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 arm(int[], int);
void swap(int *, int *);
int main() {
  int *A;
  int n, cost = 0;
  int i;
  scanf("%d", &n);
  A = (int *)malloc(n * sizeof(int));
  for (i = 0; i < n; i++) scanf("%d", &A[i]);
  cost = arm(A, n);
  printf("%d\n", cost);
  free(A);
  return 0;
}
int arm(int A[], int n) {
  int cost = 0;
  int i;
  for (i = 0; i < n; i++) {
    if ((i + 1) != A[i]) {
      cost += A[i] + A[A[i] - 1];
      swap(&A[i], &A[A[i] - 1]);
    }
  }
  return cost;
}
void swap(int *a, int *b) {
  int tmp;
  tmp = *a;
  *a = *b;
  *b = tmp;
}
