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
# INPUT
n = int(input())
W = list(map(int, input().split()))


# PROCESS
cost = 0
W_sorted = sorted(W)
W_min = W_sorted[0]

for i in range(n - 1):
    cycle_min = W_sorted[i]
    cost_cycle_in = 0
    cnt_change = 0

    index_cycle_min = W.index(cycle_min)

    while index_cycle_min != i:
        cycle_change = W_sorted[index_cycle_min]
        index_cycle_change = W.index(cycle_change)

        W[index_cycle_min], W[index_cycle_change] = cycle_change, cycle_min
        cost_cycle_in += cycle_min + cycle_change

        cnt_change += 1
        index_cycle_min = index_cycle_change

    if cnt_change:
        cost_cycle_out = (
            cost_cycle_in
          + (cycle_min + W_min) * 2
          - (cycle_min - W_min) * cnt_change
        )

        cost += min(cost_cycle_in, cost_cycle_out)


# OUTPUT
print(cost)

