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 <algorithm>
#include <iostream>
#include <cstring>
#include <list>
#include <cmath>
#include <vector>
#include <stack>
#include <set>
#include <map>
#define sf scanf
#define pf printf
#define show(x) cout<<"x:"<<x<<endl;
using namespace std;
typedef long long ll;
const int maxn=1000;
const int vmaxn=10000;
const int inf=1e9+5;
int n,a[maxn],s;
int b[maxn],t[vmaxn+1];

ll 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=vmaxn;
        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=vmaxn;
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
        s=min(s,a[i]);
    }
    int ans=solve();
    cout<<ans<<endl;

    return 0;
}

