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
A = []
N.times do |i|
    A << [gets.chomp.to_i, i]
end
A.sort!
ans = 0
while !A.empty?
    a, i = A.shift
    while i_delete = A.find_index{|aa, ii| a < aa && i < ii}
        a, i = A.delete_at(i_delete)
    end
    ans += 1
end
puts ans