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<cstdio>
#include<cstdlib>
#include<algorithm>
#include<vector>
#include<string>
#include<sstream>
using namespace std;
const int MAX=1000;
const int VMAX=10000;
int n,A[MAX],s,B[MAX],T[VMAX+1];

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;
	for(int i=0;i<n;i++)
	{
		if(V[i])continue;
		int cur=i;
		int S=0;
		int m=VMAX;
		int an=0;
		while(1)
		{
			V[cur]=true;
			an++;
			int v=A[cur];
			m=min(m,v);
			S+=v;
			cur=T[v];
			if(V[cur])break;
		}
		ans+=min(S+(an-2)*m,m+S+(an+1)*s);
	}
	return ans;
}
int main()
{
	cin>>n;
	s=VMAX;
	for(int i=0;i<n;i++)
	{
		cin>>A[i];
		s=min(s,A[i]);
	}
	cout<<solve()<<endl;
	return 0;
}