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, cost1 = 0, cost2 = 0;
  cin >> n;
  int arr1[n], arr2[n], sorted[n];
  for (int i = 0; i < n; i++) {
    cin >> arr1[i];
    arr2[i] = sorted[i] = arr1[i];
  }
  sort(sorted, sorted + n);
  vector<pair<int, int> > vec;
  int mini = 0;
  while (mini < n) {
    int s1, s2;
    for (int i = 0; i < n; i++) {
      if (arr1[i] == sorted[mini]) {
        s1 = i;
        break;
      }
    }
    for (int i = 0; i < n; i++) {
      if (arr1[i] == sorted[s1]) {
        s2 = i;
        break;
      }
    }
    if (s1 != s2) {
      cost1 += arr1[s1] + arr1[s2];
      vec.push_back(make_pair(s1, s2));
      swap(arr1[s1], arr1[s2]);
    } else {
      mini++;
    }
  }
  cout << cost1 << endl;
  return 0;
}
