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 <iostream>
#include <vector>
#include <algorithm>
#include <map>
using namespace std;

int main() {
	int n,w,l;
	vector<pair< int, pair<int,int> > > a; 
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>w;
		a.push_back(make_pair(w,make_pair(i,0)));
	}
	sort(a.begin(), a.end());
	for(int i=0;i<n;i++){
		(a[i].second).second=i;
		l=a[i].first;
		a[i].first=(a[i].second).first;
		(a[i].second).first=l;
//	cout<<"a[i]"<<a[i].first<<" "<<(a[i].second).first<<endl;
	}
	int mi=(a[0].second).first;
	sort(a.begin(),a.end());
//for(int i=0;i<n;i++) cout<<"a[i]"<<a[i].first<<" "<<(a[i].second).first<<" "<<(a[i].second).second<<endl;
	
	bool b[1010]={0};
	int ans=0;
	for(int i=0;i<n;i++){
		if (b[i]!=0) continue;
	//	cout<<i<<" "<<b[i]<<endl;
		b[i]=1;
		int j=i,k=1,sum=(a[i].second).first,mini=(a[i].second).first;
		while(1){
			if(i==(a[j].second).second) break;
			j=(a[j].second).second;
			b[j]=1;
			sum=sum+(a[j].second).first;
			k++;
			if(mini>(a[j].second).first) mini=(a[j].second).first;
		}
//		cout<<k<<" "<<mini <<" "<<sum<<" "<<mi<<endl;
		if(k>1) ans=ans+min(sum+(k-2)*mini,sum+(k+1)*mi+mini); 
		
	}
	cout<<ans<<endl;
	return 0;
}