Unique Staff Booth Assignment

You are given a number n representing the number of different booth types and a list of n integers representing the number of staff members required for each booth. Your task is to determine whether it is possible to assign the booths such that the total number of staff members used in each assignment combination is unique.

In other words, if any two booth types have the same staff requirement, the assignment is considered impossible. Otherwise, the assignment is possible.

Note: The input values follow the format described below and the output should be exactly either Possible or Impossible.

The underlying mathematical condition can be represented in \( \LaTeX \) as:

[ \text{If } \forall i \neq j,\ s_i \neq s_j \text{ then assignment is \textbf{Possible}}, \text{ otherwise, it is \textbf{Impossible}}. ]

inputFormat

The input is given via standard input (stdin) and has the following format:

1. An integer n on the first line, which represents the number of different booth types.
2. A line containing n space-separated integers, each representing the number of staff members required for the corresponding booth.

outputFormat

Output a single line to standard output (stdout) containing the string Possible if the staff requirements are all unique. Otherwise, output Impossible.

4
1 2 3 4

Possible