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 <cstdio>
#include <list>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <cstring>
#include <cmath>
#include <string>
#define N 1005
#define INF (1 << 30)
typedef long long ll;
using namespace std;

int main()
{
	int weight[N];
	int sorted[N];
	int idx[40005];
	int n, x = INF, ans = 0;
	cin >> n;
	for (int i = 0; i < n; ++i)
	{
		scanf("%d", weight + i);
		sorted[i] = weight[i];
		if (x > weight[i])
			x = weight[i];
	}
	sort(sorted, sorted + n);
	for (int i = 0; i < n; ++i)
		idx[sorted[i]] = i;
	bool visited[N]{ false };
	for (int i = 0; i < n; ++i)
	{
		if (visited[i] || i == idx[weight[i]])
			continue;
		int Min = weight[i], num = 1, sum1 = weight[i];
		int j = i;
		while (true)
		{
			visited[j] = true;
			j = idx[weight[j]];
			if (visited[j])
				break;
			Min = min(Min, weight[j]);
			sum1 += weight[j];
			++num;
			
		}
		ans += min(Min + (num + 1) * x, (num - 2) * Min) + sum1;
	}
	cout << ans << endl;
	return 0;
}