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>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

typedef long long ll;
const int maxn=10000+5;
const int minn=1000+5;
const int inf=2e9+2;
int n,a[minn],po[maxn];
void solve()
{

    sort(a+1,a+n+1);
    int f=0,tp=inf,t=0,tmin=a[1];
    ll w=0,ans=0;
    for (int i = 1; i <= n; ++i)
    {
        if(po[a[i]]==i){continue;}
        tp=inf;t=1;w=0;
        int f=po[a[i]];
        w+=a[i];
        tp=a[i];
        while(f!=i)
        {
            t++;tp=min(a[f],tp);
            w+=a[f];
            int tm=f;
            f=po[a[f]];
            po[a[tm]]=tm;
        }
        ans+=min(w+(t-2)*tp,w+tp+(t+1)*tmin);
    }
    printf("%lld\n",ans);
}
int main()
{
    scanf("%d",&n);
	for (int i = 1; i <= n; ++i)
    {
        scanf("%d",&a[i]);
        po[a[i]]=i;
    }
    solve();
    return 0;
}
