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 minCostSort(int A[], int n);
int main(void) {
  int n;
  int baggage[1000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> baggage[i];
  }
  int cost;
  cost = minCostSort(&baggage[0], n);
  cout << cost << endl;
  return 0;
}
int minCostSort(int A[], int n) {
  int cost = 0;
  int count = 0;
  int min_pos;
  for (int i = 0; i < n - 1; i++) {
    min_pos = i;
    for (int j = i; j < n; j++) {
      if (A[j] < A[min_pos]) {
        min_pos = j;
      }
    }
    if (i != min_pos) {
      swap(A[i], A[min_pos]);
      count++;
      cost += A[i] + A[min_pos];
    }
  }
  return cost;
}
