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: Wrong Answer)

N=gets.to_i
as =[]
for i in 0...N
  as << gets.to_i
end
as.reverse!

color_min=[as[0]]
for i in 1...N
  color_min.sort!
  if as[i]<color_min[0]
    judge=0
  elsif color_min.size == 1
    judge=nil
  else
    judge=(1..color_min.size-1).bsearch{|j|color_min[j-1]<as[i] && as[i]<color_min[j]}
  end
  $stderr.puts judge
  if judge
    color_min[judge]+=-1
  else
    color_min << as[i]
  end
end
puts color_min.size