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 <vector>
#include <algorithm>

#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

int n;
int w[1000];
int k[1000];
int u[1000];

int main(){
	scanf("%d", &n);
	rep(i, n){
		scanf("%d", &w[i]);
	}

	vector<int> v(w, w + n);
	sort(v.begin(), v.end());
	rep(i, n){
		k[i] = lower_bound(v.begin(), v.end(), w[i]) - v.begin();
	}

	int x = *min_element(w, w + n);
	int ans = 0;
	rep(i, n){
		if(u[i]){
			continue;
		}
		int c = 1;
		int s = w[i];
		int m = w[i];
		u[i] = true;
		int j = k[i];
		while(!u[j]){
			++c;
			s += w[j];
			m = min(m, w[j]);
			u[j] = true;
			j = k[j];
		}
		ans += min(s + m * (c - 2), (s - m + x) + x * (c - 2) + 2 * (m + x));
	}
	printf("%d\n", ans);
	return 0;
}