`n` passengers board an airplane with exactly `n` seats. The first passenger has lost the ticket and picks a seat randomly. But after that, the rest of the passengers will:

- Take their own seat if it is still available, and
- Pick other seats randomly when they find their seat occupied

Return the probability that the `nth` person gets his own seat.

Example 1:

    Input: n = 1
    Output: 1.00000
    Explanation: The first person can only get the first seat.

Example 2:

    Input: n = 2
    Output: 0.50000
    Explanation: The second person has a probability of 0.5 to get the second seat (when first person gets the first seat).

Constraints:

- `1 <= n <= 105`