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, arr[1000], _arr[1000], dest[10001];
  bool used[1000];
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> arr[i];
    used[i] = false;
    _arr[i] = arr[i];
  }
  sort(_arr, _arr + N);
  for (int i = 0; i < N; i++) {
    dest[_arr[i]] = i;
  }
  int ans = 0;
  for (int i = 0; i < N; i++) {
    if (dest[arr[i]] == i || used[i]) {
      used[i] = true;
      continue;
    }
    int cnt = -1, sum = 0, min = arr[i], next = i;
    for (; !used[next];) {
      sum += arr[next];
      cnt++;
      min = std::min(min, arr[next]);
      used[next] = true;
      next = dest[arr[next]];
    }
    sum -= min;
    ans += sum + min * cnt;
  }
  cout << ans << endl;
  return 0;
}
