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<stdio.h>
#include<algorithm>
using namespace std;

int main() {
	int n;
  scanf("%d", &n);
  int A[n], B[n], C[n];
  for ( int i = 0; i < n; i++ ) scanf("%d", &A[i]);
  for ( int i = 0; i < n; i++ ) B[i] = A[i];
  sort(B, B+n);
  for ( int i = 0; i < n; i++ ) {
    for ( int j = 0; j < n; j++ ) {
      if (A[i] == B[j]) {
        C[i] = j;
        break;
      }
    }
  }
  int k = 0, count = 0, min = B[0], count1 = 0, count2 = 0;
  while ( k < n ) {
    int i, j;
    for (i = 0; i < n; i++) if (C[i] == k) break;
    for (j = 0; j < n; j++) if (C[j] == i) break;
    if (C[k] == k) {
			if (count1 > count2+2*(min+B[k])) {
				count += count2+2*(min+B[k]);
			} else {
				count += count1;
			}
			count1 = 0;
			count2 = 0;
      k++;
    } else {
      count1 += A[i]+A[j];
			count2 += min+A[j];
      swap(A[i], A[j]);
      swap(C[i], C[j]);
    }
  }

  printf("%d\n", count);

  return 0;
}

