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 A[1005],B[1005],T[10005],V[1005];
int solve(int mini,int n)
{
	int ans=0;
	for(int i=0;i<n;i++){
		if(V[i]) continue;
		int cur=i,ssum=0,mmini=1e5,cnt=0;
		do{
			V[cur] = 1;
			int v = A[cur];
			ssum += v;
			mmini = min(mmini,v);
			cur = T[v];
			cnt++;
		} while (!V[cur]);
		ans += min(ssum+(cnt-2)*mmini,mmini+ssum+(cnt+1)*mini);
	}
	return ans;
}
int main()
{
	int n,mini=1e5; 
	cin>>n;
	for(int i=0;i<n;i++){
		scanf("%d",&A[i]);
		B[i] = A[i];
		mini = min(A[i],mini);
	}

	sort(B,B+n);
	for(int i=0;i<n;i++) T[B[i]] = i;
	memset(V,0,sizeof(V));

	int ans = solve(mini,n);
	cout<<ans<<endl;
	return 0;
}
