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 slove() {
    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]);
    }

    int ans = slove();
    cout << ans << endl;
    return 0;
}
