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, i, j;
  int min, minj, wsum = 0;
  scanf("%d", &n);
  int w[n];
  for (i = 0; i < n; i++) scanf("%d", &w[i]);
  for (i = 0; i < n; i++) {
    min = w[i];
    minj = i;
    for (j = i + 1; j < n; j++) {
      if (min > w[j]) {
        min = w[j];
        minj = j;
      }
    }
    if (minj != i) {
      wsum = wsum + w[i] + w[minj];
      swap(w[i], w[minj]);
    } else {
    }
  }
  printf("%d\n", wsum);
  return 0;
}
