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 <algorithm>
using namespace std;
int a[1005],b[1005],to[10005];
bool vis[1005];
int main () {
	int n,ans=0;
	scanf ("%d",&n);
	for (int i=0;i<n;i++) {
		scanf ("%d",&a[i]);
		b[i]=a[i];
	}
	sort (b,b+n);
	for (int i=0;i<n;i++) {
		to[b[i]]=i;
	}
	for (int i=0;i<n;i++) {
		if (vis[i]) continue;
		int pos=i,sum=0,mn=1e4+7,cnt=0;
		while (!vis[pos]) {
			vis[pos]=true;
			sum+=a[pos];
			mn=min(mn,a[pos]);
			cnt++;
			pos=to[a[pos]];
		}
		ans+=min(sum+(cnt-2)*mn,sum+mn+(cnt+1)*b[0]);
	}
	printf ("%d\n",ans);
    return 0;
}
