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>
using namespace std;

int main()
{
	int x = 10000, y = 0;
	int n = 0;
	cin >> n;
	int* W = new int[n];
	int* B = new int[n];
	for (int i = 0; i < n; ++i)
	{
		cin >> W[i];
		B[i] = W[i];
		x = min(x, W[i]);
		y = max(y, W[i]);
	}
	int* T = new int[y + 1];
	sort(B, B + n);
	for (int i = 0; i < n; ++i)
	{
		T[B[i]] = i;
	}
	bool* visit = new bool[n];
	for (int i = 0; i < n; ++i)
	{
		visit[i] = false;
	}
	int result = 0;
	for (int i = 0; i < n; ++i)
	{
		if (visit[i])
		{
			continue;
		}
		int cur = i, sum = 0, num = 0, m = y;
		while (!visit[cur])
		{
			visit[cur] = true;
			m = min(m, W[cur]);
			sum = sum + W[cur];
			num++;
			cur = T[W[cur]];
		}
		if (num)
		{
			int a = sum + (num - 2) * m;
			int b = sum + m + (num + 1) * x;
			result = result + min(sum + (num - 2) * m, sum + m + (num + 1) * x);
		}
	}
	cout << result << endl;
	return 0;
}
