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 n, mini = 10000, w[1000], A[1000], T[10001];
bool used[1000];

int solve() {
	int res = 0;
	for (int i = 0; i < n; ++i) A[i] = w[i];
	sort(A, A + n);
	for (int i = 0; i < n; ++i) T[A[i]] = i;
	for (int i = 0; i < n; ++i) {
		if (used[i]) continue;
		int now = i, S = 0, m = 10000, an = 0;
		while (true) {
			used[now] = true;
			an++;
			int v = w[now];
			m = min(m, v);
			S += v;
			now = T[v];
			if (used[now]) break;
		}
		res += min(S + (an - 2) * m, m + S + (an + 1) * mini);
	}
	return res;
}

int main() {
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> w[i];
		mini = min(mini, w[i]);
	}
	cout << solve() << endl;

	return 0;
}
