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 <algorithm>
using namespace std;
#define MAX 1000
int n,x,a[MAX],b[MAX],t[10001];

int solve(){
	int ans=0;
	bool v[MAX];
	for(int i=0;i<n;i++){
		b[i]=a[i];	v[i]=false;
	}
	sort(b,b+n);
	for(int i=0;i<n;i++)	t[b[i]]=i;//ソート後の位置を記録
	for(int i=0;i<n;i++){
		if(v[i])	continue;
		int current=i;
		int s=0;
		int m=10000;
		int count=0;
		while(1){
			v[current]=true;
			count++;
			m=min(m,a[current]);
			s+=a[current];
			current=t[a[current]];
			if(v[current])	break;
		}
		ans+=min(s+(count-2)*m,s+m+(count+1)*x);
	}
	return ans;
}
		

int main(){
	cin>>n;
	x=10000;
	for(int i=0;i<n;i++){
		cin>>a[i];
		x=min(x,a[i]);
	}
	cout<<solve()<<endl;
	return 0;
}