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
A = (1..N).map { |_| gets.to_i }
  
colors = [ [0, A[0]] ]

(1..N-1).each do |i|
  if A[i] <= A[i - 1]
    c_idx = colors.index { |c| c[1] < A[i] }

    if c_idx
      colors[c_idx] = [i, A[i]]
    else
      colors << [i, A[i]]
    end
  end
end

puts colors.size