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>
#define MAX 1000
using namespace std;

int n, W[MAX], s;
int T[MAX*10+1],A[MAX+1];

int solve()
{
	int ans = 0;
	bool V[MAX];
	for(int i = 0; i < n; i++){
		A[i] = W[i];V[i] = false;
	}
	sort(A, A+n);
	for(int i = 0; i < n; i++)	T[A[i]] = i;
	for(int i = 0; i < n; i++){
		int cur = i; 
		int S = 0; 
		int an = 0; 
		int m = MAX*10+1;
		while(1){
			V[cur] = true;
			an++;
			int v = W[cur];
			S += v;
			m = min(m, v);
			cur = T[v];
			if(V[cur])	break;
		}
		ans += min(S+m*(an-2), (an+1)*s+m+S);
	}
	return ans;
}
int main(){
	s = MAX*10+1;
	cin>>n;
	for(int i = 0; i < n; i++){
		cin>>W[i]; s = min(s, W[i]);
	}
	cout<<solve()<<endl;
	return 0;
}





