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

int do_cycle(vector<int> &v,int x){
	int s=0,m=1<<30;
	for(auto &e:v)s+=e,m=min(m,e);
	return min(s+(v.size()-2)*m,s+m+(v.size()+1)*x);
}

int main(){
	int N,x=1<<30,r=0;
	scanf("%d",&N);
	vector<int>v(N),b(N),se(N);
	map<int,int>m;
	vector<vector<int> >cycles;
	for(int i=0;i<N;i++)scanf("%d",&v[i]),x=min(x,v[i]),se[i]=v[i];
	sort(se.begin(),se.end());
	int i=0;for(auto &e:se){m[e]=i++;}
	for(int i=0;i<N;i++)if(!b[i]){
		vector<int>cycle;
		int k=i;
		do{
			cycle.push_back(se[k]);
			b[k]=1;
			k=m[v[k]];
		}while(k!=i);
		r+=do_cycle(cycle,x);
	}
	printf("%d\n",r);
}