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>
int cost = 0, W[1024] = {0}, C[1024] = {0};
void swap(int *x, int *y) {
  int tmp;
  tmp = *x;
  *x = *y;
  *y = tmp;
}
int partition(int p, int r) {
  int i, j, x;
  x = W[r];
  i = p - 1;
  for (j = p; j < r; j++) {
    if (W[j] <= x) {
      i++;
      swap(&W[i], &W[j]);
    }
  }
  swap(&W[i + 1], &W[r]);
  return i + 1;
}
void quickSort(int p, int r) {
  int q;
  if (p < r) {
    q = partition(p, r);
    quickSort(p, q - 1);
    quickSort(q + 1, r);
  }
}
int main(void) {
  int i, j, n;
  const char *sp;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &W[i]);
  memcpy(C, W, sizeof(W));
  quickSort(0, n - 1);
  for (i = n - 1; 0 < i; i--) {
    for (j = 0; j < n; j++) {
      if (W[i] == C[j] && i != j) {
        cost += C[i];
        cost += C[j];
        swap(&C[i], &C[j]);
        break;
      }
    }
  }
  printf("%d\n", cost);
  return 0;
}
