return 0;
}
