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 <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
#define maxx 1010
#define maxn 10010

int C[maxn];

int main(){
	int n,ans=0;
	int A[maxx],B[maxx];
	bool V[maxx];
	cin>>n;
	for(int i =0;i<n;i++) {
		cin>>A[i];
		B[i]=A[i];
		V[i]=false;
	}
	sort(B,B+n);
	for(int i=0;i<n;i++) C[B[i]]=i;
	int x=*min_element(A,A+n);
	for(int i=0;i<n;i++){
		if(V[i]==true) continue;
		int s=0,minn=maxn,c_len=0;
		int cur=i;
		while(V[cur]==false){
			c_len++;
			s+=A[cur];
			minn=min(minn,A[cur]);
			V[cur]=true;
			cur=C[A[cur]];
		}
		ans+=min(s+(c_len-2)*minn,s+minn+(c_len+1)*x);
	}
	cout<<ans<<endl;
	return 0;
}
