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.

-----Sample Input-----
5
2
1
4
5
3

-----Sample Output-----
2

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

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