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 i, j, min, sum = 0, flag;
  int n;
  int W[1001];
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &W[i]);
  }
  i = -1;
  while (i != n - 1) {
    flag = 0;
    i = i + 1;
    min = i;
    for (j = i + 1; j < n; j++) {
      if (W[min] > W[j]) {
        min = j;
        flag = 1;
      }
    }
    if (flag) {
      swap(&W[min], &W[i]);
      sum += W[i] + W[min];
    }
  }
  printf("%d\n", sum);
  return 0;
}
void swap(int* w, int* min) {
  int tmp;
  tmp = *w;
  *w = *min;
  *min = tmp;
}
