Problem:
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Minimum Cost Sort

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.

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.

Constraints

$1 \leq n \leq 1,000$

$0 \leq w_i\leq 10^4$

$w_i$ are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

Solution in Python3 (judge verdict: Accepted)

if __name__ == "__main__":
    n = int(input())
    elements = list(map(lambda x: int(x), input().split()))
    sorted_elements = sorted(elements)
    total_cost = 0

    for i in range(n - 1):
        cost = 0
        cnt = 0
        x_idx = elements.index(sorted_elements[i])
        while i != x_idx:
            y_idx = elements.index(sorted_elements[x_idx])
            elements[x_idx], elements[y_idx] = (sorted_elements[x_idx],
                                                sorted_elements[i])
            cnt += 1
            cost += sorted_elements[x_idx] + sorted_elements[i]
            x_idx = y_idx
        if cnt:
            total_cost += min(cost,
                              (sorted_elements[i] + sorted_elements[0]) * 2 + cost
                              - (sorted_elements[i] - sorted_elements[0]) * cnt)

    print(total_cost)