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>
#include<utility>
#include<numeric>
#include<iostream>
#include<array>
#include<string>
#include<sstream>
#include<stack>
#include<queue>
#include<list>
#define _USE_MATH_DEFINES

#include<math.h>
#include<map>

#define SENTINEL 1000000001

#define min(a,b) (a)>(b)?(b):(a)
#define max(a,b) (a)>(b)?(a):(b)

using namespace std;

int A[1000];
int dupA[1000];
int pos[10001];
int dupPos[10001];
bool checked[1000];

int main()
{
	int N;
	int mini = 100000;
	scanf("%d", &N);

	for (int i = 0; i < N; i++)
	{
		cin >> A[i];
		dupA[i] = A[i];
		pos[A[i]] = i;
		dupPos[A[i]] = pos[A[i]];
		mini = min(mini, A[i]);
	}

	sort(A, A + N);

	int cost = 0;
	for (int i = 0; i < N; i++)
	{
		if (checked[i])
		{
			continue;
		}
		int mini2 = 100000, counter = 0, now = i, sum = 0;
		
		while (true)
		{
			if (checked[now])
			{
				break;
			}
			checked[now] = true;
			mini2 = min(mini2, A[now]);
			sum += A[now];
			counter++;
			now = pos[A[now]];
		}
		cost += min(sum + mini2*(counter - 2), sum + mini + mini2 + mini*counter);
	}

	cout << cost << endl;

	return 0;
}
