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 minimumCostSort(arr, arr_size):
    cost = 0
    sortarr = sorted(arr)
    cyclecontainer = []
    for i in range(arr_size):
        cycle = [arr[i]]
        next = sortarr.index(arr[i])
        while arr[next] != arr[i]:
            cycle += [arr[next]]
            next = sortarr.index(arr[next])
        cycle = sorted(cycle)
        if cycle not in cyclecontainer:
            cyclecontainer.append(cycle)
            if len(cycle) == 1:
                pass
            elif len(cycle) == 2:
                cost += sum(cycle)
            elif len(cycle) >= 3:
                cost += min(sum(cycle)+((len(cycle)-2)*min(cycle)), sum(cycle)+min(cycle)+((len(cycle)+1)*min(arr)))
    return cost
n = int(input())
w = list(map(int, input().split()))
print(minimumCostSort(w, n))
