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>
int main() {
  int N, r = 0;
  scanf("%d", &N);
  std::vector<int> v(N);
  for (int i = 0; i < N; i++) scanf("%d", &v[i]);
  for (int i = N - 1; i >= 0; i--) {
    int ma = v[i], idx = i;
    for (int j = i - 1; j >= 0; j--)
      if (ma < v[j]) ma = v[j], idx = j;
    if (ma > v[i]) {
      r += v[i] + v[idx];
      std::swap(v[i], v[idx]);
    }
  }
  printf("%d\n", r);
}
