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;
  int A[1000];
  int B[1000];
  int aW[10001] = {-1};
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    B[i] = A[i];
    aW[A[i]] = i;
  }
  sort(B, B + n);
  int glMin = B[0];
  int rm = 0;
  for (int i = 0; i < n; i++) {
    if (aW[B[i]] == -1) continue;
    int c = 0;
    int lcMin = B[i];
    int j = aW[lcMin];
    aW[lcMin] = -1;
    rm -= lcMin;
    while (j != -1) {
      rm += A[j];
      c++;
      j = aW[B[j]];
    }
    rm += min(lcMin * (c - 1), 2 * (lcMin + glMin) + glMin * (c - 1));
  }
  cout << rm << endl;
}
