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 Sort(int *, int, int);
int Cost_Sort(int *, int, int);
int sum = 0;
int main() {
  int i, n, *A;
  scanf("%d", &n);
  A = (int *)malloc(sizeof(int) * n);
  for (i = 0; i < n; i++) {
    scanf("%d", &A[i]);
  }
  Sort(A, 0, n - 1);
  printf("%d\n", sum);
  return 0;
}
void Sort(int *A, int i, int n) {
  int p, j;
  if (i < n) {
    p = Cost_Sort(A, i, n);
    Sort(A, i, p);
  }
}
int Cost_Sort(int *A, int i, int n) {
  int k, j, tmp, max = A[i];
  for (j = i + 1; j <= n; j++) {
    if (max < A[j]) {
      max = A[j];
      k = j;
    }
  }
  if (k != n) {
    sum += A[k] + A[n];
    tmp = A[k];
    A[k] = A[n];
    A[n] = tmp;
  }
  return n - 1;
}
