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;

#define MAX 1000
#define VMAX 10000

int n, A[MAX], s;
int B[VMAX], T[VMAX + 1];

int solve()
{
	int ans = 0;
	bool V[MAX];
	for (int i = 0; i < n; i++)
	{
		V[i] = false;
		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++)
	{
		if (V[i])
			continue;
		int an = 0;//记录圈内元素个数
		int m = VMAX;//记录圈内最小元素
		int S = 0;//记录圈内所有元素之和
		int cur = i;//记录当前下标位置
		while (1)
		{
			V[cur] = true;
			int v = A[cur];
			an++;
			m = min(m, v);
			S += v;
			cur = T[v];
			if (V[cur])
				break;
		}
		ans += min(S + (an - 2) * m, S + m + (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;
	return 0;
}
