Problem:
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Minimum Cost Sort

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.

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.

Constraints

$1 \leq n \leq 1,000$

$0 \leq w_i\leq 10^4$

$w_i$ are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

Solution in C (judge verdict: Time Limit Exceeded)

#include <stdio.h>

#define MAX 1000

int solve(int*, int);
int check(int*,int);

int main(){
  int n, i, arr[MAX];

  scanf("%d" ,&n);
  for(i = 0 ; i < n ; i++){
    scanf("%d" ,arr + i);
    arr[i]--;
  }
  printf("%d\n" ,solve(arr, n));

  return 0;
}

int check(int arr[], int n){
  int i;

  for(i = 0 ; i < n ; i++){
    if(arr[i] != i){
      return 0;
    }
  }
  return 1;
}

int solve(int arr[], int n){
  int i, j, res = 0, tmp;

  for(i = 0 ; i < n-1 ; i++){
    if(arr[i] != i){
      for(j = i+1 ; j < n ; j++){
        if(arr[j] != j && arr[i] == j && arr[j] == i){
          res += arr[i] + arr[j] + 2;     
          tmp = arr[i];
          arr[i] = arr[j];
          arr[j] = tmp;
        }
      }
    }
  }

  for(i = 0 ; i < n-1 ; i++){
    if(arr[i] != i){
      for(j = i+1 ; j < n ; j++){
        if(arr[i] == j){
          res += arr[i] + arr[j] + 2;     
          tmp = arr[i];
          arr[i] = arr[j];
          arr[j] = tmp;
        }
      }
    }
  }

  if(check(arr, n)){
    return res;
  }else{
    return res += solve(arr, n);
  }
}