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<stdio.h>
#include<algorithm>

using namespace std;

static const int MAX = 1000;
static const int MAXS = 10005;

int s = MAXS;
int C[MAXS] = {0};
int minCostSort(int A[], int n)
{
	int cost = 0;
	int i,B[MAX];
	bool V[MAX];

	for (i = 0; i < n; i++)
	{
		V[i] = false;
		B[i] = A[i];
	}
	sort(&B[0],&B[n]);

	for (i = 0; i < n; i++)
	{
		C[B[i]] = i;
	}

	for (i = 0; i < n; i++)
	{
		int a = i;
		int S = 0;
		int mini = MAXS;
		int num = 0;
		while (1)
		{
			V[a] = true;
			num++;
			mini = min(mini, A[a]);
			S = S + A[a];
			a = C[A[a]];
			if (V[a]==true)
				break;				
		}

		cost += min(S+mini*(num-2),S+mini+(num+1)*s);
	}

	return cost;
}

int main()
{
	int cost;
	int n,i, A[MAX];
	scanf("%d",&n);

	for (i = 0; i < n; i++)
	{
		scanf("%d", &A[i]);
		s = min(A[i],s);
	}

	cost = minCostSort(A,n);
	printf("%d\n", cost);

	return 0;
}
