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 = 10001;
int n, x;
int A[MAX], B[MAX];
bool V[MAX];

int solve()
{
    int T[VMAX];
    int ans = 0;

    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 s = 0;
        int an = 0;
        int cur = i;
        int m = VMAX;

        while (true)
        {
            int v = A[cur];   
            V[cur] = true;
            ++an;
            m = min(m, v);
            s += v;
            cur = T[v];
            
            if (V[cur] == true) break;
        }
        ans += min(s +(an -2) * m, s + m + (an + 1) * x);
    }
    return ans;
}

int main()
{
    cin >> n;

    x = VMAX;

    for (int i = 0; i != n; ++i)
    {
        cin >> A[i];
        x = min(A[i], x);
    }

    cout << solve() << endl;

    return 0;
}
