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;
static const int MAX = 200000;
void trace(int data[], int n) {
  cout << data[0];
  for (int i = 1; i < n; i++) {
    printf("%2d ", data[i]);
  }
  cout << endl;
}
int bsearch(int data[], int target, int left, int right) {
  int mid;
  while (left <= right) {
    mid = (left + right) / 2;
    if (data[mid] == target) {
      return mid;
    } else if (data[mid] < target) {
      left = mid + 1;
    } else {
      right = mid - 1;
    }
  }
  return -1;
}
int main() {
  int n;
  int data[MAX];
  int sorted[MAX];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> data[i];
    sorted[i] = data[i];
  }
  sort(sorted, sorted + n);
  int total = 0;
  for (int i = 0; i < n; i++) {
    int ans = sorted[i];
    int x = data[i];
    if (ans == x) continue;
    int count = 0;
    int min = x;
    int sum = x;
    while (ans != x) {
      int j = bsearch(sorted, x, 0, n - 1);
      swap(x, data[j]);
      sum += x;
      if (x < min) min = x;
      count++;
    }
    data[i] = x;
    total += sum + (count - 1) * min;
  }
  cout << total << endl;
}
