CF1628A Meximum Array

Mihai has just learned about the [MEX](https://en.wikipedia.org/wiki/Mex_(mathematics)) concept and since he liked it so much, he decided to use it right away. Given an array $ a $ of $ n $ non-negative integers, Mihai wants to create a new array $ b $ that is formed in the following way: While $ a $ is not empty: - Choose an integer $ k $ ( $ 1 \leq k \leq |a| $ ). - Append the MEX of the first $ k $ numbers of the array $ a $ to the end of array $ b $ and erase them from the array $ a $ , shifting the positions of the remaining numbers in $ a $ . But, since Mihai loves big arrays as much as the MEX concept, he wants the new array $ b $ to be the lexicographically maximum. So, Mihai asks you to tell him what the maximum array $ b $ that can be created by constructing the array optimally is. An array $ x $ is lexicographically greater than an array $ y $ if in the first position where $ x $ and $ y $ differ $ x_i > y_i $ or if $ |x| > |y| $ and $ y $ is a prefix of $ x $ (where $ |x| $ denotes the size of the array $ x $ ). The MEX of a set of non-negative integers is the minimal non-negative integer such that it is not in the set. For example, MEX({ $ {1, 2, 3} $ }) $ = 0 $ and MEX({ $ {0, 1, 2, 4, 5} $ }) $ = 3 $ .

The first line of the input contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) — the number of elements in the array $ a $ . The second line of each test case contains $ n $ non-negative integers $ a_1, \ldots, a_n $ ( $ 0 \leq a_i \leq n $ ), where $ a_i $ is the $ i $ -th integer from the array $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case print $ m $ — the length of the maximum array $ b $ Mihai can create, followed by $ m $ integers denoting the elements of the array $ b $ .

In the first test case, the lexicographically maximum array $ b $ is obtained by selecting $ k=5 $ , resulting in the $ MEX $ of the whole array $ a $ . It is lexicographically maximum because an array starting with a smaller number than $ 4 $ is lexicographically smaller, and choosing a $ k