Find the Missing Puzzle Pieces

You are given a list of puzzle pieces represented by integers. The puzzle pieces are part of a consecutive sequence, but some pieces may be missing. Your task is to determine the missing integers that would complete the sequence from the smallest to the largest integer.

If there are no missing pieces, output None.

You can think of the missing pieces as those numbers in the set \[ \{ x \in \mathbb{Z} \mid \min(pieces) \le x \le \max(pieces) \text{ and } x \notin pieces \}\] that are not present in the given list.

inputFormat

The first line of input contains an integer \(T\), denoting the number of test cases. Each test case is described in one line starting with an integer \(N\) (the number of puzzle pieces) followed by \(N\) space-separated integers representing the puzzle pieces.

outputFormat

For each test case, print a single line containing the missing integers in ascending order separated by a space. If there are no missing integers, print None.

## sample

2
5 4 2 7 1 6
3 10 11 13

3 5
12

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