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;

const int MAX_N = 1000;
const int MAX_W = 10000;

int n, s, A[MAX_N], B[MAX_N], T[MAX_W+1];

int solve(){
    int sum = 0;
    bool V[MAX_N];
    
    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, S = 0, m = MAX_W, an =  0;
        while(!V[cur]){
            V[cur] = true;
            an++;
            m = min(m, A[cur]);
            S += A[cur];
            cur = T[A[cur]];
        }
        sum += min(S + (an - 2) * m, m + S + (an + 1) * s);
    }
    return sum;
}

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