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 <vector>
#include <algorithm>
const int MAX_W = 10000;
using namespace std;

int s = MAX_W;

int minCostSort(vector<int>& A) {
    int ret = 0;

    vector<bool> V(A.size());
    vector<int> B = A;
    vector<int> T(MAX_W+1);
    for (auto i = 0; i < A.size(); i++) {
        V[i] = false;
    }
    sort(B.begin(), B.end());
    for (auto i = 0; i < A.size(); i++) {
        T[B[i]] = i;
    }

    for (auto i = 0; i < A.size(); i++) {
        if (V[i]) continue;

        int cur = i;
        int S = 0;
        int m = MAX_W;
        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;
        }
        ret += min(S + (an-2)*m, m + S + (an+1)*s);
    }
    return ret;
}

int main(void) {
    int n;
    cin >> n;

    vector<int> W(n);
    for (int i = 0; i < n; i++) {
        cin >> W[i];
        s = min(s, W[i]);
    }

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