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
n = int(input())
w = list(map(int,input().split()))
A = dict(zip(sorted(w), w))
min_value = min(A)
A = {k:v for k,v in A.items() if k != v or k == min_value}
totalcost = 0

while len(A) > 1:
    i_move_count = 0
    i = min_value
    if min_value == A[min_value]:
        i = min([v for v in A if v != min_value])

    while A[i] != i:
        j = A[i]
        A[i] = A[j]
        A.pop(j)
        i_move_count += 1
        totalcost += j

    if i != min_value:
        A.pop(i)

    totalcost += min((i * i_move_count), ((min_value * i_move_count) + (min_value + i) * 2))

print(totalcost)
