#P1575L. Longest Array Deconstruction
Longest Array Deconstruction
Description
Mr. Chanek gives you a sequence $a$ indexed from $1$ to $n$. Define $f(a)$ as the number of indices where $a_i = i$.
You can pick an element from the current sequence and remove it, then concatenate the remaining elements together. For example, if you remove the $3$-rd element from the sequence $[4, 2, 3, 1]$, the resulting sequence will be $[4, 2, 1]$.
You want to remove some elements from $a$ in order to maximize $f(a)$, using zero or more operations. Find the largest possible $f(a)$.
The first line contains one integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the initial length of the sequence.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 2 \cdot 10^5$) — the initial sequence $a$.
Output an integer denoting the largest $f(a)$ that can be obtained by doing zero or more operations.
Input
The first line contains one integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the initial length of the sequence.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 2 \cdot 10^5$) — the initial sequence $a$.
Output
Output an integer denoting the largest $f(a)$ that can be obtained by doing zero or more operations.
Samples
7
2 1 4 2 5 3 7
3
4
4 2 3 1
2
Note
In the first example, $f(A) = 3$ by doing the following operations.
$[2,1,\textbf{4},2,5,3,7] \rightarrow [\textbf{2},1,2,5,3,7] \rightarrow [1,2,5,3,\textbf{7}] \rightarrow [1,2,\textbf{5},3] \rightarrow [1,2,3]$
In the second example, $f(A) = 2$ and no additional operation is needed.