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;
  scanf("%d", &n);
  int A[n], B[n], C[n];
  for (int i = 0; i < n; i++) scanf("%d", &A[i]);
  for (int i = 0; i < n; i++) B[i] = A[i];
  sort(B, B + n);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (A[i] == B[j]) {
        C[i] = j;
        break;
      }
    }
  }
  int k = 0, count = 0;
  while (k < n) {
    int i, j;
    for (i = 0; i < n; i++)
      if (C[i] == k) break;
    for (j = 0; j < n; j++)
      if (C[j] == i) break;
    if (C[k] == k) {
      k++;
    } else {
      count += A[i] + A[j];
      swap(A[i], A[j]);
      swap(C[i], C[j]);
    }
  }
  printf("%d\n", count);
  return 0;
}
