Sequence Deletion

Everyone knows the functions $\min$ and $\max$, which return the smallest and largest value in a set. Now consider the function $\text{mex}$, which takes a set of numbers and returns the smallest non-negative integer that is not in the set. The name comes from minimal excluded. For example, $\text{mex}(\{1,2,3\}) = 0$ and $\text{mex}(\{0,1,2,4,5\}) = 3$. Magnus learned the definition of mex and immediately built a game on it. The player gets a sequence $A$ of $N$ non-negative integers and builds a sequence $B$ by repeating the following steps while $A$ still has elements: (1) Choose a positive integer $k$ that does not exceed the length of $A$. (2) Append the mex of the first $k$ elements of $A$ to the end of $B$. (3) Delete the first $k$ elements from $A$. The player's task is to choose $k$ at each step so that the resulting sequence $B$ is lexicographically maximum among all possible choices. A sequence $x = x_1, x_2, \ldots, x_n$ is lexicographically greater than $y = y_1, y_2, \ldots, y_m$ if either there exists an $i$ with $i \le n$ and $i \le m$ such that $x_1 = y_1$, $x_2 = y_2$, $\ldots$, $x_{i-1} = y_{i-1}$ and $x_i > y_i$, or $n > m$ and $x_1 = y_1$, $x_2 = y_2$, $\ldots$, $x_m = y_m$.

The first line contains the length $N$ of sequence $A$ ($1 \le N \le 500,000$). The second line contains the $N$ elements $A_i$ ($0 \le A_i \le N$), separated by spaces.

Print the length $M$ of the found sequence $B$ on the first line. On the second line, print the elements $B_1, B_2, \ldots, B_M$ separated by spaces.