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<cstdio>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<stack>
#include<vector>
#include<queue>
#define MAX 2000
#define VMAX 20000
using namespace std;
#define WHITE 0
#define BLACK 1

typedef long long ll;

int A[MAX],B[MAX],n,mini=2000000000,C[VMAX];

int color[MAX],myans;

void start(int x){
  color[x]=BLACK;
  int xvalue=A[x];
  int xsort=C[xvalue];
  int sum=xvalue,num=1,s=xvalue;
  while(true){
    xvalue=A[xsort];
    if(xsort==x) break;
    num++;
    s=min(s,xvalue);
    sum+=xvalue;
    color[xsort]=BLACK;
    xsort=C[xvalue];
  }
  if(num==1) return;
  else myans+=min(sum+s*(num-2),sum+mini*(num+1)+s);
  
}


void go(){
  for(int i=0;i<n;i++){
    if(color[i]==0) start(i);
  }
  cout<<myans<<endl;
}

int main(){
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>A[i];
    mini=min(A[i],mini);
    B[i]=A[i];
  }
  sort(B,B+n);
  for(int i=0;i<n;i++){
    C[B[i]]=i;
  }

  go();






}

