Problem:
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.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

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

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.to_i

as = []
n.times{
	as << gets.to_i
}

color_count = 0

while as.size > 0
	indexes = []
	temp = -1

	(0 ... as.size).each{ |x|
		if temp < as[x] then
			temp = as[x]
			indexes << x
		end
	}
	
	indexes.reverse.each{ |i|
		as.delete_at(i)
	}

	color_count += 1
end

puts color_count