Strictly Increasing Sequence

Given a sequence of integers, determine whether it is possible to rearrange the sequence to form a strictly increasing sequence.

A strictly increasing sequence is defined as a sequence \(a_1, a_2, \dots, a_n\) such that \(a_1 < a_2 < \cdots < a_n\). In other words, no two elements are equal and each element is less than its subsequent element.

If it is possible to rearrange the sequence into a strictly increasing order, output possible; otherwise, output impossible.

inputFormat

The first line of input contains a single integer (n), representing the number of elements in the sequence. The second line contains (n) space-separated integers.

outputFormat

Output a single word: "possible" if the sequence can be rearranged to form a strictly increasing sequence; otherwise, output "impossible".## sample

5
1 3 2 4 5

possible