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;
static const int MAX=1000;
static const int VMAX=10000;
int n,A[MAX],s;
int B[MAX],T[VMAX+1];

int solve()
{
    int ans=0;

    bool V[MAX];
    for(int i=0;i<n;++i)
    {
        B[i]=A[i];
        V[i]=false;
    }
    sort(B,B+n);
    for(int i=0;i<n;i++)
    {
        T[B[i]]=i;
    }
    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=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)*s);
    }
    return ans;
}

int main()
{
	cin>>n;
	s=VMAX;
	for(int i=0;i<n;i++)
    {
        cin>>A[i];
        s=min(s,A[i]);
    }
    int ans=solve();
    cout<<ans<<endl;
 	return 0;
}
