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 VMAX 10000

int main()
{
	int n;
	cin >> n;
	vector<int> w( n );
	vector<int> b( n );
	int s = VMAX;
	for( int i = 0; i < n; i++ ) {
		cin >> w[i];
		s = min( s, w[i] );
		b[i] = w[i];
	}

	vector<bool> V( n );
	vector<int> T( VMAX + 1 );
	sort( b.begin(), b.end() );
	for( int i = 0; i < n; i++ ) {
		T[ b[i] ] = i;
	}
	int ans = 0;
	for( int i = 0; i < n; i++ ) {
		if( V[i] ) continue;
		int cur = i;
		int S = 0;
		int m = VMAX;
		int an = 0;
		while( 1 ) {
			V[cur] = true;
			an++;
			int v = w[cur];
			m = min( m, v );
			S += v;
			cur = T[v];
			if( V[cur] ) break;
		}
		ans += min( S + (an - 2)*m, m + S + (an + 1)*s );
	}

	cout << ans << endl;
}

