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;
const int num = 1001,num1 = 10000, INF = 2000000000;
int n, a[num], b[num], c[num1], tf[num], s = INF;
inline int mini() {
	int an = 0;
	int cu = 0;
	for (int i = 0; i < n; i++) {
		if (tf[i]) continue;
		cu = i;
		int m = INF;
		int sum = 0;
		int cnt = 0;
		while (true) {
			tf[cu] = 1;
			int v = a[cu];
			cnt++;
			m = min(v, m);
			sum += v;
			cu = c[v];
			if (tf[cu]) break;
		}
		an += min(sum + m*(cnt - 2), sum + m*(cnt - 2) + 2 * (m + s) - (m - s)*(cnt - 1));
	}
	return an;
}
int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		s = min(a[i], s);
		b[i] = a[i];
		tf[i] = 0;
	}
	sort(b, b + n);
	for (int i = 0; i < n; i++) 
		c[b[i]] = i;
	int ans = mini();
	cout << ans << endl;
	return 0;
}