Meximum Array

2000ms

262144K

Description:

Mihai has just learned about the MEX 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({$$${0, 1, 2, 4, 5}$$$}) $$$= 3$$$.

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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 $$$b$$$.

Sample Input:

6
5
1 0 2 0 3
8
2 2 3 4 0 1 2 0
1
1
5
0 1 2 3 4
4
0 1 1 0
10
0 0 2 1 1 1 0 0 1 1

Sample Output:

Note:

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 $$$k<5$$$ would result in an array starting with a number smaller than $$$4$$$.

In the second test case, there are two ways to obtain the maximum array: first selecting $$$k=6$$$, then $$$k=2$$$, or first selecting $$$k=7$$$ and then $$$k=1$$$.

Informação

Provedor Codeforces

Código CF1628A