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
def minimum_cost_sort():
    sorted_positions = {str(val):i for i, val in enumerate(sorted(W))}
    is_passed = [False]*n
    minimum_weight = min(W)
    ans = 0
    for i in range(n):
        if is_passed[i]:
            continue
        pointer = i
        total_weight = 0
        local_minimum_weight = 10000
        counter = 0
        while not is_passed[pointer]:
            is_passed[pointer] = True
            total_weight += W[pointer]
            local_minimum_weight = min(local_minimum_weight, W[pointer])
            pointer = sorted_positions[str(W[pointer])]
            counter += 1
        ans += min(total_weight+local_minimum_weight*(counter-2), total_weight+minimum_weight*(counter+1)+local_minimum_weight)
    print(ans)

if __name__ == "__main__":
    n = int(input())
    W = list(map(int, input().split()))
    minimum_cost_sort()
