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.chomp.to_i
a = []
n.times do |i|
  a << gets.chomp.to_i
end
if a.all? {|i| i == 0 } then
  puts a.length
  exit
end
colors = 0
buf = []
now_idx = nil
a.each_with_index do |i, idx|
  break if idx == ( a.length - 1 )
  if a[idx] > a[idx + 1] then
    buf << a[idx]
    min = buf.min
    if min < a[idx + 1] then
      min_idx = buf.index(min)
      buf[min_idx] = a[idx + 1]
    end
  else
    if now_idx.nil? then
      buf << a[idx]
      now_idx = 0
    end
    buf[now_idx] = a[idx]
  end
end
puts buf.length