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>
static const int MAX = 10000;
static const int VMAX = 100000;

int n,A[MAX],s;
int B[MAX],T[VMAX+1];

int solve(){
    int i,ans = 0;
    
    bool V[MAX];
    for(i=0;i<n;i++){
        B[i] = A[i];
        V[i] = false;
    }
    sort(B,B+n);
    for(i=0;i<n;i++) T[B[i]] = i;
    for(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(){
    int i;
    scanf("%d",&n);
    s=VMAX;
    for(i=0;i<n;i++){
        scanf("%d",&A[i]);
        s=min(s,A[i]);
    }
    int ans = solve();
    printf("%d\n",ans);
    return 0;
}
