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 <bits/stdc++.h>
using namespace std;

#define for_(i,a,b) for(int i=(a);i<(b);++i)

int n, w[1010], s[1010], ind[10001];

int main() {
	cin >> n;
	
	for_(i,0,n) {
		cin >> w[i];
		s[i] = w[i];
		ind[w[i]] = i;
	}
	
	sort(s, s + n);
	
	int ans = 0;
	
	for_(i,0,n) {
		if (w[i] == s[i]) continue;
		
		int piv = w[i], cur = i, sum = w[i], cnt = 0;
		w[i] = s[i];
		
		while ((cur = ind[s[cur]]) != i) {
			piv = min(piv, w[cur]);
			sum += w[cur];
			++cnt;
			w[cur] = s[cur];
		}
		
		ans += min((sum - piv) + piv * cnt, 2 * (piv + s[0]) + (sum - piv) + s[0] * cnt);
	}
	
	cout << ans << endl;
}