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 A[1000];
int dupA[1000];
int pos[10001];
int main() {
  int N;
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    dupA[i] = A[i];
    pos[A[i]] = i;
  }
  sort(A, A + N);
  int cost = 0;
  int i = 0;
  while (i < N) {
    if (pos[A[i]] != i) {
      cost += (A[i] + A[pos[A[i]]]);
      int temp = pos[A[i]];
      pos[A[i]] = pos[A[temp]];
      pos[A[temp]] = temp;
    } else {
      i++;
    }
  }
  cout << cost << endl;
  return 0;
}
