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<bits/stdc++.h>

using namespace std;

int n,A[1010],O[1010];
bool used[1010]; 

bool cmp(int a,int b)
{
	return A[a]<A[b];
}

int main()
{
	scanf("%d",&n);
	int mi=INT_MAX;
	for(int i=0;i<n;i++)
	{
		scanf("%d",&A[i]);
		O[i]=i;
		mi=min(mi,A[i]);
	}
	sort(O,O+n,cmp);
	//for(int i=0;i<n;i++) printf("%d\n",O[i]);
	memset(used,false,sizeof(used));
	int ans=0;
	for(int i=0;i<n;i++)
		if(!used[i])
		{
			int tot=0,tn=0,tmi=INT_MAX;
			for(int j=i;!used[j];used[j]=true,j=O[j])
			{
				tmi=min(tmi,A[j]);
				tot+=A[j];
				tn++;
			}
			ans+=min(tot+(tn-2)*tmi,tot+tmi+(tn+1)*mi);
		}
	printf("%d\n",ans);
	return 0;
}