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, r = 0;
  scanf("%d", &N);
  std::vector<int> v(N);
  for (int i = 0; i < N; i++) scanf("%d", &v[i]);
  for (int i = 0; i < N; i++) {
    auto ma = max_element(v.begin(), v.end() - i);
    if (ma != v.begin() + (N - 1 - i)) {
      r += *ma + v[N - 1 - i];
      swap(*ma, v[N - 1 - i]);
    }
    auto mi = min_element(v.begin() + i, v.end());
    if (mi != v.begin() + i) {
      r += *mi + v[i];
      swap(*mi, v[i]);
    }
  }
  printf("%d\n", r);
}
