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;
int sort(int *A, int n) {
  int i, j;
  int tmp;
  int min = 1000, max = 0;
  int im, iM;
  for (i = 0; i < n - 1; i++) {
    if (A[i] > max) {
      max = A[i];
      iM = i;
    }
  }
  for (i = 1; i < n; i++) {
    if (A[i] < min) {
      min = A[i];
      im = i;
    }
  }
  if (iM > im) return 1;
  tmp = A[im];
  A[im] = A[iM];
  A[iM] = tmp;
  cost = cost + max + min;
  sort(&A[0], n);
}
int main() {
  int i, n, a;
  int A[1000];
  cost = 0;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &A[i]);
  a = sort(&A[0], n);
  printf("%d\n", cost);
  return 0;
}
