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
alist = []
n.times do |ni|
  alist[ni] = gets.chomp.to_i
end
 
 
col = []
col[0] = alist[0]
maxcol = 0
1.upto(n-1) do |i|
  check = alist[i]
  newcol = true
  col.each_with_index do |coli,i|
    if coli < check
      col.delete_at(i)
      set = false
      col.each_with_index do |nnum,ii|
        if nnum < check
          col.insert(ii,check)
          set = true
          break
        end
      end
      col.push(check) if set == false
      newcol = false
      break
    end
  end
  col.push(check) if newcol
end
puts col.size