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 main() {
  int i, j;
  int n, swapTotal = 0;
  scanf("%d", &n);
  int a[n];
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  for (j = 0; j < n - 1; j++) {
    int iMin = j;
    for (i = j + 1; i < n; i++) {
      if (a[i] < a[iMin]) {
        iMin = i;
      }
    }
    if (iMin != j) {
      int temp = a[j];
      a[j] = a[iMin];
      a[iMin] = temp;
      swapTotal += a[j] + a[iMin];
    }
  }
  printf("%d\n", swapTotal);
}
