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 r(i,n) for(auto i=0;i<n;i++)

int main(){
	int n;
	cin >> n;
	int A[n], B[n], T[10001], minw = 10000;
	r(i, n){
		cin >> A[i];
		minw = min(minw, A[i]);
	}

	int ans = 0;
	bool V[n];
	r(i, n){
		B[i] = A[i];
		V[i] = false;
	}
	sort(B, B+n);
	r(i, n) T[B[i]] = i;
	r(i, n){
		if(V[i]) continue;
		int cur = i, S = 0, m = 10000, an = 0;
		while(true){
			V[cur] = true;
			an++;
			int v = A[cur];
			m = min(m, v);
			S += v;
			cur = T[v];
			if(V[cur])break;
		}
		ans += min(S + (an-2)*m, m + S + (an+1)*minw);
	}
	cout << ans << endl;
	return 0;
}
