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.chomp.to_i
numbers = N.times.map { gets.chomp.to_i }

stack = [numbers[0]]
stack_index = 0

1.upto(N-1) do |i|
    target = numbers[i]
    stack_index.downto(0) do |cursor|
        if cursor == 0 && target <= stack[0]
            stack.push target
            stack_index = stack.size - 1
            break
        end
        if target > stack[cursor]
            stack[cursor] = target
            break
        end
    end
end

puts stack.size