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 <string.h>
#include <algorithm>
using namespace std;

int main()
{
	int n, c = 0;
	int a[1000], b[1000];
	bool f[1000];

	cin >> n;

	for (int i = 0; i < n; i++)
		cin >> a[i];

	memcpy(b, a, sizeof(a));
	sort(b, b + n);
	memset(f, 0, sizeof(f));

	for (int i = 0; i < n; i++) {
		if (a[i] == b[i])
			f[i] = 1;
	}

	for (int i = 0; i < n; i++) {
		if (f[i] == 0){
			int s = 0;
			while (a[i] != b[i]) {
				int j = i, k = i;
				while (f[j] == 1 || a[j] != b[i])
					j++;
				while (f[k] == 1 || a[k] != b[j])
					k++;
				swap(a[j], a[k]);
				c += a[j] + a[k];
				f[j] = 1;
				s++;
			}
			if ((s - 2) * b[i] > (s + 2) * b[0])
				c -= (s - 2) * b[i] - (s + 2) * b[0];
			f[i] = 1;
		}
	}

	cout << c << endl;

	return 0;
}
