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>
struct rist {
  int n;
  int p;
} typedef rist;
void QuickSort(int, int);
int Partition(int, int);
int MinimumCost(int);
rist A[1000];
int main() {
  int i;
  int n;
  int cost;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &A[i].n);
    A[i].p = i;
  }
  QuickSort(0, n - 1);
  cost = MinimumCost(n);
  printf("%d\n", cost);
  return 0;
}
void QuickSort(int p, int r) {
  int q;
  if (p < r) {
    q = Partition(p, r);
    QuickSort(p, q - 1);
    QuickSort(q + 1, r);
  }
}
int Partition(int p, int r) {
  int i, j;
  rist tmp;
  i = p - 1;
  for (j = p; j < r; j++) {
    if (A[j].n <= A[r].n) {
      i = i + 1;
      tmp = A[i];
      A[i] = A[j];
      A[j] = tmp;
    }
  }
  tmp = A[i + 1];
  A[i + 1] = A[r];
  A[r] = tmp;
  return i + 1;
}
int MinimumCost(int n) {
  int i;
  int tmp;
  int cost;
  for (i = n - 1; i >= 0; i--) {
    if (A[i].p != i) {
      cost += A[i].n + A[A[i].p].n;
      tmp = A[A[i].p].p;
      A[A[i].p].p = A[i].p;
      A[i].p = tmp;
    }
  }
  return cost;
}
