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;

static const int MAX = 1000;
static const int VMAX = 10000;

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

int solve(){
    int ans = 0;

    bool V[MAX];
    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 = VMAX;
        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 = VMAX;
    for(int i=0; i<n; ++i){
        cin >> A[i];
        s = min(s, A[i]);
    }

    cout << solve() << endl;
}

