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>
void swap(int *, int *);
int main(int argc, char const *argv[]) {
  int i, j;
  int n;
  int w[10000];
  int min = 200000;
  int key;
  int memj;
  int flag = 0;
  int min_sum = 0;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &w[i]);
  }
  for (i = 0; i < n; i++) {
    key = w[i];
    for (j = i + 1; j < n; j++) {
      if (key > w[j]) {
        memj = j;
        key = w[j];
        flag = 1;
      }
    }
    if (flag) {
      min_sum += w[i] + w[memj];
      swap(&w[i], &w[memj]);
      flag = 0;
    }
  }
  printf("%d\n", min_sum);
  return 0;
}
void swap(int *x, int *y) {
  int temp;
  temp = *x;
  *x = *y;
  *y = temp;
}
