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<iostream>
#include<algorithm>
using namespace std;
#define maxn 1005
#define maxv 10005
int n,a[maxn],s;
int b[maxn],t[maxv];
int solve()
{
    int ans=0;
    bool v[maxn];
    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=maxv;
        int 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)*s);
    }
    return ans;
}
int main()
{
    cin>>n;
    s=maxv;
    for(int i=0;i<n;++i)
    {
        cin>>a[i];
        s=min(a[i],s);
    }
    int ans=solve();
    cout<<ans<<endl;
    return 0;
}