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;
int MIN=10010,n;
int a[1010],b[1010],t[10010];
bool V[1010];
int solve(){
	int ans=0;
	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=10010;
		int an=0;
		while(1){
			V[cur]=1;
			++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)*MIN);
	}
	return ans;
}
int main(){
	cin>>n;
	for(int i=0;i<n;++i){
		cin>>a[i];
		b[i]=a[i];
		V[i]=0;
		MIN=min(MIN,a[i]);
	}
	cout<<solve()<<endl;
	return 0;
}
