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>
#include <stdlib.h> 
using namespace std;
static const int MAX = 1000;
static const int VMAX = 10000;

int n, s;
int A[MAX], B[MAX], T[VMAX + 1]; //"+ 1" is important.

int solve()
{
	int ans = 0;
	
	bool V[MAX];
	for(int i = 0; i < n; i++)
	{
		B[i] = A[i];
		V[i] = false;
	}
	
	sort(B, B+n);
	
	//Build a map from value to ideal order. 
	for(int i = 0; i < n; i++) T[B[i]] = i;
	//Tranverse.
	for(int i = 0; i < n; i++)
	{
		if(V[i]) continue;
		int cur = i;
		int S = 0;
		int m = VMAX;
		int an = 0;
		while(1)
		{
			V[cur] = true;
			an++; 
			int v = A[cur];
			m = min(v, m);
			S += v;
			cur = T[v];
			if(V[cur]) break;
		}
		ans += min(S + (an - 2) * m, m + S + (an + 1) * s);
	}
	
	return ans;
}
int main() {
	
	cin >> n;
	s = VMAX;
	for( int i = 0; i < n; i++)
	{
		cin >> A[i];
		s = min(s, A[i]);
	}
	
	int ans = solve();
	cout << ans << endl;
	
//	system("pause");
	return 0;
}
