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 <cstdio>
#include <algorithm>
#pragma warning(disable : 4996)
using namespace std;
int n, a[1009], c[1009]; bool vis[1009];
int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) scanf("%d", &a[i]);
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			if (a[i] > a[j]) c[i]++;
		}
	}
	int z = *min_element(a, a + n);
	int ret = 0;
	for (int i = 0; i < n; i++) {
		if (vis[i]) continue;
		int pos = i, m = 1012345678, cnt = 0;
		while (!vis[pos]) {
			vis[pos] = true;
			ret += a[pos];
			m = min(m, a[pos]);
			pos = c[pos];
			cnt++;
		}
		ret += min(m * (cnt - 2), z * (cnt + 1) + m);
	}
	printf("%d\n", ret);
	return 0;
}