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 cmp(const int n1, const int n2) { return n1 < n2; }
int main() {
  int n;
  int ary[1000];
  int sortAry[1000];
  int cost = 0;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int temp;
    cin >> temp;
    ary[i] = sortAry[i] = temp;
  }
  sort(sortAry, sortAry + n);
  while (true) {
    int c = 100000;
    int index = -1;
    for (int i = 0; i < n; i++) {
      if (ary[i] < sortAry[i]) {
        if (c > ary[i]) {
          c = ary[i];
          index = i;
        }
      }
    }
    if (index < 0) break;
    cost += c + sortAry[index];
    for (int i = 0; i < n; i++) {
      if (ary[i] == sortAry[index]) {
        swap(ary[i], ary[index]);
        break;
      }
    }
  }
  cout << cost << endl;
  return 0;
}
