Meximum Array
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({${0, 1, 2, 4, 5}$}) $= 3$.
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 $b$.
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 $b$.
Samples
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
1
4
2
5 1
1
0
1
5
2
2 2
4
3 2 2 0
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 $k=1$.