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 <map>

using namespace std;

int main() {
	int n, ans = 0;
	cin >> n;
	int arr[n], sorted[n];
	bool visit[n] = { false };
	map<int, int> mp;

	for (int i = 0; i < n; i++) {
		cin >> arr[i];
		sorted[i] = arr[i];
	}
	sort(sorted, sorted + n);

	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			if (arr[i] == sorted[j]) {
				mp[i] = j;
			}
		}
	}

	while (1) {
		int suffix = -1;
		for (int i = 0; i < n; i++) {
			if (visit[i] == false) {
				suffix = i;
			}
		}
		if (suffix == -1) {
			break;
		}

		int m = 0, min_in = 10001, min_out = 10001, sum = 0;
		bool used[n] = { false };
		while (used[suffix] == false) {
			m++;
			sum += arr[suffix];
			min_in = min(min_in, arr[suffix]);

			used[suffix] = visit[suffix] = true;
			suffix = mp[suffix];
		}

		if (m > 1) {
			for (int i = 0; i < n; i++) {
				if (used[i] == false) {
					min_out = min(min_out, arr[suffix]);
				}
			}

			ans += sum + min((m - 2) * min_in, min_in + (m + 1) * min_out);
		}
	}

	cout << ans << endl;

	return 0;
}