#K4776. Make the Sequence Strictly Increasing

    ID: 28270 Type: Default 1000ms 256MiB

Make the Sequence Strictly Increasing

Make the Sequence Strictly Increasing

You are given multiple queries. In each query, you are provided with a sequence of integers. Your task is to rearrange the sequence into non-decreasing order and then check whether the sorted sequence is strictly increasing (i.e. for every \(i\), \(a_i < a_{i+1}\)).

If the sorted sequence is strictly increasing, print the sequence (with elements separated by a single space). Otherwise, print Impossible.

Note: A sequence is strictly increasing if and only if every two consecutive elements satisfy \(a_i < a_{i+1}\). Duplicates are not allowed in the finalized sequence.

Example:

Input:
3
5
1 2 3 4 5
4
3 1 2 4
3
7 5 7

Output: 1 2 3 4 5 1 2 3 4 Impossible

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inputFormat

The input is read from stdin and has the following format:

  1. The first line contains a single integer \(T\) indicating the number of queries.
  2. For each query, the first line contains an integer \(n\), the number of elements in the sequence, followed by a line with \(n\) space-separated integers.

For example:

3
5
1 2 3 4 5
4
3 1 2 4
3
7 5 7

outputFormat

For each query, output the result on a new line to stdout. If the sorted sequence is strictly increasing, output the numbers (separated by a space). Otherwise, output Impossible.

## sample
3
5
1 2 3 4 5
4
3 1 2 4
3
7 5 7
1 2 3 4 5

1 2 3 4 Impossible

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