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<stdlib.h>
#define MAX 2000001
#define VMAX 10000

int main() {
  unsigned short *A, *B;
  
  int C[VMAX+ 1];
  int n, i, j;
  scanf("%d", &n);
  
  A = malloc(sizeof(short) * n + 1);
  B = malloc(sizeof(short) * n + 1);
  
  for ( i = 0; i <= VMAX; i++ ) C[i] = 0;
  
  for ( i = 0; i < n; i++ ) {
    scanf("%hu", &A[i + 1]);
    C[A[i + 1]]++;
  }
  
  for ( i = 1; i <= VMAX; i++ ) C[i] = C[i] + C[i - 1];
  
  for ( j = 1; j <= n; j++ ) {
    B[C[A[j]]] = A[j];
    C[A[j]]--;
  }
  
  for ( i = 1; i <= n; i++ ) {
    if ( i > 1 ) printf(" ");
    printf("%d", B[i]);
  }
  printf("\n");
  
  return 0;
}