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 weight[1005];
  int sorted[1005];
  int idx[1005];
  int n, x = (1 << 30), ans = 0;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    scanf("%d", weight + i);
    sorted[i] = weight[i];
    if (x > weight[i]) x = weight[i];
  }
  sort(sorted, sorted + n);
  for (int i = 0; i < n; ++i) idx[sorted[i]] = i;
  bool visited[1005]{false};
  for (int i = 0; i < n; ++i) {
    if (visited[i] || i == idx[weight[i]]) continue;
    int Min = weight[i], num = 1, sum1 = weight[i];
    int j = i;
    while (true) {
      visited[j] = true;
      j = idx[weight[j]];
      if (visited[j]) break;
      Min = min(Min, weight[j]);
      sum1 += weight[j];
      ++num;
    }
    ans += min(Min + (num + 1) * x, (num - 2) * Min) + sum1;
  }
  cout << ans << endl;
  return 0;
}
