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.