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E - Sequence Decomposing

Score : $500$ points

Problem Statement

You are given a sequence with $N$ integers: $A = \{ A_1, A_2, \cdots, A_N \}$. For each of these $N$ integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

• If $A_i$ and $A_j$ $(i < j)$ are painted with the same color, $A_i < A_j$.

Find the minimum number of colors required to satisfy the condition.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq A_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$A_1$

$:$

$A_N$

Output

Print the minimum number of colors required to satisfy the condition.

5
2
1
4
5
3

2

We can satisfy the condition with two colors by, for example, painting $2$ and $3$ red and painting $1$, $4$, and $5$ blue.

4
0
0
0
0

4

We have to paint all the integers with distinct colors.