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<map>
#include<algorithm>
using namespace std;
int n;
int s;
int a[1001];
int v[1001];
int t[10001];
int all2=0;
void solve() {
	int b[1001];
	for (int i = 0; i < n; i++) {
		b[i] = a[i];
	}
	sort(b, b + n);
	for (int i = 0; i < n; i++) {
		t[b[i]] = i;
	}
	for (int i = 0; i < n; i++) {
		int key = 0;
		int all = 0;
		int j = i;
		int count = 0;
		while (!v[i])
		{
			key = a[j];
			if (key == b[i])
			{
				v[i] = 1;
				break;
			}
			all += b[i] + a[j];
			v[t[a[j]]] = 1;
			j = t[a[j]];
			count++;
		}
		all2 += min(all,all+2*(b[i]+b[0])-count*(b[i]-b[0]));
	}
}
int main() {
	cin >> n;
	s = 10000;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		s = min(s, a[i]);
	}
	solve();
	cout << all2<<endl;
}
