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 swap(a, b):
    return (b, a)


def selectionSortWithCosts(array):
    n = len(array)
    cost = 0
    for i in range(n):
        minimumElement = min(array[i:])
        if minimumElement == array[i]:
            continue
        else:
            indexOfTheMinimumElement = array.index(minimumElement)
            swappedElements = swap(array[i], array[indexOfTheMinimumElement])
            array[i] = swappedElements[0]
            array[indexOfTheMinimumElement] = swappedElements[1]
            cost += sum(swappedElements)

    return {"cost": cost, "sortedArray": array}


n = int(input())
array = list(map(int, input().split()))

print(selectionSortWithCosts(array)["cost"])

